Models for MI Group
1 Purpose for Analysis
The Society of Actuaries is interested in better understanding whether life insurance data, as currently provided in the Individual Life Experience Committee’s (ILEC) data compilation, can be used to calibrate trends in industry mortality. Life actuaries have avoided using this dataset for trend analysis. Significant heterogeneity underlies the ILEC data which is known to obscure the true underlying mortality trend. Factors known to alter the composition of the dataset over time include changes in underwriting practices across face amount and product type, changes in company mix, and changes in target markets of individual companies. Moreover, the latest public dataset covers 2009-2017, a window that is too short for credible and reliable estimates of long-term trend. Therefore, life insurance actuaries have relied on population-based mortality trend models despite the basis risk.
Mortality analysis in life insurance is almost always done against an industry-standard table whenever appropriate. Actuaries tend to rely on the most recent tables such as the 2015 Valuation Basis Table (2015VBT). This table provides mortality rates by issue age, sex, smoker status, and policy duration and was calibrated using data collected for observation years 2002-2009. Other known drivers of mortality, like face amount and underwriting, are not included. Therefore, assessing secular mortality trends against this table is challenging, since any observable trend will be the combination of underlying secular trends and of shifts in the prevalence of drivers not included in the table. For example, if the distribution of face amounts shifts higher much faster than inflation, then average mortality is expected to decline over time against the 2015 VBT given that mortality declines with increasing face amount in well-underwritten portfolios.
The aim of what follows is to provide a mortality model which “raises the floor” of analysis away from the 2015VBT. The model aims to control for additional drivers not yet accounted for in industry tables and adjust for changes in known drivers. The new benchmark is then available for an actuary to attempt additional analysis of mortality trend in the ILEC dataset.
Conspicuously absent is any provision for mortality trend in this analysis. This is intentional. The paper which this model supports is intended to explore and compare the observed trends in the ILEC data against the same information in population trend studies. Additionally, calibrating a model for trend is subject to significant research on its own:
- The traditional approach is to use variants of Lee-Carter models. The current regression approach can be extended using mixed-effects modeling or Bayesian methods.
- One can also use splines of varying complexity. For example, in prior corporate work, I have used the mgcv package to model time trends which vary by attained age where the spline is based on attained age and the “by” parameter of the spline is set to calendar year. This has the effect of setting a custom slope for the trend line by attained age.
Other authors have taken a variety of other approaches, and search engines and LLMs are available to learn more.
Given the many potential shapes, I opted to leave the analysis of trend to the main body of the study. Nonetheless, a high-level illustration of the impact on trend of controlling for other drivers is provided toward the end of this document.
2 Summary of Results
Two different types of models were built. One type based on boosted decision trees was used primarily for exploratory data analysis. The other type based on elastic net regression was used to adjust the 2015 VBT table.
Selected findings from the boosted decision trees:
- In general, there are substantial differences between low face term and high face term prior to the end of the level term period, defined as below or above 100,000 of face amount, and interactions among variables are most prevalent in the low face amount term.
- Significant elevations are noted in 2-class preferred systems in the term subset.
- Curiously, the subset of term other than post-level term exhibits multimodality in the distribution of SHAP values in certain cases, such as with residual standard of the 2-class preferred systems. This suggests heterogeneity in the subset.
Selected findings from the elastic net modeling:
- Five models were necessary, one each for post-level term, low face other than post level term, high face other than post level term, permanent unismoke, and other permanent business.
- The model for low face other than post level term was the most complicated with the greatest number of interactions.
At the end of this document is a discussion of the impact on mortality trend of adjusting out unmodeled variation. The per annum trend of ratios against the 2015 VBT is approximately -1.5%, while the same against the elastic net model is -0.8%. While not the sole reason for the movement, we note the rapid upward shift in UL/VL exposures over the same time period. These patterns provide evidence that the nominal shift is in part due to shifts in face amount distribution. Other shifts in prevalence can be found, and mortality trends vary by subset both before and after adjusting for unmodeled variation.
3 Setup
The following sets up the environment for further analysis.
Code
library(catboost)
library(data.table)
library(tidyverse)
library(dtplyr)
library(shapviz)
library(patchwork)
library(doParallel)
library(glmnet)
library(openxlsx)
library(flextable)
library(ftExtra)
library(Matrix)
library(MatrixModels)
library(ggridges)
library(arrow)
source('catboost.shapviz.R') # Function which adapts catboost to shapviz
source('glmnet_support.R') # Support functions
source('support_fns.R')
bUseCache <- TRUE # Use cached objects where available
bInvalidateCaches <- FALSE # Force computation even if cached
training.fraction <- 0.7 # Fraction of data for boosting
cb.task.type <- "GPU" # Use the GPU, set to "CPU" if needed
nFolds <- 10
cvfit.seed <- 13579
catboost.seed <- 12321
traintest.seed <- 1337
fit_params <- list(iterations = 50000,
task_type=cb.task.type,
loss_function = 'Poisson',
verbose=250,
od_pval=0.05,
random_seed = catboost.seed)
# Labels for relabeling face amount for nicer looking plots and tables
fa.remap <- data.table(
Face_Amount_Band.Old = c(
"01: 0 - 9,999",
"02: 10,000 - 24,999",
"03: 25,000 - 49,999",
"04: 50,000 - 99,999",
"05: 100,000 - 249,999",
"06: 250,000 - 499,999",
"07: 500,000 - 999,999",
"08: 1,000,000 - 2,499,999",
"09: 2,500,000 - 4,999,999",
"10: 5,000,000 - 9,999,999",
"11: 10,000,000+"
),
Face_Amount_Band.New = c(
"<10K",
"10K - <25K",
"25K - <50K",
"50K - <100K",
"100K - <250K",
"250K - <500K",
"500K - <1M",
"1M - <2.5M",
"2.5M - <5M",
"5M - <10M",
"10M+"
)
)4 Data Prep
The data were extracted from the ILEC dataset and restricted to experience years 2011-2017. The data prep steps are included in the embedded code but not executed in this document.
4.1 Term Data Preparation
Code
library(arrow)
library(data.table)
library(tidyverse)
library(dtplyr)
ilec_arrow_src <- '/workspace/Projects/ILEC/VBT/Data/ilecdata'
dat.arrow <- arrow::open_dataset(ilec_arrow_src)
# Term No PLT
dat.arrow %>%
filter(Observation_Year >= 2011
& Observation_Year <= 2017
& Insurance_Plan == 'Term'
& SOA_Post_Lvl_Ind != 'PLT') %>%
select(!Observation_Year) %>%
group_by(
Sex,
Smoker_Status,
Attained_Age,
Duration,
Face_Amount_Band,
SOA_Post_Lvl_Ind,
Number_of_Pfd_Classes,
Preferred_Class
) %>%
summarize(
Death_Count=sum(Death_Count),
Policies_Exposed=sum(Policies_Exposed),
ExpDth_Cnt_VBT2015=sum(ExpDth_Cnt_VBT2015),
Death_Claim_Amount=sum(Death_Claim_Amount),
Amount_Exposed=sum(Amount_Exposed),
ExpDth_Amt_VBT2015=sum(ExpDth_Amt_VBT2015)
) %>%
collect() %>%
as.data.table() ->
dat.term.noplt
dat.term.noplt[,
`:=`(Smoker_Status=as.character(Smoker_Status),
Number_of_Pfd_Classes=as.character(Number_of_Pfd_Classes),
Preferred_Class=as.character(Preferred_Class))]
dat.term.noplt[is.na(Number_of_Pfd_Classes),
Number_of_Pfd_Classes:="U"]
dat.term.noplt[is.na(Preferred_Class),
Preferred_Class:="U"]
dat.term.noplt[,UW:=paste0(Smoker_Status,"/",Preferred_Class,"/",
Number_of_Pfd_Classes)]
saveRDS(dat.term.noplt,"dat.term.noplt.rds")
# Term With PLT
dat.arrow %>%
filter(Observation_Year >= 2011
& Observation_Year <= 2017
& Insurance_Plan == 'Term'
& SOA_Post_Lvl_Ind == 'PLT') %>%
select(!Observation_Year) %>%
group_by(
Sex,
Smoker_Status,
Attained_Age,
Duration,
Face_Amount_Band,
SOA_Post_Lvl_Ind,
Number_of_Pfd_Classes,
Preferred_Class,
SOA_Antp_Lvl_TP
) %>%
summarize(
Death_Count=sum(Death_Count),
Policies_Exposed=sum(Policies_Exposed),
ExpDth_Cnt_VBT2015=sum(ExpDth_Cnt_VBT2015),
Death_Claim_Amount=sum(Death_Claim_Amount),
Amount_Exposed=sum(Amount_Exposed),
ExpDth_Amt_VBT2015=sum(ExpDth_Amt_VBT2015)
) %>%
collect() %>%
as.data.table() ->
dat.term.plt
dat.term.plt[,
`:=`(Smoker_Status=as.character(Smoker_Status),
Number_of_Pfd_Classes=as.character(Number_of_Pfd_Classes),
Preferred_Class=as.character(Preferred_Class))]
dat.term.plt[is.na(Number_of_Pfd_Classes),
Number_of_Pfd_Classes:="U"]
dat.term.plt[is.na(Preferred_Class),
Preferred_Class:="U"]
dat.term.plt[,UW:=paste0(Smoker_Status,"/",Preferred_Class,"/",
Number_of_Pfd_Classes)]
saveRDS(dat.term.plt,"dat.term.plt.rds")4.2 Perm Data Preparation
Code
library(arrow)
library(data.table)
library(tidyverse)
library(dtplyr)
ilec_arrow_src <- '/workspace/Projects/ILEC/VBT/Data/ilecdata'
dat.arrow <- arrow::open_dataset(ilec_arrow_src)
# Term No PLT
dat.arrow %>%
filter(Observation_Year >= 2011
& Observation_Year <= 2017
& Insurance_Plan != 'Term') %>%
select(!Observation_Year) %>%
group_by(
Sex,
Smoker_Status,
Attained_Age,
Duration,
Face_Amount_Band,
Insurance_Plan,
Number_of_Pfd_Classes,
Preferred_Class
) %>%
summarize(
Death_Count=sum(Death_Count),
Policies_Exposed=sum(Policies_Exposed),
ExpDth_Cnt_VBT2015=sum(ExpDth_Cnt_VBT2015),
Death_Claim_Amount=sum(Death_Claim_Amount),
Amount_Exposed=sum(Amount_Exposed),
ExpDth_Amt_VBT2015=sum(ExpDth_Amt_VBT2015)
) %>%
collect() %>%
as.data.table() ->
dat.perm
dat.perm[,
`:=`(Smoker_Status=as.character(Smoker_Status),
Number_of_Pfd_Classes=as.character(Number_of_Pfd_Classes),
Preferred_Class=as.character(Preferred_Class))]
dat.perm[is.na(Number_of_Pfd_Classes),
Number_of_Pfd_Classes:="U"]
dat.perm[is.na(Preferred_Class),
Preferred_Class:="U"]
dat.perm[,UW:=paste0(Smoker_Status,"/",Preferred_Class,"/",Number_of_Pfd_Classes)]
saveRDS(dat.perm,"dat.perm.rds")4.3 Data Adjustments
Variables like attained age and duration were discretized into relatively small buckets. Because of the aggregation bias in boosted decision trees when analyzing feature importance, any variable with a lot of levels will tend to “hoard” feature importance, especially if they have a lot of variability between levels of the predictor.
Attained age was broken into quinquennial ranges, with 0-17 and 18-25 being the exceptions.
Duration was broken into buckets whose width increased with duration. Thus, there are singleton groups for durations 1, 2, and 3, a doublet for 4 and 5, then quinquennial through duration 20, decennial to 30, and one large bucket thereafter.
There were other minor changes.
Face amount band has had labels adjusted for better plotting and rendering in tables.
The smoker status, number of preferred classes, and preferred class was combined into a single factor where applicable.
The data were assigned into training/test partitions.
A/E ratios were computed.
A Noise column of standard normal random samples was added. While this was a by-product of some bug testing with catboost, it proved to be an interesting addition as a predictor for boosted decision trees. It provides a useful frame of reference when comparing variables in the feature importance plots.
It became apparent during modeling that the data should be subdivided. There are three reasons for this.
There are differences in the underlying variable structure. Term length and pre-/post-level term information are populated for Term insurance plans but meaningless for the other insurance plans. Duration also has a different semantic interpretation in the presence of term length.
There are imbalances in the exposures or claims. The subset of unismoke Perm experience has total claims which dwarf the rest of the non-term insurance plans. For perm, there is also far less 4-class non-smoker coverage than there is for the 3-class, while term carries a meaningful amount of 4-class relative to 3-class non-smoker.
A sufficiently different mortality pattern exists, such that a separate model is more efficient than a unified model. This occurred in the no-post-level-term Term model, where a single model had difficulty fitting for face amounts under 100,000.
Therefore, there are five models in four subdocuments.
Term other than PLT, PLT term, unismoke Perm, and the smoker-distinct permanent plans
Within term other than PLT, there are separate models for under and over 100K face amounts.
5 How To Read This Document
This is laid out similarly to a traditional modeling exercise where the data are prepared, the models are built and evaluated from a statistical perspective, and results and other outputs are available at the end of the process. There is no need to read it linearly. It might useful to start at the results (Factor Tables, Plots of Terms, Tables of Terms, Goodness-of-Fit tables) before approaching other parts. The table of contents to the left expands down to those sections.
Each subdivision is formatted the same way, although some details may differ:
Feature Discovery, where gradient boosting is applied to the data.
Feature Importance, where the univariate and bivariate important features are explored.
Elastic net modeling, where data are prepped and models calibrated. These include typical plots for the cross-validation and the coefficient shrinkage by penalization parameter.
Factor Table, where a table of non-trivial factors from the model are presented. These are slates of credible factors.
Plots of Terms, where the predicted terms are plotted together and variables not part of the plot are fixed at certain values.
Tables of Terms, same as the plots, but in tabular form.
Goodness-of-Fit Tables, where actual-to-model ratios are shown for univariate and bivariate slices of the data.
6 Brief Introduction to the Model Types
6.1 Choice of Models
While survival modeling, specifically Cox modeling, is the norm in other disciplines, Poisson regression is frequently used in mortality modeling due to the structure of actuarial experience studies. A justification for why Poisson regression models are equivalent to Cox models and therefore acceptable for mortality modeling can be found in Whitehead (1980). More complex models were not considered given the need for transparency and explainability.
6.2 Gradient Boosting
Gradient boosting is a technique which recursively fits models of the same type on a dataset until some stopping rule is reached. Here, gradient boosted decision trees are used. First, a shallow decision tree is fit to the data using a random subset of columns, where the tree is relatively shallow. The fitted values are applied and removed from the response variable, and another shallow decision tree is fit on those residuals. On and on this goes, until it hits a stopping rule. In this case, the stopping rule is when the prediction error on an out-of-sample subset increases for more than a specified number of iterations.
6.3 Interpretation Example for Gradient Boosting
Gradient boosting can produce SHAP values for each observation or row of covariates. For our purposes, the SHAP value for a given row of data and given covariate can be thought of as the marginal contribution of that covariate to the outcome for that row of data. There is additionally a baseline term analogous to an intercept in GLMs.
Consider the first row of SHAP values for the Term, no PLT model. The exponentiated baseline of the model is 81.9%, compared to the A/E vs 2015VBT of 83%. For this row, face amount band and underwriting increase the predicted factor above 100%.
| Variable Name | Variable Value | SHAP Value | Exponentiated SHAP |
|---|---|---|---|
| Noise | 0.189766 | 0.00275 | 100.3% |
| Sex | F | -0.02366 | 97.7% |
| Face_Amount_Band | 03 - 25,000-49,999 | 0.166174 | 118.1% |
| SOA_Post_Lvl_Ind | ULT | 0.004194 | 100.4% |
| UW | NS/U/U | 0.091807 | 109.6% |
| AA_Grp | 61-65 | -0.00502 | 99.5% |
| Dur_Grp | 6-10 | -0.02374 | 97.7% |
| Baseline | -0.19927 | 81.9% | |
| Total Prediction | 0.013243 | 101.3% |
In isolation, these can be interesting in an underwriting context. However, to understand the broader picture, we use summary statistics.
Variable importance plot displays the average of absolute values of SHAP values for a given variable. This differs from feature importance which measures how much variability in the outcome is attributable to that factor. It is neither a measure of statistical significance nor an analysis of variance through. If a variable participates in lots of splits, then it will get partial credit for the variability explained by other variables in the trees.
The addition of the Noise term to feature importance creates a baseline of comparison. Noise is uncorrelated Gaussian noise. Thus, if another feature has similar SHAP patterns as to noise, there may be reason to believe it is not as influential or significant. One should be cautious about using this to dismiss a variable. For example, Sex appears similar to Noise in some cases in the one-dimensional plot. Yet, it appears with another variable in a highly influential interaction.
Importance of interactions is also extracted and shown. The table of scores is not informative. However, more informative are the plots of the distributions of SHAP values. If present, these can reveal shapes in the data, and if the shapes differ from subgroup to subgroup, then that is strong visual evidence for an interaction. Interesting potential interactions are pointed out in the description of the plots.
6.4 Elastic Net GLMs
Elastic net regularization allows the modeler to combine both LASSO and ridge penalties into a single model.
Ordinary least squares regression requires minimizing the squared difference of the response variable and the predicted values. In symbols,
\[ \underset{\beta}{\arg\min} \sum_{n}(y-X\beta)^{2} \]
This is equivalent to maximum likelihood estimation, where one assumes that the response variable \(y\) is normally distributed with mean \(X\beta\) and variance \(\sigma^{2}I_{k \times k}\). The maximum is taken with respect to \(\beta\), and the variance parameter is assumed to be fixed but unknown.
The LASSO and ridge regression methods each add an additional penalty term on the coefficients \(\beta\). The LASSO adds the sum of the absolute values of the parameters \(\beta\) subject to a tunable weight, \(\lambda\). The effect of the penalty on the coefficients is to optimize them toward zero. For the LASSO, some coefficients are optimized all the way to zero. Geometric and analytic explanations for this are readily available, with one available at https://en.wikipedia.org/wiki/Lasso_(statistics).
\[ \underset{\beta}{\arg\min} \sum_{n}(y-X\beta)^{2}+ \lambda\sum_{k}|\beta_{k}|\]
The ridge penalty adds the sum of the squares of the parameters \(\beta\), subject to a tunable weight, \(\alpha\).
\[ \underset{\beta}{\arg\min} \sum_{n}(y-X\beta)^{2}+ \alpha\sum_{k}\beta_{k}^{2}\]
The effect of this sort of penalty is still to optimize toward zero. However, unlike the LASSO, they are never driven to zero. Also, a squared-error penalty tends to assymetrically reward small deviations and punish large deviations.
In both cases, for special \(\lambda\) or \(\alpha\), the minimizers of these expressions correspond to the Bayesian maximum a posteriori (MAP) estimators for specific prior distributions for \(\beta\). In the ridge case, the Bayesian prior is the normal distribution with mean 0 and covariance \(\tau^{2} I_{k x k}\) for some assumed \(\tau^{2}\). For the LASSO, the Bayesian prior is the double-exponential or Laplace distribution with mean 0 and parameter \(\tau\). In either case, it can be shown that if \(\sigma^{2}\) and \(\tau\) are known, the penalizing weights have unique solutions equal to the k factor of B
It is also possible to combine the LASSO and ridge. When combined in the glmnet package, the \(\alpha\) parameter is intended as a mixing parameter between the two penalties, and \(\lambda\) controls the overall strength of the penalty.
\[ \underset{\beta}{\arg\min} \sum_{n}(y-X\beta)^{2}+ \lambda(\frac{1-\alpha}{2} \sum_{k}\beta_{k}^{2} + \alpha\sum_{k}|\beta_{k}|)\]
6.5 Interpretation for Elastic Net
Elastic net GLMs differ from GLMs via the penalization term, \(\lambda\). There are two plots related to this. The first is the plot of \(\lambda\) versus the cross-validation. The second is the plot of \(\lambda\) versus the coefficients of the model. Lower values of \(\lambda\) yield lighter penalization and more non-zero terms. Cross-validation is used to find the value which minimizes the out-of-sample error. These plots illustrate the model choices.
Just like GLMs though, the table of factors can be displayed for each variable and interaction term. Absent here are confidence intervals and standard errors. These are not implemented here. However, penalization yields credible parameter estimates. Thus, the factors can be arguably deemed credible.
7 Term Modeling by Amount
7.1 Excluding PLT
Code
dat.term.noplt <- readRDS("dat.term.noplt.rds")
dat.term.noplt <- dat.term.noplt[Policies_Exposed > 0]
# Force usage of all interactions
# This was a setting used in early experiments.
bUseAllInteractions <- FALSE
# Set up the age and durational breaks to group those columns
AA.brks <- c(-1,17,
seq(25,115,5))
AA.lbls <- paste0(
AA.brks[1:(length(AA.brks)-1)]+1,
"-",
AA.brks[2:length(AA.brks)]
)
Dur.brks <- c(0,1,2,3,5,10,15,20,30,100)
Dur.lbls <- paste0(
Dur.brks[1:(length(Dur.brks)-1)]+1,
"-",
Dur.brks[2:length(Dur.brks)]
)
dat.term.noplt[,`:=`(
AA_Grp=cut(Attained_Age,
breaks=AA.brks,
labels=AA.lbls),
Dur_Grp=cut(Duration,
breaks=Dur.brks,
labels=Dur.lbls)
)]
# Aside the names of the columns we want to use for the model
pred.cols <- names(dat.term.noplt)[c(1,5:6,15:17)]
# Declare the factor columns and ensure that those columns of
# the data.table are classed accordingly
factor.cols <- c("Sex",
"Face_Amount_Band",
"SOA_Post_Lvl_Ind",
"UW",
"AA_Grp",
"Dur_Grp")
dat.term.noplt[,
(factor.cols):=lapply(.SD,factor),
.SDcols=factor.cols]
# The UW variable sorts alphabetically when it is created.
# We want the sort to follow a lexicographic convention of
# smoker status, number of risk classes, and risk class
UW.levels<-data.table(UW.levels=dat.term.noplt[,levels(UW)])
UW.levels[,c("NS","Pref_Class","NClasses"):=tstrsplit(UW.levels,"/")]
setkeyv(UW.levels,c("NS","NClasses","Pref_Class"))
# Mark rows for the train test split for boosting,
# create a Noise column, and rewrite the
# face amount band labels to the more compact version.
set.seed(traintest.seed)
dat.term.noplt %>%
mutate(
IsTraining = (runif(nrow(.)) < training.fraction),
Noise = rnorm(nrow(.)),
.before = 1
) %>%
mutate(Face_Amount_Band=fct_relabel(
Face_Amount_Band,
#function(.) sub(":"," -",.,fixed=T)
function(.) fa.remap[Face_Amount_Band.Old==.,Face_Amount_Band.New]
),
AE_Count=Death_Count/ExpDth_Cnt_VBT2015,
AE_Amount=Death_Claim_Amount/ExpDth_Amt_VBT2015,
UW=factor(UW,levels=UW.levels$UW.levels)
) ->
dat.term.noplt
# Set aside the names of the variables for boosting
gbm.pred.cols <- c("Noise",pred.cols)Here is a data preview.
Code
dat.term.noplt %>%
head(10) %>%
flextable()IsTraining | Noise | Sex | Smoker_Status | Attained_Age | Duration | Face_Amount_Band | SOA_Post_Lvl_Ind | Number_of_Pfd_Classes | Preferred_Class | Death_Count | Policies_Exposed | ExpDth_Cnt_VBT2015 | Death_Claim_Amount | Amount_Exposed | ExpDth_Amt_VBT2015 | UW | AA_Grp | Dur_Grp | AE_Count | AE_Amount |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
TRUE | 0.1083568294 | F | NS | 64 | 6 | 25K - <50K | ULT | U | U | 0 | 17.645228 | 0.05716894 | 0 | 468,393.7 | 1,518.3502 | NS/U/U | 61-65 | 6-10 | 0.0000000 | 0.0000000 |
TRUE | -1.3291942329 | F | NS | 64 | 6 | 25K - <50K | NLT | 2 | 2 | 0 | 3.208219 | 0.01068337 | 0 | 118,677.0 | 395.1945 | NS/2/2 | 61-65 | 6-10 | 0.0000000 | 0.0000000 |
TRUE | -0.6640067577 | F | NS | 64 | 6 | 50K - <100K | WLT | U | U | 3 | 488.605865 | 1.61422224 | 180,000 | 27,738,248.8 | 91,612.1638 | NS/U/U | 61-65 | 6-10 | 1.8584802 | 1.9648046 |
TRUE | 1.3605113635 | F | NS | 64 | 6 | 50K - <100K | WLT | 4 | 1 | 0 | 196.833091 | 0.62903674 | 0 | 10,295,065.5 | 32,898.3426 | NS/1/4 | 61-65 | 6-10 | 0.0000000 | 0.0000000 |
TRUE | 2.1257419799 | F | NS | 64 | 6 | 50K - <100K | WLT | 3 | 3 | 0 | 247.835381 | 0.80761878 | 0 | 13,608,728.6 | 44,349.2771 | NS/3/3 | 61-65 | 6-10 | 0.0000000 | 0.0000000 |
TRUE | -0.0009361084 | F | NS | 64 | 6 | 50K - <100K | WLT | 3 | 2 | 0 | 14.466719 | 0.04732497 | 0 | 763,336.0 | 2,495.2484 | NS/2/3 | 61-65 | 6-10 | 0.0000000 | 0.0000000 |
FALSE | 0.0614656053 | F | NS | 64 | 6 | 100K - <250K | WLT | 4 | 1 | 8 | 2,087.237293 | 6.73676967 | 1,135,000 | 265,749,659.5 | 857,260.6139 | NS/1/4 | 61-65 | 6-10 | 1.1875128 | 1.3239848 |
TRUE | 0.6263000098 | F | NS | 64 | 6 | 100K - <250K | WLT | 3 | 2 | 2 | 1,080.443395 | 3.52259762 | 340,000 | 131,023,579.0 | 427,448.7273 | NS/2/3 | 61-65 | 6-10 | 0.5677628 | 0.7954170 |
TRUE | -0.9311761277 | F | NS | 64 | 6 | 100K - <250K | WLT | 3 | 1 | 1 | 890.999727 | 2.91249311 | 100,000 | 109,272,289.0 | 357,230.3786 | NS/1/3 | 61-65 | 6-10 | 0.3433485 | 0.2799314 |
TRUE | -0.6049300509 | F | NS | 64 | 6 | 100K - <250K | WLT | 4 | 3 | 1 | 1,302.159170 | 4.21731010 | 100,000 | 158,445,453.8 | 513,118.1666 | NS/3/4 | 61-65 | 6-10 | 0.2371180 | 0.1948869 |
7.1.1 Feature Discovery with Catboost
As in the predictive analytics framework, gradient boosted machines as implemented with Catboost are used for exploratory data analysis. The framework uses LightGBM, while Catboost is used here. This was done to take advantage of GPUs.
Code
### Create two pools for training and testing data.
### Note that due to a seeming bug in catboost, we
### convert the binary category of Sex to numeric.
### Then fit a catboost model
dat.term.noplt %>%
filter(IsTraining == TRUE) %>%
select(all_of(gbm.pred.cols)) %>%
mutate(Sex = as.numeric(Sex)) %>%
catboost.load_pool(
data=.,
label = dat.term.noplt[IsTraining==TRUE,AE_Amount],
weight = dat.term.noplt[IsTraining==TRUE,ExpDth_Amt_VBT2015]) ->
train_pool_notplt
dat.term.noplt %>%
filter(IsTraining == FALSE) %>%
select(all_of(gbm.pred.cols)) %>%
mutate(Sex = as.numeric(Sex)) %>%
catboost.load_pool(
data=.,
label = dat.term.noplt[IsTraining==FALSE,AE_Amount],
weight = dat.term.noplt[IsTraining==FALSE,ExpDth_Amt_VBT2015]) ->
test_pool_notplt
if(bUseCache & file.exists(
'dat.term.mod.notplt.cbm'
) & !bInvalidateCaches)
{
cb.model.notplt <- catboost.load_model(model_path = 'dat.term.mod.notplt.cbm')
} else {
cb.model.notplt <- catboost.train(learn_pool=train_pool_notplt,
test_pool = test_pool_notplt,
params=fit_params)
catboost.save_model(cb.model.notplt,
model_path = 'dat.term.mod.notplt.cbm')
}7.1.2 Feature Importance
Next is to check for the variables with most variability. Face amount band and underwriting top the list, with importance declining for the others. Note that “importance” is a measure of relative variability and not “significance”.
Code
### Extract the shap values. This implicitly relies on a custom function.
shp.notplt <- shapviz(
cb.model.notplt,
X=as.data.frame(dat.term.noplt[IsTraining==TRUE,..gbm.pred.cols] %>% mutate(Noise=runif(nrow(.)),.before = 1)),
X_pred=train_pool_notplt
)
setDT(shp.notplt$X)
shp.notplt$X[,c("NS","Pref_Class","NClasses"):=tstrsplit(UW,"/")]
sv_importance(shp.notplt) + theme_minimal()
7.1.3 Feature Interactions
The top four interactions are face amount band with each of underwriting and duration, and post-level term indicator with underwriting. We look at only those here. For the sake of thoroughness, the top eight are used for the elastic net.
Note that in this subset, SOA_Post_Lvl_Ind contains the levels “WLT = within level term”, “NLT = not level term”, and “ULT = unknown level term”.
Code
### Extract feature interactions, which are unfortunately indexed by column.
### Thus, they need to be returned to their proper names.
imp.int.notplt <- catboost.get_feature_importance(
cb.model.notplt,
train_pool_notplt,
type="Interaction"
)
mod.ft.map.notplt <- data.table(
FeatureNames=names(dat.term.noplt[IsTraining==TRUE,..gbm.pred.cols])
)
mod.ft.map.notplt[,ID:=1:nrow(.SD)-1]
imp.int.notplt %>%
merge(mod.ft.map.notplt,
by.x="feature1_index",
by.y="ID") %>%
merge(mod.ft.map.notplt,
by.x="feature2_index",
by.y="ID") %>%
setnames(
old=c("FeatureNames.x","FeatureNames.y"),
new=c("Feature1","Feature2")
) %>%
mutate(feature1_index=NULL,feature2_index=NULL) %>%
as.data.table() %>%
setcolorder(c("Feature1","Feature2","score")) ->
imp.int.notplt
imp.int.notplt[order(-score)] %>%
filter(Feature1 != "Noise") %>%
flextable() %>%
colformat_double(j="score",digits = 2)Feature1 | Feature2 | score |
|---|---|---|
Face_Amount_Band | UW | 14.95 |
Face_Amount_Band | Dur_Grp | 10.17 |
SOA_Post_Lvl_Ind | UW | 5.07 |
Face_Amount_Band | AA_Grp | 4.88 |
Face_Amount_Band | SOA_Post_Lvl_Ind | 4.26 |
UW | Dur_Grp | 3.92 |
UW | AA_Grp | 3.01 |
Sex | UW | 2.37 |
SOA_Post_Lvl_Ind | Dur_Grp | 2.21 |
Sex | Face_Amount_Band | 2.14 |
AA_Grp | Dur_Grp | 1.45 |
Sex | Dur_Grp | 1.18 |
SOA_Post_Lvl_Ind | AA_Grp | 0.99 |
Sex | SOA_Post_Lvl_Ind | 0.66 |
Sex | AA_Grp | 0.33 |
7.1.4 Feature Interaction Plots
Each of the interactions are discussed below with plots using SHAP values from both sides of the interaction. Focus is on the top three. For each interaction, we look at the SHAP values arising from each side of the interaction. For example, the ridge plots under UW for “Face Amount Band SHAPs” are from the face amount effect, while the same for “UW SHAPs” is for the UW effect. Evidence for an interaction can be in one or both collections of SHAP values.
7.1.4.1 UW
7.1.4.1.1 Face Amount Band SHAPs
While the SHAP values for face amount tend to be stable across preferred classes within a given class system, two phenomena stand out:
- The SHAP value distribution is shifted rightward for face amounts 25K - <100K.
- The SHAP value distribution for those face amounts exhibits greater spread and also multiple modes, suggesting the presence of multiple distinct cohorts.
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"Face_Amount_Band"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"Face_Amount_Band"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"Face_Amount_Band"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '3') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, 3 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"Face_Amount_Band"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '4') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, 4 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"Face_Amount_Band"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"Face_Amount_Band"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"Face_Amount_Band"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for unismokers")) +
theme_minimal()
7.1.4.1.2 UW SHAPs
There is much to unpack from the UW SHAP values stratified by face amount band.
- For 2-, 3-, and 4-class systems, there is a persistent pattern of bimodality in the SHAP values.
- For 2-class non-smoker systems, the residual standard class exhibits bimodality and a distinct arc of shifting distributions for lower face amounts.
- For 3-class non-smoker systems, the bimodality is present across all three levels.
- For 4-class non-smoker systems, the bimodality is evident for the best two preferred classes at face amounts above 100K.
- Bimodality is evident in the smoker 2-class as well.
- Somewhat less obvious is the gradual shifting to the left or right with changes in face amount band across the plots.
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '3') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 3 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '4') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 4 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for unismokers")) +
theme_minimal()
7.1.4.2 Duration Group
Among face amount SHAPs, there is not a clear interaction by duration. However, an interaction is apparent in the duration SHAPs. Note the gradual shifting rightward for durations 21-30 and leftward for durations 31+ in the right-most panel of the second plot.
7.1.4.2.1 Face Amount Band SHAPs
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
Dur_Grp)],
shap=shp.notplt$S[,"Face_Amount_Band"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(Dur_Grp2=fct_collapse(
Dur_Grp,
' 1- 5' = c('1-1','2-2','3-3','4-5'),
' 6-20' = c('6-10','11-15','16-20'),
other_level = '21+'
)) %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Dur_Grp,fill=Dur_Grp)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,1.5)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = "by duration group") +
theme_minimal() + facet_wrap(vars(Dur_Grp2))
7.1.4.2.2 Duration Group SHAPs
Code
data.table(
cbind(
shp.notplt$X[,.(Face_Amount_Band,
Dur_Grp)],
shap=shp.notplt$S[,"Dur_Grp"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(Dur_Grp2=fct_collapse(
Dur_Grp,
' 1- 5' = c('1-1','2-2','3-3','4-5'),
' 6-20' = c('6-10','11-15','16-20'),
other_level = '21+'
)) %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Dur_Grp,fill=Dur_Grp)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,1.25)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Dur_Grp"),
subtitle = "by duration group") +
theme_minimal() + facet_wrap(vars(Dur_Grp2))
7.1.4.3 SOA PLT Indicator vs UW
There are some differences in the spread of preferred factors across the PLT types, specifically for the NLT subgroup.
7.1.4.3.1 UW SHAPs
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == 'U') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '2') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '3') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 3 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '4') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 4 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == 'U') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == '2') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"UW"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'U') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for unismokers")) +
theme_minimal()
7.1.4.3.2 SOA PLT Indicator SHAPs
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"SOA_Post_Lvl_Ind"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == 'U') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect SOA_Post_Lvl_Ind"),
subtitle = paste0("for non-smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"SOA_Post_Lvl_Ind"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '2') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect SOA_Post_Lvl_Ind"),
subtitle = paste0("for non-smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"SOA_Post_Lvl_Ind"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '3') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect SOA_Post_Lvl_Ind"),
subtitle = paste0("for non-smokers, 3 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"SOA_Post_Lvl_Ind"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '4') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect SOA_Post_Lvl_Ind"),
subtitle = paste0("for non-smokers, 4 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"SOA_Post_Lvl_Ind"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == 'U') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect SOA_Post_Lvl_Ind"),
subtitle = paste0("for smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"SOA_Post_Lvl_Ind"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == '2') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect SOA_Post_Lvl_Ind"),
subtitle = paste0("for smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.notplt$X[,.(SOA_Post_Lvl_Ind,
NS,
Pref_Class,
NClasses)],
shap=shp.notplt$S[,"SOA_Post_Lvl_Ind"],
response=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',AE_Amount],
offset=dat.term.noplt[IsTraining==TRUE & SOA_Post_Lvl_Ind != 'PLT',ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'U') %>%
ggplot(aes(y=SOA_Post_Lvl_Ind, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect SOA_Post_Lvl_Ind"),
subtitle = paste0("for unismokers")) +
theme_minimal()
7.1.5 Next Steps in Modeling
The catboost modeling is informative here for exploratory analytics. We next build an elastic net model which includes the main effects plus the interactions identified by catboost. Elastic net modeling will reveal which is truly important in a mortality model.
While the work for supporting this is omitted here, it became clear that separate models should be fit for above and below 100K face amounts. A unified model had difficulty adequately fitting face amounts below 100K.
7.1.6 Elastic Net Models
The following formula is used throughout all non-PLT, term models.
Code
if(bUseAllInteractions) {
glmnetFormula <- as.formula(
paste0(
"~ -1 + (",
paste(pred.cols,collapse=" + "),
")^2"
)
)
} else {
glmnetFormula <- as.formula(
paste(c("~ -1",
pred.cols,
imp.int.notplt[order(-score)][Feature1 != "Noise",
paste0(Feature1,":",Feature2)]),
collapse=" + ")
)
}
print(glmnetFormula)~-1 + Sex + Face_Amount_Band + SOA_Post_Lvl_Ind + UW + AA_Grp +
Dur_Grp + Face_Amount_Band:UW + Face_Amount_Band:Dur_Grp +
SOA_Post_Lvl_Ind:UW + Face_Amount_Band:AA_Grp + Face_Amount_Band:SOA_Post_Lvl_Ind +
UW:Dur_Grp + UW:AA_Grp + Sex:UW + SOA_Post_Lvl_Ind:Dur_Grp +
Sex:Face_Amount_Band + AA_Grp:Dur_Grp + Sex:Dur_Grp + SOA_Post_Lvl_Ind:AA_Grp +
Sex:SOA_Post_Lvl_Ind + Sex:AA_GrpThe interactions included in the model are as follows:
Code
data.table(Interaction=imp.int.notplt[order(-score)][Feature1 != "Noise",
paste0(Feature1,":",Feature2)]) %>%
flextable()Interaction |
|---|
Face_Amount_Band:UW |
Face_Amount_Band:Dur_Grp |
SOA_Post_Lvl_Ind:UW |
Face_Amount_Band:AA_Grp |
Face_Amount_Band:SOA_Post_Lvl_Ind |
UW:Dur_Grp |
UW:AA_Grp |
Sex:UW |
SOA_Post_Lvl_Ind:Dur_Grp |
Sex:Face_Amount_Band |
AA_Grp:Dur_Grp |
Sex:Dur_Grp |
SOA_Post_Lvl_Ind:AA_Grp |
Sex:SOA_Post_Lvl_Ind |
Sex:AA_Grp |
7.1.6.1 Term Model Under 100K, Excluding PLT
The elastic net model is fitted. Note the use of the sparse option. This enables efficient matrix algebra when using the elastic net routines.
Code
### The prepELData function delivers the items
### needed for fitting the elastic net model.
### Then, fit the model
dat.term.noplt.lt100k <- prepELData(
formula=glmnetFormula,
data=dat.term.noplt[
Face_Amount_Band %in% c("<10K",
"10K - <25K",
"25K - <50K",
"50K - <100K")
],
predictors = setdiff(pred.cols,"Smoker_Status"),
response = "AE_Amount",
weights = "ExpDth_Amt_VBT2015",
useSparse = T,
dropunused = T
)
set.seed(cvfit.seed)
if(bUseCache & file.exists(
'term.model.el.noplt.lt100k.rds'
) & !bInvalidateCaches)
{
cvfit.term.noplt.lt100k <- readRDS('term.model.el.noplt.lt100k.rds')
} else
{
cvfit.term.noplt.lt100k <- fitCVGLMNet(
dat.term.noplt.lt100k,
nfolds = nFolds
)
if(bUseCache)
saveRDS(cvfit.term.noplt.lt100k, 'term.model.el.noplt.lt100k.rds')
}7.1.6.1.1 Usual plots for Elastic Net Models
When presenting elastic net models, the cross validation plot for \(\lambda\) and the coefficient shrinkage plots are provided.
At the minimum \(\lambda\) of 0.0003212, which minimizes the cross-validation error, the model has 382 parameters.
Code
plot(cvfit.term.noplt.lt100k)
Code
plot(cvfit.term.noplt.lt100k$glmnet.fit,xvar="lambda")
7.1.6.1.2 Factor Table
Their exponentiated coefficients are as follows:
Code
reformatCoefs(cvfit.term.noplt.lt100k, pred.cols) %>%
filter(Coef != 0) %>%
select(Feature1Name,
Feature1Level,
Feature2Name,
Feature2Level,
Coef) %>%
mutate(Coef=exp(Coef)) %>%
flextable() %>%
set_formatter(
Coef=function(x) paste0(sprintf("%.01f", 100*x),"%")
) %>%
theme_vanilla()Feature1Name | Feature1Level | Feature2Name | Feature2Level | Coef |
|---|---|---|---|---|
(Intercept) | (Intercept) | 178.2% | ||
Sex | F | 94.7% | ||
Sex | M | 106.8% | ||
Face_Amount_Band | 10K - <25K | 108.8% | ||
Face_Amount_Band | 25K - <50K | 99.1% | ||
Face_Amount_Band | 50K - <100K | 80.6% | ||
SOA_Post_Lvl_Ind | ULT | 100.7% | ||
UW | NS/2/2 | 166.1% | ||
UW | NS/1/3 | 92.0% | ||
UW | NS/2/3 | 113.6% | ||
UW | NS/3/3 | 109.0% | ||
UW | NS/1/4 | 78.7% | ||
UW | NS/2/4 | 90.3% | ||
UW | NS/4/4 | 126.1% | ||
UW | NS/U/U | 142.0% | ||
UW | S/2/2 | 112.0% | ||
UW | S/U/U | 112.0% | ||
UW | U/U/U | 90.1% | ||
AA_Grp | 26-30 | 140.4% | ||
AA_Grp | 31-35 | 141.3% | ||
AA_Grp | 36-40 | 108.1% | ||
AA_Grp | 41-45 | 109.0% | ||
AA_Grp | 46-50 | 111.8% | ||
AA_Grp | 51-55 | 118.3% | ||
AA_Grp | 61-65 | 93.2% | ||
AA_Grp | 71-75 | 102.1% | ||
AA_Grp | 76-80 | 99.0% | ||
AA_Grp | 81-85 | 98.0% | ||
AA_Grp | 86-90 | 84.3% | ||
AA_Grp | 91-95 | 74.3% | ||
AA_Grp | 96-100 | 90.1% | ||
Dur_Grp | 2-2 | 98.3% | ||
Dur_Grp | 4-5 | 85.6% | ||
Dur_Grp | 6-10 | 80.5% | ||
Dur_Grp | 11-15 | 75.5% | ||
Dur_Grp | 16-20 | 88.7% | ||
Dur_Grp | 21-30 | 78.1% | ||
Dur_Grp | 31-100 | 66.2% | ||
Face_Amount_Band | 10K - <25K | UW | NS/2/2 | 88.8% |
Face_Amount_Band | 50K - <100K | UW | NS/2/2 | 112.6% |
Face_Amount_Band | 25K - <50K | UW | NS/2/3 | 110.6% |
Face_Amount_Band | 50K - <100K | UW | NS/3/3 | 114.9% |
Face_Amount_Band | 50K - <100K | UW | NS/1/4 | 89.3% |
Face_Amount_Band | 50K - <100K | UW | NS/2/4 | 95.9% |
Face_Amount_Band | 50K - <100K | UW | NS/4/4 | 111.2% |
Face_Amount_Band | 10K - <25K | UW | NS/U/U | 100.1% |
Face_Amount_Band | 25K - <50K | UW | NS/U/U | 92.3% |
Face_Amount_Band | 50K - <100K | UW | NS/U/U | 99.0% |
Face_Amount_Band | 10K - <25K | UW | S/U/U | 95.9% |
Face_Amount_Band | 50K - <100K | UW | S/U/U | 113.6% |
Face_Amount_Band | 50K - <100K | UW | U/U/U | 109.8% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 2-2 | 90.9% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 2-2 | 83.5% |
Face_Amount_Band | 10K - <25K | Dur_Grp | 3-3 | 100.1% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 3-3 | 94.0% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 3-3 | 99.5% |
Face_Amount_Band | 10K - <25K | Dur_Grp | 4-5 | 93.1% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 4-5 | 93.5% |
Face_Amount_Band | 10K - <25K | Dur_Grp | 6-10 | 100.0% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 6-10 | 99.9% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 6-10 | 96.3% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 11-15 | 100.4% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 11-15 | 94.6% |
Face_Amount_Band | 10K - <25K | Dur_Grp | 16-20 | 79.4% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 16-20 | 83.1% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 16-20 | 72.3% |
Face_Amount_Band | 10K - <25K | Dur_Grp | 21-30 | 84.6% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 21-30 | 98.3% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 31-100 | 114.4% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 31-100 | 115.7% |
SOA_Post_Lvl_Ind | NLT | UW | NS/2/2 | 77.4% |
SOA_Post_Lvl_Ind | ULT | UW | NS/2/2 | 106.0% |
SOA_Post_Lvl_Ind | ULT | UW | NS/1/3 | 110.6% |
SOA_Post_Lvl_Ind | NLT | UW | NS/2/3 | 95.4% |
SOA_Post_Lvl_Ind | NLT | UW | NS/3/3 | 102.0% |
SOA_Post_Lvl_Ind | NLT | UW | NS/U/U | 102.9% |
SOA_Post_Lvl_Ind | ULT | UW | NS/U/U | 99.6% |
SOA_Post_Lvl_Ind | ULT | UW | S/1/2 | 106.1% |
SOA_Post_Lvl_Ind | NLT | UW | S/U/U | 97.0% |
SOA_Post_Lvl_Ind | ULT | UW | S/U/U | 98.0% |
SOA_Post_Lvl_Ind | NLT | UW | U/U/U | 110.4% |
SOA_Post_Lvl_Ind | ULT | UW | U/U/U | 103.5% |
Face_Amount_Band | 25K - <50K | AA_Grp | 18-25 | 91.0% |
Face_Amount_Band | 25K - <50K | AA_Grp | 26-30 | 112.9% |
Face_Amount_Band | 25K - <50K | AA_Grp | 31-35 | 101.2% |
Face_Amount_Band | 50K - <100K | AA_Grp | 36-40 | 105.2% |
Face_Amount_Band | 25K - <50K | AA_Grp | 41-45 | 107.9% |
Face_Amount_Band | 50K - <100K | AA_Grp | 46-50 | 95.6% |
Face_Amount_Band | 25K - <50K | AA_Grp | 51-55 | 101.3% |
Face_Amount_Band | 50K - <100K | AA_Grp | 51-55 | 89.6% |
Face_Amount_Band | 10K - <25K | AA_Grp | 56-60 | 103.9% |
Face_Amount_Band | 50K - <100K | AA_Grp | 56-60 | 96.3% |
Face_Amount_Band | 25K - <50K | AA_Grp | 61-65 | 98.1% |
Face_Amount_Band | 50K - <100K | AA_Grp | 61-65 | 95.5% |
Face_Amount_Band | 10K - <25K | AA_Grp | 66-70 | 100.7% |
Face_Amount_Band | 25K - <50K | AA_Grp | 66-70 | 93.5% |
Face_Amount_Band | 50K - <100K | AA_Grp | 66-70 | 95.4% |
Face_Amount_Band | 25K - <50K | AA_Grp | 71-75 | 100.3% |
Face_Amount_Band | 50K - <100K | AA_Grp | 71-75 | 104.4% |
Face_Amount_Band | 50K - <100K | AA_Grp | 76-80 | 114.1% |
Face_Amount_Band | 25K - <50K | AA_Grp | 86-90 | 89.9% |
Face_Amount_Band | 50K - <100K | AA_Grp | 86-90 | 101.8% |
Face_Amount_Band | 50K - <100K | AA_Grp | 91-95 | 97.5% |
Face_Amount_Band | 10K - <25K | SOA_Post_Lvl_Ind | NLT | 82.0% |
Face_Amount_Band | 25K - <50K | SOA_Post_Lvl_Ind | NLT | 70.4% |
Face_Amount_Band | 50K - <100K | SOA_Post_Lvl_Ind | NLT | 78.3% |
Face_Amount_Band | 10K - <25K | SOA_Post_Lvl_Ind | ULT | 118.4% |
Face_Amount_Band | 25K - <50K | SOA_Post_Lvl_Ind | ULT | 118.3% |
Face_Amount_Band | 50K - <100K | SOA_Post_Lvl_Ind | ULT | 126.7% |
UW | NS/2/2 | Dur_Grp | 2-2 | 104.5% |
UW | NS/U/U | Dur_Grp | 2-2 | 109.3% |
UW | NS/2/2 | Dur_Grp | 3-3 | 100.3% |
UW | NS/2/4 | Dur_Grp | 3-3 | 103.8% |
UW | NS/3/4 | Dur_Grp | 3-3 | 86.9% |
UW | NS/U/U | Dur_Grp | 3-3 | 98.2% |
UW | S/1/2 | Dur_Grp | 3-3 | 102.9% |
UW | S/2/2 | Dur_Grp | 3-3 | 103.3% |
UW | NS/2/2 | Dur_Grp | 4-5 | 102.3% |
UW | NS/3/3 | Dur_Grp | 4-5 | 108.5% |
UW | S/1/2 | Dur_Grp | 4-5 | 87.1% |
UW | S/U/U | Dur_Grp | 4-5 | 98.4% |
UW | NS/2/2 | Dur_Grp | 6-10 | 93.6% |
UW | NS/3/3 | Dur_Grp | 6-10 | 112.5% |
UW | NS/1/4 | Dur_Grp | 6-10 | 109.3% |
UW | NS/4/4 | Dur_Grp | 6-10 | 111.1% |
UW | NS/U/U | Dur_Grp | 6-10 | 98.4% |
UW | S/1/2 | Dur_Grp | 6-10 | 93.7% |
UW | S/U/U | Dur_Grp | 6-10 | 93.6% |
UW | NS/2/2 | Dur_Grp | 11-15 | 91.2% |
UW | NS/3/3 | Dur_Grp | 11-15 | 105.2% |
UW | NS/2/4 | Dur_Grp | 11-15 | 105.5% |
UW | NS/3/4 | Dur_Grp | 11-15 | 110.0% |
UW | NS/4/4 | Dur_Grp | 11-15 | 103.7% |
UW | NS/U/U | Dur_Grp | 11-15 | 87.6% |
UW | S/2/2 | Dur_Grp | 11-15 | 107.9% |
UW | S/U/U | Dur_Grp | 11-15 | 108.9% |
UW | U/U/U | Dur_Grp | 11-15 | 110.0% |
UW | NS/1/3 | Dur_Grp | 16-20 | 88.1% |
UW | NS/2/3 | Dur_Grp | 16-20 | 111.4% |
UW | NS/3/3 | Dur_Grp | 16-20 | 111.2% |
UW | NS/1/4 | Dur_Grp | 16-20 | 96.6% |
UW | NS/3/4 | Dur_Grp | 16-20 | 98.8% |
UW | NS/U/U | Dur_Grp | 16-20 | 85.4% |
UW | S/1/2 | Dur_Grp | 16-20 | 115.3% |
UW | S/2/2 | Dur_Grp | 16-20 | 121.3% |
UW | S/U/U | Dur_Grp | 16-20 | 118.4% |
UW | NS/2/2 | Dur_Grp | 21-30 | 68.7% |
UW | NS/3/3 | Dur_Grp | 21-30 | 88.5% |
UW | NS/U/U | Dur_Grp | 21-30 | 72.8% |
UW | S/2/2 | Dur_Grp | 21-30 | 101.0% |
UW | S/U/U | Dur_Grp | 21-30 | 104.0% |
UW | NS/2/2 | Dur_Grp | 31-100 | 64.8% |
UW | NS/U/U | Dur_Grp | 31-100 | 68.1% |
UW | S/U/U | Dur_Grp | 31-100 | 79.5% |
UW | U/U/U | Dur_Grp | 31-100 | 98.3% |
UW | NS/2/2 | AA_Grp | 18-25 | 83.8% |
UW | NS/U/U | AA_Grp | 18-25 | 69.1% |
UW | S/U/U | AA_Grp | 18-25 | 110.0% |
UW | NS/4/4 | AA_Grp | 26-30 | 108.5% |
UW | NS/U/U | AA_Grp | 26-30 | 77.5% |
UW | S/U/U | AA_Grp | 26-30 | 120.5% |
UW | U/U/U | AA_Grp | 26-30 | 101.2% |
UW | NS/2/2 | AA_Grp | 31-35 | 116.6% |
UW | NS/1/4 | AA_Grp | 31-35 | 119.1% |
UW | NS/U/U | AA_Grp | 31-35 | 87.5% |
UW | S/U/U | AA_Grp | 31-35 | 111.9% |
UW | NS/2/2 | AA_Grp | 36-40 | 124.8% |
UW | NS/3/3 | AA_Grp | 36-40 | 114.7% |
UW | S/2/2 | AA_Grp | 36-40 | 99.6% |
UW | S/U/U | AA_Grp | 36-40 | 98.6% |
UW | NS/3/3 | AA_Grp | 41-45 | 127.2% |
UW | NS/U/U | AA_Grp | 41-45 | 115.4% |
UW | S/U/U | AA_Grp | 41-45 | 85.4% |
UW | NS/2/2 | AA_Grp | 46-50 | 96.1% |
UW | NS/4/4 | AA_Grp | 46-50 | 100.6% |
UW | NS/U/U | AA_Grp | 46-50 | 102.3% |
UW | S/1/2 | AA_Grp | 46-50 | 95.0% |
UW | S/2/2 | AA_Grp | 46-50 | 97.4% |
UW | U/U/U | AA_Grp | 46-50 | 114.5% |
UW | NS/2/2 | AA_Grp | 51-55 | 90.3% |
UW | NS/2/3 | AA_Grp | 51-55 | 111.2% |
UW | NS/3/3 | AA_Grp | 51-55 | 108.1% |
UW | NS/3/4 | AA_Grp | 51-55 | 101.4% |
UW | S/1/2 | AA_Grp | 51-55 | 91.5% |
UW | S/2/2 | AA_Grp | 51-55 | 106.1% |
UW | S/U/U | AA_Grp | 51-55 | 86.3% |
UW | NS/2/2 | AA_Grp | 56-60 | 99.5% |
UW | NS/2/3 | AA_Grp | 56-60 | 109.3% |
UW | NS/3/3 | AA_Grp | 56-60 | 102.7% |
UW | NS/2/4 | AA_Grp | 56-60 | 93.5% |
UW | NS/3/4 | AA_Grp | 56-60 | 74.2% |
UW | NS/4/4 | AA_Grp | 56-60 | 100.2% |
UW | NS/U/U | AA_Grp | 56-60 | 110.2% |
UW | S/2/2 | AA_Grp | 56-60 | 89.7% |
UW | S/U/U | AA_Grp | 56-60 | 102.5% |
UW | U/U/U | AA_Grp | 56-60 | 107.0% |
UW | NS/2/2 | AA_Grp | 61-65 | 103.7% |
UW | NS/1/3 | AA_Grp | 61-65 | 98.5% |
UW | NS/2/3 | AA_Grp | 61-65 | 91.9% |
UW | NS/1/4 | AA_Grp | 61-65 | 97.3% |
UW | NS/2/4 | AA_Grp | 61-65 | 97.1% |
UW | NS/3/4 | AA_Grp | 61-65 | 102.2% |
UW | NS/4/4 | AA_Grp | 61-65 | 112.0% |
UW | NS/U/U | AA_Grp | 61-65 | 105.4% |
UW | S/U/U | AA_Grp | 61-65 | 98.0% |
UW | NS/2/2 | AA_Grp | 66-70 | 113.3% |
UW | NS/1/3 | AA_Grp | 66-70 | 98.5% |
UW | NS/2/3 | AA_Grp | 66-70 | 101.1% |
UW | NS/4/4 | AA_Grp | 66-70 | 94.5% |
UW | NS/U/U | AA_Grp | 66-70 | 112.7% |
UW | S/1/2 | AA_Grp | 66-70 | 107.9% |
UW | S/U/U | AA_Grp | 66-70 | 106.4% |
UW | U/U/U | AA_Grp | 66-70 | 116.9% |
UW | NS/2/2 | AA_Grp | 71-75 | 104.6% |
UW | NS/2/3 | AA_Grp | 71-75 | 93.3% |
UW | NS/3/3 | AA_Grp | 71-75 | 91.2% |
UW | NS/2/4 | AA_Grp | 71-75 | 110.8% |
UW | NS/4/4 | AA_Grp | 71-75 | 78.5% |
UW | NS/U/U | AA_Grp | 71-75 | 103.3% |
UW | S/1/2 | AA_Grp | 71-75 | 100.0% |
UW | S/U/U | AA_Grp | 71-75 | 101.0% |
UW | NS/2/2 | AA_Grp | 76-80 | 104.0% |
UW | NS/3/3 | AA_Grp | 76-80 | 90.8% |
UW | NS/2/4 | AA_Grp | 76-80 | 99.0% |
UW | NS/4/4 | AA_Grp | 76-80 | 76.0% |
UW | NS/U/U | AA_Grp | 76-80 | 102.7% |
UW | S/1/2 | AA_Grp | 76-80 | 112.8% |
UW | S/2/2 | AA_Grp | 76-80 | 115.7% |
UW | S/U/U | AA_Grp | 76-80 | 103.1% |
UW | U/U/U | AA_Grp | 76-80 | 87.0% |
UW | NS/1/3 | AA_Grp | 81-85 | 119.1% |
UW | NS/2/3 | AA_Grp | 81-85 | 98.3% |
UW | NS/1/4 | AA_Grp | 81-85 | 137.4% |
UW | NS/2/4 | AA_Grp | 81-85 | 116.1% |
UW | NS/4/4 | AA_Grp | 81-85 | 76.3% |
UW | NS/U/U | AA_Grp | 81-85 | 97.1% |
UW | U/U/U | AA_Grp | 81-85 | 76.1% |
UW | NS/2/2 | AA_Grp | 86-90 | 84.6% |
UW | U/U/U | AA_Grp | 86-90 | 80.2% |
UW | NS/U/U | AA_Grp | 91-95 | 107.0% |
Sex | M | UW | NS/2/2 | 105.4% |
Sex | M | UW | NS/1/3 | 99.8% |
Sex | M | UW | NS/2/3 | 95.4% |
Sex | M | UW | NS/3/3 | 97.3% |
Sex | M | UW | NS/2/4 | 102.3% |
Sex | M | UW | NS/3/4 | 108.2% |
Sex | M | UW | NS/4/4 | 100.4% |
Sex | M | UW | S/1/2 | 89.6% |
Sex | M | UW | S/2/2 | 96.9% |
Sex | M | UW | S/U/U | 95.4% |
SOA_Post_Lvl_Ind | NLT | Dur_Grp | 2-2 | 170.1% |
SOA_Post_Lvl_Ind | NLT | Dur_Grp | 3-3 | 89.2% |
SOA_Post_Lvl_Ind | ULT | Dur_Grp | 3-3 | 88.5% |
SOA_Post_Lvl_Ind | ULT | Dur_Grp | 4-5 | 91.9% |
SOA_Post_Lvl_Ind | NLT | Dur_Grp | 6-10 | 106.0% |
SOA_Post_Lvl_Ind | ULT | Dur_Grp | 6-10 | 85.0% |
SOA_Post_Lvl_Ind | NLT | Dur_Grp | 11-15 | 99.4% |
SOA_Post_Lvl_Ind | ULT | Dur_Grp | 11-15 | 73.0% |
SOA_Post_Lvl_Ind | ULT | Dur_Grp | 16-20 | 71.7% |
SOA_Post_Lvl_Ind | NLT | Dur_Grp | 21-30 | 100.0% |
SOA_Post_Lvl_Ind | ULT | Dur_Grp | 21-30 | 81.7% |
SOA_Post_Lvl_Ind | ULT | Dur_Grp | 31-100 | 87.5% |
Sex | M | Face_Amount_Band | 10K - <25K | 99.9% |
Sex | M | Face_Amount_Band | 25K - <50K | 104.3% |
Sex | M | Face_Amount_Band | 50K - <100K | 102.0% |
AA_Grp | 18-25 | Dur_Grp | 2-2 | 87.5% |
AA_Grp | 31-35 | Dur_Grp | 2-2 | 94.8% |
AA_Grp | 36-40 | Dur_Grp | 2-2 | 106.9% |
AA_Grp | 41-45 | Dur_Grp | 2-2 | 96.8% |
AA_Grp | 46-50 | Dur_Grp | 2-2 | 106.0% |
AA_Grp | 51-55 | Dur_Grp | 2-2 | 98.5% |
AA_Grp | 56-60 | Dur_Grp | 2-2 | 94.3% |
AA_Grp | 61-65 | Dur_Grp | 2-2 | 91.4% |
AA_Grp | 71-75 | Dur_Grp | 2-2 | 114.7% |
AA_Grp | 76-80 | Dur_Grp | 2-2 | 134.7% |
AA_Grp | 81-85 | Dur_Grp | 2-2 | 151.6% |
AA_Grp | 18-25 | Dur_Grp | 3-3 | 75.3% |
AA_Grp | 26-30 | Dur_Grp | 3-3 | 101.4% |
AA_Grp | 31-35 | Dur_Grp | 3-3 | 100.6% |
AA_Grp | 36-40 | Dur_Grp | 3-3 | 85.6% |
AA_Grp | 41-45 | Dur_Grp | 3-3 | 100.8% |
AA_Grp | 46-50 | Dur_Grp | 3-3 | 107.5% |
AA_Grp | 56-60 | Dur_Grp | 3-3 | 99.1% |
AA_Grp | 66-70 | Dur_Grp | 3-3 | 98.5% |
AA_Grp | 71-75 | Dur_Grp | 3-3 | 98.6% |
AA_Grp | 81-85 | Dur_Grp | 3-3 | 123.6% |
AA_Grp | 26-30 | Dur_Grp | 4-5 | 132.5% |
AA_Grp | 36-40 | Dur_Grp | 4-5 | 86.8% |
AA_Grp | 51-55 | Dur_Grp | 4-5 | 102.4% |
AA_Grp | 61-65 | Dur_Grp | 4-5 | 97.3% |
AA_Grp | 66-70 | Dur_Grp | 4-5 | 97.8% |
AA_Grp | 71-75 | Dur_Grp | 4-5 | 101.8% |
AA_Grp | 18-25 | Dur_Grp | 6-10 | 102.1% |
AA_Grp | 26-30 | Dur_Grp | 6-10 | 115.5% |
AA_Grp | 31-35 | Dur_Grp | 6-10 | 119.8% |
AA_Grp | 36-40 | Dur_Grp | 6-10 | 112.9% |
AA_Grp | 41-45 | Dur_Grp | 6-10 | 96.6% |
AA_Grp | 46-50 | Dur_Grp | 6-10 | 118.0% |
AA_Grp | 56-60 | Dur_Grp | 6-10 | 108.8% |
AA_Grp | 61-65 | Dur_Grp | 6-10 | 97.0% |
AA_Grp | 66-70 | Dur_Grp | 6-10 | 89.5% |
AA_Grp | 71-75 | Dur_Grp | 6-10 | 91.0% |
AA_Grp | 76-80 | Dur_Grp | 6-10 | 87.4% |
AA_Grp | 81-85 | Dur_Grp | 6-10 | 84.2% |
AA_Grp | 18-25 | Dur_Grp | 11-15 | 97.6% |
AA_Grp | 36-40 | Dur_Grp | 11-15 | 109.2% |
AA_Grp | 41-45 | Dur_Grp | 11-15 | 103.4% |
AA_Grp | 46-50 | Dur_Grp | 11-15 | 99.0% |
AA_Grp | 56-60 | Dur_Grp | 11-15 | 103.4% |
AA_Grp | 61-65 | Dur_Grp | 11-15 | 108.0% |
AA_Grp | 71-75 | Dur_Grp | 11-15 | 91.3% |
AA_Grp | 76-80 | Dur_Grp | 11-15 | 96.3% |
AA_Grp | 81-85 | Dur_Grp | 11-15 | 90.3% |
AA_Grp | 36-40 | Dur_Grp | 16-20 | 86.2% |
AA_Grp | 41-45 | Dur_Grp | 16-20 | 120.8% |
AA_Grp | 51-55 | Dur_Grp | 16-20 | 112.0% |
AA_Grp | 56-60 | Dur_Grp | 16-20 | 110.4% |
AA_Grp | 61-65 | Dur_Grp | 16-20 | 109.7% |
AA_Grp | 66-70 | Dur_Grp | 16-20 | 105.0% |
AA_Grp | 71-75 | Dur_Grp | 16-20 | 89.2% |
AA_Grp | 76-80 | Dur_Grp | 16-20 | 88.8% |
AA_Grp | 81-85 | Dur_Grp | 16-20 | 88.4% |
AA_Grp | 86-90 | Dur_Grp | 16-20 | 95.2% |
AA_Grp | 41-45 | Dur_Grp | 21-30 | 125.2% |
AA_Grp | 46-50 | Dur_Grp | 21-30 | 106.1% |
AA_Grp | 51-55 | Dur_Grp | 21-30 | 90.5% |
AA_Grp | 56-60 | Dur_Grp | 21-30 | 96.3% |
AA_Grp | 66-70 | Dur_Grp | 21-30 | 102.5% |
AA_Grp | 76-80 | Dur_Grp | 21-30 | 97.1% |
AA_Grp | 91-95 | Dur_Grp | 21-30 | 98.8% |
AA_Grp | 46-50 | Dur_Grp | 31-100 | 134.0% |
AA_Grp | 51-55 | Dur_Grp | 31-100 | 102.2% |
AA_Grp | 56-60 | Dur_Grp | 31-100 | 90.6% |
AA_Grp | 61-65 | Dur_Grp | 31-100 | 93.7% |
AA_Grp | 71-75 | Dur_Grp | 31-100 | 96.0% |
AA_Grp | 76-80 | Dur_Grp | 31-100 | 96.9% |
AA_Grp | 81-85 | Dur_Grp | 31-100 | 97.7% |
AA_Grp | 86-90 | Dur_Grp | 31-100 | 100.0% |
Sex | M | Dur_Grp | 2-2 | 99.9% |
Sex | M | Dur_Grp | 4-5 | 103.6% |
Sex | M | Dur_Grp | 6-10 | 104.0% |
Sex | M | Dur_Grp | 16-20 | 100.6% |
Sex | M | Dur_Grp | 21-30 | 99.7% |
Sex | M | Dur_Grp | 31-100 | 102.5% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 18-25 | 115.9% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 26-30 | 104.5% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 31-35 | 81.1% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 36-40 | 93.3% |
SOA_Post_Lvl_Ind | NLT | AA_Grp | 41-45 | 89.3% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 41-45 | 86.3% |
SOA_Post_Lvl_Ind | NLT | AA_Grp | 46-50 | 94.5% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 46-50 | 103.0% |
SOA_Post_Lvl_Ind | NLT | AA_Grp | 51-55 | 106.1% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 51-55 | 99.5% |
SOA_Post_Lvl_Ind | NLT | AA_Grp | 61-65 | 112.5% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 61-65 | 113.2% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 66-70 | 106.6% |
SOA_Post_Lvl_Ind | NLT | AA_Grp | 71-75 | 111.0% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 71-75 | 127.0% |
SOA_Post_Lvl_Ind | NLT | AA_Grp | 76-80 | 104.7% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 76-80 | 127.0% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 81-85 | 131.5% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 86-90 | 131.9% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 91-95 | 94.4% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 96-100 | 90.3% |
Sex | M | SOA_Post_Lvl_Ind | NLT | 90.6% |
Sex | M | SOA_Post_Lvl_Ind | ULT | 102.5% |
Sex | M | AA_Grp | 18-25 | 111.9% |
Sex | M | AA_Grp | 26-30 | 105.6% |
Sex | M | AA_Grp | 31-35 | 132.2% |
Sex | M | AA_Grp | 36-40 | 137.3% |
Sex | M | AA_Grp | 41-45 | 105.5% |
Sex | M | AA_Grp | 46-50 | 104.4% |
Sex | M | AA_Grp | 51-55 | 113.1% |
Sex | M | AA_Grp | 56-60 | 102.6% |
Sex | M | AA_Grp | 61-65 | 104.7% |
Sex | M | AA_Grp | 71-75 | 90.8% |
Sex | M | AA_Grp | 76-80 | 91.0% |
Sex | M | AA_Grp | 81-85 | 93.8% |
Sex | M | AA_Grp | 86-90 | 93.4% |
Sex | M | AA_Grp | 91-95 | 97.5% |
Sex | M | AA_Grp | 96-100 | 98.3% |
Note that interaction terms must be considered together. For example, UW interacts with Face Amount Band, so these should be considered in combination. The slate of UW without a second feature apply to the base level of Face Amount Band (and any other factor with which UW interacts).
Since penalization is roughly equivalent to Bayesian credibility using a combination of Gaussian and Laplace priors, these factors are arguably credible. This is true even when dealing with factors with small effect sizes, such as the standalone factor for Duration 3.
Plots and tables of effects are much more digestible. As it happens, all but Sex are involved in feature interactions. Those factors can be read from the table above.
In the plots and tables that follow, we fix all of the other variables at their middle values when extracting final factors.
We generate some supporting tables: a factor grid for attaching to the experience, and a list of interactions present in the model
Code
### The following code creates a grid of factors,
### saves the grid to an Excel file, and
### saves a listing of interactions present in the model.
dat.term.noplt[(Face_Amount_Band %in% c("<10K",
"10K - <25K",
"25K - <50K",
"50K - <100K")),..pred.cols] %>%
mutate(Face_Amount_Band=fct_drop(Face_Amount_Band)) %>%
lapply(levels) %>%
expand.grid() ->
dat.term.noplt.lt100k.grid
dat.term.noplt.lt100k.grid %>%
model.Matrix(
object=glmnetFormula,
data=.,
sparse=T
) %>%
predict(
cvfit.term.noplt.lt100k,
newx=.,
s="lambda.min"
) %>%
as.vector() ->
newCoef
dat.term.noplt.lt100k.grid %>%
add_column(
Factor=exp(newCoef)
) %>%
setDT() ->
dat.term.noplt.lt100k.grid
write.xlsx(dat.term.noplt.lt100k.grid,
file="dat.term.noplt.lt100k.grid.xlsx")
reformatCoefs(cvfit.term.noplt.lt100k, pred.cols) %>%
filter(Coef != 0 & !is.na(Feature2Name)) %>%
select(Feature1Name,Feature2Name) %>%
distinct() %>%
as.list() %>%
purrr::list_transpose() ->
term.no.plt.lt100k.int.list7.1.6.1.3 Plots of Terms
Below are plots of the 2-way interaction terms, with external factors fixed at their middle values.
Some of the effects are subtle and can be confirmed by reviewing the factor table.
- Face Amount Band x UW: While factors decline with increasing face amount, the slope of the decline is qualitatively different. Moreover, the first two bands do not always obey this pattern across UW classes.
- Dur Group x Face Amount Band: While factors tend to decline with duration, the slope of the decline changes with face amount.
- SOA Post Level Ind vs UW: As foreshadowed in the review of SHAP values, there are differences in the spread of preferred factors by post level indicator, particularly in the 2-class systems.
- Attained Age x Face Amount Band: there are some differences at the younger attained ages and lowest band.
- Face Amount Band x Post Level Indicator: Factors tend to decrease, although the shapes of that decrease differ by post level indicator.
- Duration x UW: There is a pattern in the 2-class and 3-class residual standard non-smoker duration patterns, with a pronounced elevation through duration 20.
- Attained age x UW: To the extent an interaction is being detected, it is mostly at the younger attained ages.
- Sex x UW: The interaction appears most prominent with NS/2/2 which shares a wider spread.
- Duration x Post Level Indicator: ULT and NLT deviate from WLT in the earlier durations.
- Face Amount Band x Sex: no obvious interaction.
- Attained age x Duration: There are some interactions in the earliest durations for both the youngest and the middle attained ages.
- Duration x Sex: Nothing stands out. A review of the factor table shows subtle shifts.
- Attained Age x Post Level Indicator: Qualitatively, the slope seems different for ULT here.
- Post-Level Indicator x Sex: The interaction here appears to be with NLT and males.
- Attained age x Sex: There appears to be a different attained slope, most prominent amount younger males.
7.1.6.1.4 Tables of Terms
Below are tables of the 2-way interaction terms, with external factors fixed at their middle values.
Face_Amount_Band | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
<10K | 130.8% | 230.7% | 118.6% | 136.6% | 154.7% | 100.1% | 114.7% | 133.7% | 184.6% | 195.7% | 113.9% | 146.5% | 141.2% | 117.8% |
10K - <25K | 132.4% | 207.2% | 120.0% | 138.2% | 156.5% | 101.3% | 116.0% | 135.3% | 186.8% | 198.3% | 115.3% | 148.2% | 136.9% | 119.2% |
25K - <50K | 119.0% | 209.8% | 107.8% | 137.4% | 140.7% | 91.1% | 104.3% | 121.6% | 167.9% | 164.3% | 103.6% | 133.2% | 128.4% | 107.2% |
50K - <100K | 100.7% | 200.0% | 91.3% | 105.1% | 136.8% | 68.8% | 84.7% | 102.9% | 158.0% | 149.1% | 87.7% | 112.7% | 123.4% | 99.6% |
Dur_Grp | <10K | 10K - <25K | 25K - <50K | 50K - <100K |
|---|---|---|---|---|
1-1 | 137.8% | 149.8% | 134.0% | 101.7% |
2-2 | 123.9% | 134.7% | 109.5% | 76.3% |
3-3 | 143.0% | 155.6% | 130.6% | 105.0% |
4-5 | 114.7% | 116.0% | 104.3% | 84.7% |
6-10 | 107.6% | 117.0% | 104.5% | 76.5% |
11-15 | 118.5% | 128.9% | 115.7% | 82.7% |
16-20 | 134.1% | 115.7% | 108.3% | 71.6% |
21-30 | 107.6% | 99.0% | 104.7% | 78.1% |
31-100 | 85.5% | 93.0% | 95.1% | 73.1% |
SOA_Post_Lvl_Ind | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
WLT | 132.4% | 207.2% | 120.0% | 138.2% | 156.5% | 101.3% | 116.0% | 135.3% | 186.8% | 198.3% | 115.3% | 148.2% | 136.9% | 119.2% |
NLT | 122.1% | 147.9% | 110.7% | 121.6% | 147.3% | 93.5% | 107.0% | 124.8% | 172.4% | 188.2% | 106.3% | 136.7% | 122.5% | 121.4% |
ULT | 164.1% | 272.2% | 164.5% | 171.4% | 194.0% | 125.6% | 143.9% | 167.8% | 231.7% | 244.9% | 151.6% | 183.8% | 166.3% | 153.0% |
AA_Grp | <10K | 10K - <25K | 25K - <50K | 50K - <100K |
|---|---|---|---|---|
0-17 | 130.3% | 131.8% | 120.8% | 100.7% |
18-25 | 130.3% | 131.8% | 109.9% | 100.7% |
26-30 | 242.2% | 245.1% | 253.5% | 187.3% |
31-35 | 184.0% | 186.3% | 172.6% | 142.3% |
36-40 | 122.2% | 123.6% | 113.3% | 99.3% |
41-45 | 142.0% | 143.7% | 142.1% | 109.8% |
46-50 | 145.6% | 147.3% | 135.0% | 107.6% |
51-55 | 157.8% | 159.7% | 148.2% | 109.3% |
56-60 | 121.9% | 128.1% | 113.0% | 90.7% |
61-65 | 114.7% | 116.0% | 104.3% | 84.7% |
66-70 | 127.4% | 129.9% | 110.5% | 94.0% |
71-75 | 150.1% | 151.9% | 139.6% | 121.2% |
76-80 | 127.6% | 129.2% | 118.3% | 112.6% |
81-85 | 148.1% | 149.9% | 137.3% | 114.5% |
86-90 | 109.8% | 111.1% | 91.5% | 86.4% |
91-95 | 96.8% | 97.9% | 89.7% | 73.0% |
96-100 | 117.4% | 118.8% | 108.9% | 90.8% |
101-105 | 130.3% | 131.8% | 120.8% | 100.7% |
106-110 | 130.3% | 131.8% | 120.8% | 100.7% |
111-115 | 130.3% | 131.8% | 120.8% | 100.7% |
Face_Amount_Band | WLT | NLT | ULT |
|---|---|---|---|
<10K | 114.7% | 129.0% | 120.1% |
10K - <25K | 116.0% | 107.0% | 143.9% |
25K - <50K | 104.3% | 82.6% | 129.2% |
50K - <100K | 84.7% | 74.6% | 112.3% |
Dur_Grp | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1-1 | 170.9% | 261.3% | 154.9% | 178.5% | 186.3% | 130.8% | 149.8% | 174.7% | 241.3% | 256.0% | 170.9% | 191.4% | 179.7% | 154.0% |
2-2 | 153.6% | 245.6% | 139.3% | 160.4% | 167.4% | 117.6% | 134.7% | 157.0% | 216.9% | 251.6% | 153.6% | 172.0% | 161.5% | 138.4% |
3-3 | 171.1% | 262.3% | 155.1% | 178.7% | 186.5% | 131.0% | 155.6% | 152.1% | 241.5% | 251.7% | 176.1% | 197.9% | 179.9% | 154.1% |
4-5 | 132.4% | 207.2% | 120.0% | 138.2% | 156.5% | 101.3% | 116.0% | 135.3% | 186.8% | 198.3% | 115.3% | 148.2% | 136.9% | 119.2% |
6-10 | 133.4% | 190.9% | 120.9% | 139.3% | 163.5% | 111.6% | 117.0% | 136.4% | 209.2% | 196.7% | 125.0% | 149.4% | 131.2% | 120.2% |
11-15 | 139.4% | 194.5% | 126.3% | 145.5% | 159.7% | 106.7% | 128.9% | 156.7% | 204.1% | 182.9% | 139.4% | 168.4% | 159.6% | 138.1% |
16-20 | 132.0% | 201.9% | 105.4% | 153.6% | 160.0% | 97.6% | 115.7% | 133.4% | 186.4% | 168.9% | 152.3% | 179.4% | 164.4% | 118.9% |
21-30 | 113.0% | 118.8% | 102.4% | 118.0% | 108.9% | 86.5% | 99.0% | 115.5% | 159.5% | 123.2% | 113.0% | 127.8% | 123.6% | 101.8% |
31-100 | 106.1% | 105.2% | 96.2% | 110.8% | 115.6% | 81.2% | 93.0% | 108.5% | 149.8% | 108.3% | 106.1% | 118.8% | 88.7% | 94.0% |
AA_Grp | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0-17 | 146.0% | 220.3% | 134.4% | 166.0% | 172.7% | 114.9% | 131.8% | 146.0% | 184.1% | 207.6% | 127.2% | 163.5% | 154.2% | 131.5% |
18-25 | 146.0% | 184.6% | 134.4% | 166.0% | 172.7% | 114.9% | 131.8% | 146.0% | 184.1% | 143.5% | 127.2% | 163.5% | 169.6% | 131.5% |
26-30 | 271.5% | 409.6% | 249.9% | 308.6% | 321.0% | 213.6% | 245.1% | 271.5% | 371.4% | 299.0% | 236.4% | 304.0% | 345.4% | 247.5% |
31-35 | 206.3% | 362.9% | 189.9% | 234.5% | 243.9% | 193.3% | 186.3% | 206.3% | 260.1% | 256.6% | 179.7% | 231.0% | 243.9% | 185.8% |
36-40 | 136.9% | 257.8% | 126.0% | 155.6% | 185.7% | 107.7% | 123.6% | 136.9% | 172.6% | 194.6% | 119.2% | 152.7% | 142.6% | 123.4% |
41-45 | 159.2% | 240.1% | 146.5% | 180.9% | 239.5% | 125.2% | 143.7% | 159.2% | 200.7% | 261.2% | 138.6% | 178.2% | 143.5% | 143.4% |
46-50 | 163.2% | 236.6% | 150.2% | 185.5% | 193.0% | 128.4% | 147.3% | 163.2% | 206.9% | 237.3% | 135.0% | 178.1% | 172.3% | 168.3% |
51-55 | 176.9% | 241.0% | 162.8% | 223.6% | 226.1% | 139.2% | 159.7% | 179.4% | 223.0% | 251.4% | 140.9% | 210.2% | 161.2% | 159.4% |
56-60 | 151.7% | 227.7% | 139.7% | 188.4% | 184.3% | 119.4% | 128.1% | 112.6% | 191.6% | 237.7% | 132.1% | 152.3% | 164.2% | 146.3% |
61-65 | 132.4% | 207.2% | 120.0% | 138.2% | 156.5% | 101.3% | 116.0% | 135.3% | 186.8% | 198.3% | 115.3% | 148.2% | 136.9% | 119.2% |
66-70 | 143.9% | 245.9% | 130.4% | 165.3% | 170.1% | 113.2% | 129.9% | 143.9% | 171.4% | 230.4% | 135.2% | 161.1% | 161.6% | 151.5% |
71-75 | 151.9% | 239.6% | 139.8% | 161.0% | 163.7% | 119.5% | 151.9% | 151.9% | 150.4% | 222.9% | 132.3% | 170.1% | 162.0% | 136.8% |
76-80 | 144.6% | 226.8% | 133.1% | 164.3% | 155.2% | 113.8% | 129.2% | 144.6% | 138.5% | 211.0% | 142.1% | 187.4% | 157.4% | 113.3% |
81-85 | 143.0% | 215.8% | 156.8% | 159.8% | 169.1% | 154.6% | 149.9% | 143.0% | 137.7% | 197.4% | 124.6% | 160.2% | 151.0% | 98.1% |
86-90 | 123.1% | 157.0% | 113.3% | 139.9% | 145.5% | 96.8% | 111.1% | 123.1% | 155.1% | 174.9% | 107.2% | 137.8% | 129.9% | 88.9% |
91-95 | 108.5% | 163.7% | 99.8% | 123.3% | 128.3% | 85.3% | 97.9% | 108.5% | 136.8% | 165.0% | 94.5% | 121.5% | 114.6% | 97.7% |
96-100 | 131.6% | 198.6% | 121.1% | 149.6% | 155.6% | 103.6% | 118.8% | 131.6% | 165.9% | 187.1% | 114.6% | 147.4% | 139.0% | 118.6% |
101-105 | 146.0% | 220.3% | 134.4% | 166.0% | 172.7% | 114.9% | 131.8% | 146.0% | 184.1% | 207.6% | 127.2% | 163.5% | 154.2% | 131.5% |
106-110 | 146.0% | 220.3% | 134.4% | 166.0% | 172.7% | 114.9% | 131.8% | 146.0% | 184.1% | 207.6% | 127.2% | 163.5% | 154.2% | 131.5% |
111-115 | 146.0% | 220.3% | 134.4% | 166.0% | 172.7% | 114.9% | 131.8% | 146.0% | 184.1% | 207.6% | 127.2% | 163.5% | 154.2% | 131.5% |
Sex | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
F | 132.4% | 207.2% | 120.0% | 138.2% | 156.5% | 101.3% | 116.0% | 135.3% | 186.8% | 198.3% | 115.3% | 148.2% | 136.9% | 119.2% |
M | 161.7% | 266.7% | 146.2% | 161.0% | 185.9% | 123.7% | 145.0% | 178.7% | 229.1% | 242.2% | 126.2% | 175.4% | 159.5% | 145.6% |
Dur_Grp | WLT | NLT | ULT |
|---|---|---|---|
1-1 | 149.8% | 138.2% | 202.2% |
2-2 | 134.7% | 211.3% | 181.8% |
3-3 | 155.6% | 128.1% | 185.9% |
4-5 | 116.0% | 107.0% | 143.9% |
6-10 | 117.0% | 114.3% | 134.1% |
11-15 | 128.9% | 118.2% | 127.0% |
16-20 | 115.7% | 106.8% | 111.9% |
21-30 | 99.0% | 91.3% | 109.2% |
31-100 | 93.0% | 85.8% | 109.9% |
Face_Amount_Band | F | M |
|---|---|---|
<10K | 114.7% | 143.4% |
10K - <25K | 116.0% | 145.0% |
25K - <50K | 104.3% | 136.1% |
50K - <100K | 84.7% | 108.1% |
AA_Grp | 1-1 | 2-2 | 3-3 | 4-5 | 6-10 | 11-15 | 16-20 | 21-30 | 31-100 |
|---|---|---|---|---|---|---|---|---|---|
0-17 | 165.6% | 162.8% | 172.0% | 131.8% | 133.2% | 131.8% | 116.6% | 109.4% | 109.7% |
18-25 | 165.6% | 142.4% | 129.4% | 131.8% | 136.0% | 128.7% | 116.6% | 109.4% | 109.7% |
26-30 | 232.4% | 228.5% | 244.8% | 245.1% | 215.9% | 185.0% | 163.7% | 153.6% | 153.9% |
31-35 | 233.9% | 218.1% | 244.3% | 186.3% | 225.4% | 186.2% | 164.8% | 154.6% | 154.9% |
36-40 | 178.9% | 188.0% | 159.1% | 123.6% | 162.5% | 155.5% | 108.7% | 118.3% | 118.5% |
41-45 | 180.5% | 171.8% | 189.0% | 143.7% | 140.2% | 148.6% | 153.6% | 149.3% | 119.5% |
46-50 | 185.0% | 192.8% | 206.7% | 147.3% | 175.6% | 145.9% | 130.3% | 129.7% | 164.2% |
51-55 | 195.9% | 189.8% | 203.5% | 159.7% | 157.6% | 156.0% | 154.6% | 117.2% | 132.6% |
56-60 | 160.9% | 149.2% | 165.6% | 128.1% | 140.8% | 132.5% | 125.1% | 102.5% | 96.5% |
61-65 | 149.8% | 134.7% | 155.6% | 116.0% | 117.0% | 128.9% | 115.7% | 99.0% | 93.0% |
66-70 | 166.8% | 164.0% | 170.6% | 129.9% | 120.1% | 132.8% | 123.4% | 113.0% | 110.5% |
71-75 | 187.3% | 211.2% | 191.9% | 151.9% | 137.0% | 136.1% | 117.7% | 123.8% | 119.1% |
76-80 | 162.2% | 215.0% | 168.5% | 129.2% | 114.1% | 124.3% | 101.4% | 104.1% | 104.1% |
81-85 | 188.2% | 280.7% | 241.6% | 149.9% | 127.5% | 135.2% | 117.2% | 124.4% | 121.8% |
86-90 | 139.5% | 137.2% | 144.9% | 111.1% | 112.2% | 111.1% | 93.6% | 92.2% | 92.5% |
91-95 | 123.0% | 121.0% | 127.8% | 97.9% | 98.9% | 97.9% | 86.6% | 80.3% | 81.5% |
96-100 | 149.2% | 146.8% | 155.0% | 118.8% | 120.0% | 118.8% | 105.1% | 98.6% | 98.8% |
101-105 | 165.6% | 162.8% | 172.0% | 131.8% | 133.2% | 131.8% | 116.6% | 109.4% | 109.7% |
106-110 | 165.6% | 162.8% | 172.0% | 131.8% | 133.2% | 131.8% | 116.6% | 109.4% | 109.7% |
111-115 | 165.6% | 162.8% | 172.0% | 131.8% | 133.2% | 131.8% | 116.6% | 109.4% | 109.7% |
Dur_Grp | F | M |
|---|---|---|
1-1 | 149.8% | 180.7% |
2-2 | 134.7% | 162.3% |
3-3 | 155.6% | 187.7% |
4-5 | 116.0% | 145.0% |
6-10 | 117.0% | 146.7% |
11-15 | 128.9% | 155.4% |
16-20 | 115.7% | 140.5% |
21-30 | 99.0% | 119.1% |
31-100 | 93.0% | 115.0% |
AA_Grp | WLT | NLT | ULT |
|---|---|---|---|
0-17 | 131.8% | 108.1% | 144.4% |
18-25 | 131.8% | 108.1% | 167.3% |
26-30 | 245.1% | 201.1% | 280.4% |
31-35 | 186.3% | 152.8% | 165.4% |
36-40 | 123.6% | 101.4% | 126.3% |
41-45 | 143.7% | 105.3% | 135.8% |
46-50 | 147.3% | 114.2% | 166.2% |
51-55 | 159.7% | 139.0% | 174.1% |
56-60 | 128.1% | 105.1% | 140.3% |
61-65 | 116.0% | 107.0% | 143.9% |
66-70 | 129.9% | 106.5% | 151.6% |
71-75 | 151.9% | 138.2% | 211.3% |
76-80 | 129.2% | 111.0% | 179.7% |
81-85 | 149.9% | 122.9% | 215.9% |
86-90 | 111.1% | 91.1% | 160.5% |
91-95 | 97.9% | 80.3% | 101.3% |
96-100 | 118.8% | 97.5% | 117.5% |
101-105 | 131.8% | 108.1% | 144.4% |
106-110 | 131.8% | 108.1% | 144.4% |
111-115 | 131.8% | 108.1% | 144.4% |
SOA_Post_Lvl_Ind | F | M |
|---|---|---|
WLT | 116.0% | 145.0% |
NLT | 107.0% | 121.2% |
ULT | 143.9% | 184.2% |
AA_Grp | F | M |
|---|---|---|
0-17 | 131.8% | 157.3% |
18-25 | 131.8% | 176.1% |
26-30 | 245.1% | 309.1% |
31-35 | 186.3% | 293.8% |
36-40 | 123.6% | 202.5% |
41-45 | 143.7% | 181.0% |
46-50 | 147.3% | 183.6% |
51-55 | 159.7% | 215.5% |
56-60 | 128.1% | 156.9% |
61-65 | 116.0% | 145.0% |
66-70 | 129.9% | 155.0% |
71-75 | 151.9% | 164.5% |
76-80 | 129.2% | 140.2% |
81-85 | 149.9% | 167.8% |
86-90 | 111.1% | 123.8% |
91-95 | 97.9% | 113.9% |
96-100 | 118.8% | 139.4% |
101-105 | 131.8% | 157.3% |
106-110 | 131.8% | 157.3% |
111-115 | 131.8% | 157.3% |
7.1.6.2 Term Model 100K+, Excluding PLT
As with the under 100K model, the elastic net model is fitted. Note the use of the sparse option. This enables efficient matrix algebra when using the elastic net routines.
Code
dat.term.noplt[
!(Face_Amount_Band %in% c("<10K",
"10K - <25K",
"25K - <50K",
"50K - <100K"))
] %>%
mutate(Face_Amount_Band=fct_drop(Face_Amount_Band)) %>%
prepELData(
formula=glmnetFormula,
data=.,
predictors = pred.cols,
response = "AE_Amount",
weights = "ExpDth_Amt_VBT2015",
useSparse = T,
dropunused = F
) -> dat.term.noplt.100kp
set.seed(cvfit.seed)
if(bUseCache & file.exists(
'term.model.el.noplt.100kp.rds'
) & !bInvalidateCaches)
{
cvfit.term.noplt.100kp <- readRDS('term.model.el.noplt.100kp.rds')
} else
{
cvfit.term.noplt.100kp <- fitCVGLMNet(
dat.term.noplt.100kp,
nfolds = nFolds
)
if(bUseCache)
saveRDS(cvfit.term.noplt.100kp, 'term.model.el.noplt.100kp.rds')
}7.1.6.2.1 Usual plots for Elastic Net Models
When presenting elastic net models, the cross validation plot for \(\lambda\) and the coefficient shrinkage plots are provided.
At the minimum \(\lambda\) of 0.00128, the model has 124 parameters.
Code
plot(cvfit.term.noplt.100kp)
Code
plot(cvfit.term.noplt.100kp$glmnet.fit,xvar="lambda")
7.1.6.2.2 Factor Table
Their exponentiated coefficients are as follows:
Code
reformatCoefs(cvfit.term.noplt.100kp, pred.cols) %>%
filter(Coef != 0) %>%
select(Feature1Name,
Feature1Level,
Feature2Name,
Feature2Level,
Coef) %>%
mutate(Coef=exp(Coef)) %>%
flextable() %>%
set_formatter(
Coef=function(x) paste0(sprintf("%.01f", 100*x),"%")
) %>%
theme_vanilla()Feature1Name | Feature1Level | Feature2Name | Feature2Level | Coef |
|---|---|---|---|---|
(Intercept) | (Intercept) | 88.5% | ||
Sex | F | 94.4% | ||
Sex | M | 102.7% | ||
Face_Amount_Band | 250K - <500K | 94.3% | ||
Face_Amount_Band | 500K - <1M | 89.7% | ||
Face_Amount_Band | 1M - <2.5M | 88.5% | ||
Face_Amount_Band | 2.5M - <5M | 91.6% | ||
Face_Amount_Band | 10M+ | 77.7% | ||
SOA_Post_Lvl_Ind | NLT | 91.2% | ||
UW | NS/2/2 | 148.3% | ||
UW | NS/1/3 | 83.3% | ||
UW | NS/3/3 | 123.8% | ||
UW | NS/1/4 | 87.4% | ||
UW | NS/3/4 | 112.0% | ||
UW | NS/4/4 | 128.6% | ||
UW | S/2/2 | 121.7% | ||
UW | S/U/U | 114.3% | ||
AA_Grp | 26-30 | 100.7% | ||
AA_Grp | 56-60 | 96.2% | ||
AA_Grp | 76-80 | 102.8% | ||
Dur_Grp | 2-2 | 100.5% | ||
Dur_Grp | 6-10 | 99.9% | ||
Dur_Grp | 11-15 | 97.7% | ||
Dur_Grp | 16-20 | 94.5% | ||
Dur_Grp | 21-30 | 111.2% | ||
Dur_Grp | 31-100 | 106.8% | ||
Face_Amount_Band | 500K - <1M | UW | NS/2/2 | 98.3% |
Face_Amount_Band | 2.5M - <5M | UW | NS/1/3 | 89.8% |
Face_Amount_Band | 5M - <10M | UW | NS/1/3 | 100.8% |
Face_Amount_Band | 1M - <2.5M | UW | NS/2/3 | 100.0% |
Face_Amount_Band | 2.5M - <5M | UW | NS/2/3 | 102.2% |
Face_Amount_Band | 1M - <2.5M | UW | NS/3/3 | 108.0% |
Face_Amount_Band | 1M - <2.5M | UW | NS/1/4 | 96.8% |
Face_Amount_Band | 10M+ | UW | NS/1/4 | 130.2% |
Face_Amount_Band | 500K - <1M | UW | NS/2/4 | 100.4% |
Face_Amount_Band | 1M - <2.5M | UW | NS/2/4 | 101.8% |
Face_Amount_Band | 2.5M - <5M | UW | NS/2/4 | 96.1% |
Face_Amount_Band | 10M+ | UW | NS/2/4 | 86.1% |
Face_Amount_Band | 500K - <1M | UW | NS/3/4 | 104.8% |
Face_Amount_Band | 1M - <2.5M | UW | NS/3/4 | 102.5% |
Face_Amount_Band | 1M - <2.5M | UW | NS/4/4 | 103.8% |
Face_Amount_Band | 2.5M - <5M | UW | NS/4/4 | 105.8% |
Face_Amount_Band | 10M+ | Dur_Grp | 4-5 | 76.3% |
Face_Amount_Band | 1M - <2.5M | Dur_Grp | 6-10 | 99.3% |
Face_Amount_Band | 2.5M - <5M | Dur_Grp | 6-10 | 93.5% |
Face_Amount_Band | 5M - <10M | Dur_Grp | 6-10 | 98.3% |
Face_Amount_Band | 10M+ | Dur_Grp | 6-10 | 120.4% |
Face_Amount_Band | 500K - <1M | Dur_Grp | 11-15 | 99.4% |
Face_Amount_Band | 5M - <10M | Dur_Grp | 11-15 | 103.7% |
Face_Amount_Band | 5M - <10M | Dur_Grp | 16-20 | 92.1% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 36-40 | 96.7% |
Face_Amount_Band | 10M+ | AA_Grp | 36-40 | 120.1% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 41-45 | 98.3% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 46-50 | 99.7% |
Face_Amount_Band | 250K - <500K | AA_Grp | 51-55 | 100.3% |
Face_Amount_Band | 10M+ | AA_Grp | 51-55 | 94.3% |
Face_Amount_Band | 250K - <500K | AA_Grp | 56-60 | 97.8% |
Face_Amount_Band | 500K - <1M | AA_Grp | 56-60 | 98.0% |
Face_Amount_Band | 10M+ | AA_Grp | 56-60 | 101.8% |
Face_Amount_Band | 250K - <500K | AA_Grp | 61-65 | 99.5% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 61-65 | 101.2% |
Face_Amount_Band | 250K - <500K | AA_Grp | 66-70 | 99.8% |
Face_Amount_Band | 500K - <1M | AA_Grp | 66-70 | 99.0% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 66-70 | 107.4% |
Face_Amount_Band | 10M+ | AA_Grp | 71-75 | 98.5% |
UW | NS/3/4 | Dur_Grp | 2-2 | 100.6% |
UW | NS/1/4 | Dur_Grp | 4-5 | 100.8% |
UW | NS/U/U | Dur_Grp | 4-5 | 105.8% |
UW | NS/3/3 | Dur_Grp | 6-10 | 101.8% |
UW | S/1/2 | Dur_Grp | 6-10 | 97.9% |
UW | NS/2/3 | Dur_Grp | 11-15 | 100.0% |
UW | NS/1/4 | Dur_Grp | 11-15 | 95.8% |
UW | NS/3/4 | Dur_Grp | 11-15 | 102.3% |
UW | NS/U/U | Dur_Grp | 11-15 | 96.2% |
UW | NS/2/2 | Dur_Grp | 16-20 | 103.8% |
UW | NS/3/3 | AA_Grp | 36-40 | 104.3% |
UW | NS/2/4 | AA_Grp | 36-40 | 101.5% |
UW | NS/1/4 | AA_Grp | 46-50 | 102.2% |
UW | NS/4/4 | AA_Grp | 46-50 | 109.1% |
UW | NS/1/4 | AA_Grp | 51-55 | 93.9% |
UW | NS/U/U | AA_Grp | 51-55 | 96.4% |
UW | NS/1/4 | AA_Grp | 56-60 | 101.5% |
UW | NS/2/4 | AA_Grp | 56-60 | 99.9% |
UW | NS/1/4 | AA_Grp | 61-65 | 97.5% |
UW | NS/2/4 | AA_Grp | 61-65 | 100.2% |
UW | NS/2/4 | AA_Grp | 66-70 | 99.5% |
UW | NS/4/4 | AA_Grp | 66-70 | 99.0% |
Sex | M | UW | NS/2/2 | 104.8% |
Sex | M | UW | NS/3/3 | 107.2% |
Sex | M | UW | NS/1/4 | 98.0% |
Sex | M | UW | NS/3/4 | 104.2% |
Sex | M | UW | NS/4/4 | 113.1% |
SOA_Post_Lvl_Ind | ULT | Dur_Grp | 6-10 | 96.2% |
SOA_Post_Lvl_Ind | ULT | Dur_Grp | 16-20 | 110.8% |
SOA_Post_Lvl_Ind | ULT | Dur_Grp | 21-30 | 116.7% |
SOA_Post_Lvl_Ind | ULT | Dur_Grp | 31-100 | 107.1% |
Sex | M | Face_Amount_Band | 250K - <500K | 97.8% |
Sex | M | Face_Amount_Band | 500K - <1M | 97.2% |
Sex | M | Face_Amount_Band | 1M - <2.5M | 94.3% |
Sex | M | Face_Amount_Band | 5M - <10M | 98.5% |
AA_Grp | 46-50 | Dur_Grp | 4-5 | 107.7% |
AA_Grp | 51-55 | Dur_Grp | 4-5 | 97.8% |
AA_Grp | 61-65 | Dur_Grp | 4-5 | 102.7% |
AA_Grp | 36-40 | Dur_Grp | 6-10 | 95.4% |
AA_Grp | 51-55 | Dur_Grp | 6-10 | 100.3% |
AA_Grp | 56-60 | Dur_Grp | 6-10 | 106.3% |
AA_Grp | 61-65 | Dur_Grp | 6-10 | 91.1% |
AA_Grp | 66-70 | Dur_Grp | 6-10 | 99.0% |
AA_Grp | 56-60 | Dur_Grp | 11-15 | 99.1% |
Sex | M | Dur_Grp | 4-5 | 102.3% |
Sex | M | Dur_Grp | 16-20 | 98.6% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 36-40 | 97.0% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 46-50 | 95.7% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 61-65 | 101.6% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 66-70 | 115.2% |
SOA_Post_Lvl_Ind | ULT | AA_Grp | 71-75 | 108.3% |
Sex | M | SOA_Post_Lvl_Ind | NLT | 96.5% |
Sex | M | AA_Grp | 31-35 | 106.3% |
Sex | M | AA_Grp | 36-40 | 110.4% |
Sex | M | AA_Grp | 41-45 | 99.6% |
Sex | M | AA_Grp | 51-55 | 101.2% |
Sex | M | AA_Grp | 61-65 | 96.5% |
Sex | M | AA_Grp | 66-70 | 93.5% |
Sex | M | AA_Grp | 76-80 | 103.3% |
Plots and tables of effects are much more digestible.
In the plots and tables that follow, we fix all of the other variables at their middle values when extracting final factors.
We generate some supporting tables: a factor grid for attaching to the experience, and a list of interactions present in the model
Code
dat.term.noplt[!(Face_Amount_Band %in% c("<10K",
"10K - <25K",
"25K - <50K",
"50K - <100K")),..pred.cols] %>%
mutate(Face_Amount_Band=fct_drop(Face_Amount_Band)) %>%
lapply(levels) %>%
expand.grid() %>%
setDT() ->
dat.term.noplt.100kp.grid
dat.term.noplt.100kp.grid %>%
model.Matrix(
object=glmnetFormula,
data=.,
sparse=T
) %>%
predict(
cvfit.term.noplt.100kp,
newx=.,
s="lambda.min"
) %>%
as.vector() ->
newCoef
dat.term.noplt.100kp.grid %>%
add_column(
Factor=exp(newCoef)
) %>%
setDT() ->
dat.term.noplt.100kp.grid
write.xlsx(dat.term.noplt.100kp.grid,
file="dat.term.noplt.100kp.grid.xlsx")
reformatCoefs(cvfit.term.noplt.100kp, pred.cols) %>%
filter(Coef != 0 & !is.na(Feature2Name)) %>%
select(Feature1Name,Feature2Name) %>%
distinct() %>%
as.list() %>%
purrr::list_transpose() ->
term.no.plt.100kp.int.list7.1.6.2.3 Plots of Terms
Below are plots of the 2-way interaction terms, with external factors fixed at their middle values.
The interactions tend to be subtle. To that end, some larger ones are noted.
- Duration x Post-Level Indicator: Later duration unknown level term stands out.
- Attained Age x Post-Level Indicator: Middle attained ages for unknown level term.
- Attained Age x Sex: Some larger deviations for males between ages 26 and 80.
7.1.6.2.4 Tables of Terms
Below are tables of the 2-way interaction terms, with external factors fixed at their middle values.
Face_Amount_Band | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
100K - <250K | 85.8% | 127.2% | 71.5% | 85.8% | 106.2% | 73.6% | 86.0% | 96.1% | 110.3% | 90.8% | 85.8% | 104.4% | 98.1% | 85.8% |
250K - <500K | 80.6% | 119.5% | 67.1% | 80.6% | 99.7% | 69.1% | 80.8% | 90.2% | 103.6% | 85.2% | 80.6% | 98.0% | 92.1% | 80.6% |
500K - <1M | 77.0% | 112.3% | 64.2% | 77.0% | 95.3% | 66.1% | 77.5% | 90.4% | 99.0% | 81.5% | 77.0% | 93.7% | 88.0% | 77.0% |
1M - <2.5M | 76.8% | 113.9% | 64.0% | 76.8% | 102.7% | 63.8% | 78.4% | 88.2% | 102.6% | 81.3% | 76.8% | 93.5% | 87.8% | 76.8% |
2.5M - <5M | 78.6% | 116.5% | 58.8% | 80.3% | 97.3% | 67.4% | 75.7% | 88.0% | 106.9% | 83.1% | 78.6% | 95.6% | 89.9% | 78.6% |
5M - <10M | 85.8% | 127.2% | 72.0% | 85.8% | 106.2% | 73.6% | 86.0% | 96.1% | 110.3% | 90.8% | 85.8% | 104.4% | 98.1% | 85.8% |
10M+ | 50.9% | 75.4% | 42.4% | 50.9% | 63.0% | 56.8% | 43.9% | 57.0% | 65.4% | 53.8% | 50.9% | 61.9% | 58.1% | 50.9% |
Dur_Grp | 100K - <250K | 250K - <500K | 500K - <1M | 1M - <2.5M | 2.5M - <5M | 5M - <10M | 10M+ |
|---|---|---|---|---|---|---|---|
1-1 | 83.8% | 78.7% | 75.5% | 76.3% | 73.8% | 83.8% | 56.0% |
2-2 | 84.2% | 79.0% | 75.8% | 76.7% | 74.1% | 84.2% | 56.3% |
3-3 | 83.8% | 78.7% | 75.5% | 76.3% | 73.8% | 83.8% | 56.0% |
4-5 | 86.0% | 80.8% | 77.5% | 78.4% | 75.7% | 86.0% | 43.9% |
6-10 | 76.2% | 71.6% | 68.7% | 69.0% | 62.7% | 74.9% | 61.4% |
11-15 | 81.9% | 76.9% | 73.3% | 74.6% | 72.1% | 84.9% | 54.8% |
16-20 | 79.2% | 74.3% | 71.3% | 72.1% | 69.7% | 72.9% | 53.0% |
21-30 | 93.2% | 87.5% | 83.9% | 84.9% | 82.1% | 93.2% | 62.3% |
31-100 | 89.5% | 84.0% | 80.6% | 81.5% | 78.8% | 89.5% | 59.9% |
AA_Grp | 100K - <250K | 250K - <500K | 500K - <1M | 1M - <2.5M | 2.5M - <5M | 5M - <10M | 10M+ |
|---|---|---|---|---|---|---|---|
0-17 | 83.6% | 78.8% | 75.3% | 75.3% | 73.6% | 83.6% | 42.7% |
18-25 | 83.6% | 78.8% | 75.3% | 75.3% | 73.6% | 83.6% | 42.7% |
26-30 | 84.1% | 79.4% | 75.8% | 75.8% | 74.1% | 84.1% | 43.0% |
31-35 | 83.6% | 78.8% | 75.3% | 75.3% | 73.6% | 83.6% | 42.7% |
36-40 | 84.8% | 80.0% | 76.4% | 73.9% | 74.7% | 84.8% | 52.0% |
41-45 | 83.6% | 78.8% | 75.3% | 74.0% | 73.6% | 83.6% | 42.7% |
46-50 | 90.0% | 84.9% | 81.1% | 80.9% | 79.3% | 90.0% | 46.0% |
51-55 | 81.8% | 77.3% | 73.7% | 73.7% | 72.0% | 81.8% | 39.4% |
56-60 | 80.3% | 74.1% | 70.9% | 72.4% | 70.8% | 80.3% | 41.8% |
61-65 | 86.0% | 80.8% | 77.5% | 78.4% | 75.7% | 86.0% | 43.9% |
66-70 | 83.2% | 78.3% | 74.2% | 80.4% | 73.2% | 83.2% | 42.5% |
71-75 | 83.6% | 78.8% | 75.3% | 75.3% | 73.6% | 83.6% | 42.0% |
76-80 | 85.9% | 81.1% | 77.4% | 77.4% | 75.7% | 85.9% | 43.9% |
81-85 | 83.6% | 78.8% | 75.3% | 75.3% | 73.6% | 83.6% | 42.7% |
86-90 | 83.6% | 78.8% | 75.3% | 75.3% | 73.6% | 83.6% | 42.7% |
91-95 | 83.6% | 78.8% | 75.3% | 75.3% | 73.6% | 83.6% | 42.7% |
96-100 | 83.6% | 78.8% | 75.3% | 75.3% | 73.6% | 83.6% | 42.7% |
101-105 | 83.6% | 78.8% | 75.3% | 75.3% | 73.6% | 83.6% | 42.7% |
106-110 | 83.6% | 78.8% | 75.3% | 75.3% | 73.6% | 83.6% | 42.7% |
111-115 | 83.6% | 78.8% | 75.3% | 75.3% | 73.6% | 83.6% | 42.7% |
Dur_Grp | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1-1 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 63.9% | 75.5% | 88.1% | 96.5% | 75.0% | 75.0% | 91.3% | 85.8% | 75.0% |
2-2 | 75.4% | 109.9% | 62.8% | 75.4% | 93.3% | 64.2% | 75.8% | 89.0% | 96.9% | 75.4% | 75.4% | 91.7% | 86.2% | 75.4% |
3-3 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 63.9% | 75.5% | 88.1% | 96.5% | 75.0% | 75.0% | 91.3% | 85.8% | 75.0% |
4-5 | 77.0% | 112.3% | 64.2% | 77.0% | 95.3% | 66.1% | 77.5% | 90.4% | 99.0% | 81.5% | 77.0% | 93.7% | 88.0% | 77.0% |
6-10 | 68.2% | 99.5% | 56.9% | 68.2% | 86.0% | 58.1% | 68.7% | 80.1% | 87.8% | 68.2% | 66.8% | 83.0% | 78.0% | 68.2% |
11-15 | 72.9% | 106.3% | 60.7% | 72.9% | 90.2% | 59.4% | 73.3% | 87.5% | 93.7% | 70.1% | 72.9% | 88.7% | 83.3% | 72.9% |
16-20 | 70.9% | 107.3% | 59.1% | 70.9% | 87.7% | 60.3% | 71.3% | 83.2% | 91.2% | 70.9% | 70.9% | 86.2% | 81.0% | 70.9% |
21-30 | 83.4% | 121.7% | 69.5% | 83.4% | 103.3% | 71.0% | 83.9% | 98.0% | 107.3% | 83.4% | 83.4% | 101.5% | 95.4% | 83.4% |
31-100 | 80.1% | 116.8% | 66.8% | 80.1% | 99.2% | 68.2% | 80.6% | 94.1% | 103.1% | 80.1% | 80.1% | 97.5% | 91.6% | 80.1% |
AA_Grp | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0-17 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
18-25 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
26-30 | 75.5% | 110.1% | 62.9% | 75.5% | 93.5% | 66.5% | 75.8% | 88.7% | 97.1% | 79.9% | 75.5% | 91.9% | 86.3% | 75.5% |
31-35 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
36-40 | 75.0% | 109.4% | 62.5% | 75.0% | 96.9% | 66.0% | 76.4% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
41-45 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
46-50 | 80.8% | 117.8% | 67.3% | 80.8% | 100.0% | 72.7% | 81.1% | 94.9% | 113.3% | 85.5% | 80.8% | 98.3% | 92.4% | 80.8% |
51-55 | 73.4% | 107.0% | 61.2% | 73.4% | 90.8% | 60.7% | 73.7% | 86.2% | 94.4% | 74.9% | 73.4% | 89.3% | 83.9% | 73.4% |
56-60 | 70.7% | 103.1% | 58.9% | 70.7% | 87.5% | 63.1% | 70.9% | 83.0% | 90.9% | 74.8% | 70.7% | 86.0% | 80.8% | 70.7% |
61-65 | 77.0% | 112.3% | 64.2% | 77.0% | 95.3% | 66.1% | 77.5% | 90.4% | 99.0% | 81.5% | 77.0% | 93.7% | 88.0% | 77.0% |
66-70 | 74.3% | 108.3% | 61.9% | 74.3% | 91.9% | 65.4% | 74.2% | 87.2% | 94.5% | 78.6% | 74.3% | 90.4% | 84.9% | 74.3% |
71-75 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
76-80 | 77.1% | 112.5% | 64.3% | 77.1% | 95.5% | 67.9% | 77.4% | 90.6% | 99.2% | 81.6% | 77.1% | 93.9% | 88.2% | 77.1% |
81-85 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
86-90 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
91-95 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
96-100 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
101-105 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
106-110 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
111-115 | 75.0% | 109.4% | 62.5% | 75.0% | 92.8% | 66.0% | 75.3% | 88.1% | 96.5% | 79.4% | 75.0% | 91.3% | 85.8% | 75.0% |
Sex | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
F | 77.0% | 112.3% | 64.2% | 77.0% | 95.3% | 66.1% | 77.5% | 90.4% | 99.0% | 81.5% | 77.0% | 93.7% | 88.0% | 77.0% |
M | 80.4% | 122.9% | 67.0% | 80.4% | 106.7% | 67.6% | 80.9% | 98.4% | 117.0% | 85.0% | 80.4% | 97.8% | 91.9% | 80.4% |
Dur_Grp | WLT | NLT | ULT |
|---|---|---|---|
1-1 | 75.5% | 68.8% | 76.7% |
2-2 | 75.8% | 69.2% | 77.1% |
3-3 | 75.5% | 68.8% | 76.7% |
4-5 | 77.5% | 70.7% | 78.7% |
6-10 | 68.7% | 62.6% | 67.1% |
11-15 | 73.3% | 66.9% | 74.5% |
16-20 | 71.3% | 65.1% | 80.3% |
21-30 | 83.9% | 76.6% | 99.6% |
31-100 | 80.6% | 73.5% | 87.7% |
Face_Amount_Band | F | M |
|---|---|---|
100K - <250K | 86.0% | 92.4% |
250K - <500K | 80.8% | 84.9% |
500K - <1M | 77.5% | 80.9% |
1M - <2.5M | 78.4% | 79.4% |
2.5M - <5M | 75.7% | 81.3% |
5M - <10M | 86.0% | 91.0% |
10M+ | 43.9% | 47.2% |
AA_Grp | 1-1 | 2-2 | 3-3 | 4-5 | 6-10 | 11-15 | 16-20 | 21-30 | 31-100 |
|---|---|---|---|---|---|---|---|---|---|
0-17 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
18-25 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
26-30 | 75.8% | 76.1% | 75.8% | 75.8% | 75.7% | 73.6% | 71.6% | 84.3% | 80.9% |
31-35 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
36-40 | 76.4% | 76.8% | 76.4% | 76.4% | 72.8% | 74.3% | 72.2% | 85.0% | 81.6% |
41-45 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
46-50 | 75.3% | 75.7% | 75.3% | 81.1% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
51-55 | 75.3% | 75.7% | 75.3% | 73.7% | 75.4% | 73.2% | 71.1% | 83.7% | 80.4% |
56-60 | 70.9% | 71.3% | 70.9% | 70.9% | 75.3% | 68.3% | 67.0% | 78.9% | 75.8% |
61-65 | 75.5% | 75.8% | 75.5% | 77.5% | 68.7% | 73.3% | 71.3% | 83.9% | 80.6% |
66-70 | 74.2% | 74.5% | 74.2% | 74.2% | 73.4% | 72.1% | 70.1% | 82.5% | 79.2% |
71-75 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
76-80 | 77.4% | 77.8% | 77.4% | 77.4% | 77.3% | 75.2% | 73.2% | 86.1% | 82.7% |
81-85 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
86-90 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
91-95 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
96-100 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
101-105 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
106-110 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
111-115 | 75.3% | 75.7% | 75.3% | 75.3% | 75.2% | 73.2% | 71.1% | 83.7% | 80.4% |
Dur_Grp | F | M |
|---|---|---|
1-1 | 75.5% | 77.0% |
2-2 | 75.8% | 77.4% |
3-3 | 75.5% | 77.0% |
4-5 | 77.5% | 80.9% |
6-10 | 68.7% | 70.1% |
11-15 | 73.3% | 74.8% |
16-20 | 71.3% | 71.7% |
21-30 | 83.9% | 85.7% |
31-100 | 80.6% | 82.3% |
AA_Grp | WLT | NLT | ULT |
|---|---|---|---|
0-17 | 75.3% | 68.7% | 75.3% |
18-25 | 75.3% | 68.7% | 75.3% |
26-30 | 75.8% | 69.1% | 75.8% |
31-35 | 75.3% | 68.7% | 75.3% |
36-40 | 76.4% | 69.7% | 74.1% |
41-45 | 75.3% | 68.7% | 75.3% |
46-50 | 81.1% | 74.0% | 77.6% |
51-55 | 73.7% | 67.2% | 73.7% |
56-60 | 70.9% | 64.7% | 70.9% |
61-65 | 77.5% | 70.7% | 78.7% |
66-70 | 74.2% | 67.7% | 85.4% |
71-75 | 75.3% | 68.7% | 81.5% |
76-80 | 77.4% | 70.6% | 77.4% |
81-85 | 75.3% | 68.7% | 75.3% |
86-90 | 75.3% | 68.7% | 75.3% |
91-95 | 75.3% | 68.7% | 75.3% |
96-100 | 75.3% | 68.7% | 75.3% |
101-105 | 75.3% | 68.7% | 75.3% |
106-110 | 75.3% | 68.7% | 75.3% |
111-115 | 75.3% | 68.7% | 75.3% |
SOA_Post_Lvl_Ind | F | M |
|---|---|---|
WLT | 77.5% | 80.9% |
NLT | 70.7% | 71.2% |
ULT | 78.7% | 82.2% |
AA_Grp | F | M |
|---|---|---|
0-17 | 75.3% | 81.5% |
18-25 | 75.3% | 81.5% |
26-30 | 75.8% | 82.0% |
31-35 | 75.3% | 86.6% |
36-40 | 76.4% | 91.3% |
41-45 | 75.3% | 81.2% |
46-50 | 81.1% | 87.8% |
51-55 | 73.7% | 80.7% |
56-60 | 70.9% | 76.8% |
61-65 | 77.5% | 80.9% |
66-70 | 74.2% | 75.0% |
71-75 | 75.3% | 81.5% |
76-80 | 77.4% | 86.6% |
81-85 | 75.3% | 81.5% |
86-90 | 75.3% | 81.5% |
91-95 | 75.3% | 81.5% |
96-100 | 75.3% | 81.5% |
101-105 | 75.3% | 81.5% |
106-110 | 75.3% | 81.5% |
111-115 | 75.3% | 81.5% |
7.1.6.3 Goodness-of-Fit
Next comes checking goodness-of-fit, on both a univariate and bivariate basis. Tables are provided which show the ratio of the actual to model predicted deaths and show the associated death counts.
Code
### This code attaches the grid of predicted factors
### to the underlying data for further analysis.
dat.term.noplt.lt100k.grid %>%
rbind(dat.term.noplt.100kp.grid) %>%
right_join(dat.term.noplt) %>%
mutate(ExpDth_Amt_GLMNet=ExpDth_Amt_VBT2015*Factor) %>%
mutate(Factor=NULL) ->
dat.term.noplt7.1.6.3.1 Univariate Fit Checks
Sex | Death Count | Actual-to-Model |
|---|---|---|
F | 83,020 | 99.6% |
M | 164,796 | 100.1% |
Face_Amount_Band | Death Count | Actual-to-Model |
|---|---|---|
<10K | 13,432 | 100.9% |
10K - <25K | 11,636 | 100.2% |
25K - <50K | 16,359 | 99.9% |
50K - <100K | 29,178 | 100.0% |
100K - <250K | 89,514 | 102.7% |
250K - <500K | 47,754 | 99.6% |
500K - <1M | 25,324 | 99.6% |
1M - <2.5M | 13,090 | 99.7% |
2.5M - <5M | 1,011 | 98.3% |
5M - <10M | 410 | 98.7% |
10M+ | 108 | 96.1% |
SOA_Post_Lvl_Ind | Death Count | Actual-to-Model |
|---|---|---|
WLT | 184,673 | 100.0% |
NLT | 11,320 | 95.6% |
ULT | 51,823 | 100.6% |
UW | Death Count | Actual-to-Model |
|---|---|---|
NS/1/2 | 11,482 | 92.6% |
NS/2/2 | 41,938 | 101.5% |
NS/1/3 | 14,303 | 99.0% |
NS/2/3 | 13,519 | 100.4% |
NS/3/3 | 21,663 | 100.9% |
NS/1/4 | 19,687 | 99.5% |
NS/2/4 | 17,227 | 100.3% |
NS/3/4 | 11,695 | 101.1% |
NS/4/4 | 12,580 | 101.4% |
NS/U/U | 37,750 | 100.0% |
S/1/2 | 8,085 | 97.4% |
S/2/2 | 6,578 | 104.8% |
S/U/U | 18,522 | 103.6% |
U/U/U | 12,787 | 112.2% |
AA_Grp | Death Count | Actual-to-Model |
|---|---|---|
0-17 | 165 | 71.6% |
18-25 | 1,499 | 97.0% |
26-30 | 2,324 | 112.7% |
31-35 | 4,025 | 104.2% |
36-40 | 7,199 | 98.4% |
41-45 | 13,326 | 99.6% |
46-50 | 21,638 | 100.1% |
51-55 | 32,207 | 100.3% |
56-60 | 38,983 | 99.6% |
61-65 | 41,361 | 99.6% |
66-70 | 35,497 | 99.6% |
71-75 | 24,265 | 99.2% |
76-80 | 15,044 | 102.9% |
81-85 | 7,028 | 107.4% |
86-90 | 2,443 | 113.7% |
91-95 | 733 | 109.6% |
96-100 | 78 | 41.6% |
101-105 | 1 | 51.8% |
106-110 | 0 | 0.0% |
111-115 | 0 | 0.0% |
Dur_Grp | Death Count | Actual-to-Model |
|---|---|---|
1-1 | 5,497 | 100.6% |
2-2 | 7,141 | 102.4% |
3-3 | 8,692 | 100.5% |
4-5 | 19,420 | 99.6% |
6-10 | 65,368 | 99.8% |
11-15 | 64,799 | 99.7% |
16-20 | 39,547 | 99.3% |
21-30 | 24,005 | 102.2% |
31-100 | 13,347 | 115.5% |
Unidimensional goodness-of-fit is generally good, with some spots with poor fit. In some cases, it appears to be related to lack of claims, which may be a sign of overpenalization. In other cases, there are enough claims yet fit is genuinely suboptimal, such as UW U/U/U and N/1/2, level term NLT, and durations 31+, among others.
7.1.6.3.2 Bivariate Fit Checks
Face_Amount_Band | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
<10K | 4,179 | 102.3% | 9,253 | 100.1% | ||
10K - <25K | 5,989 | 100.7% | 5,647 | 99.7% | ||
25K - <50K | 7,376 | 99.8% | 8,983 | 100.1% | ||
50K - <100K | 12,319 | 99.9% | 16,859 | 100.0% | ||
100K - <250K | 31,763 | 100.5% | 57,751 | 103.9% | ||
250K - <500K | 13,892 | 100.0% | 33,862 | 99.5% | ||
500K - <1M | 5,525 | 100.0% | 19,799 | 99.5% | ||
1M - <2.5M | 1,855 | 100.1% | 11,235 | 99.6% | ||
2.5M - <5M | 74 | 88.9% | 937 | 99.2% | ||
5M - <10M | 39 | 108.7% | 371 | 97.7% | ||
10M+ | 9 | 62.5% | 99 | 100.2% | ||
SOA_Post_Lvl_Ind | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
WLT | 62,592 | 99.7% | 122,081 | 100.1% | ||
NLT | 4,110 | 99.2% | 7,210 | 94.5% | ||
ULT | 16,318 | 99.2% | 35,505 | 101.0% | ||
UW | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
NS/1/2 | 4,290 | 93.3% | 7,192 | 92.3% | ||
NS/2/2 | 20,589 | 101.2% | 21,349 | 101.6% | ||
NS/1/3 | 5,068 | 97.0% | 9,235 | 99.8% | ||
NS/2/3 | 3,671 | 100.2% | 9,848 | 100.4% | ||
NS/3/3 | 5,933 | 100.6% | 15,730 | 101.0% | ||
NS/1/4 | 6,928 | 99.8% | 12,759 | 99.4% | ||
NS/2/4 | 4,245 | 99.3% | 12,982 | 100.5% | ||
NS/3/4 | 2,434 | 100.4% | 9,261 | 101.2% | ||
NS/4/4 | 3,434 | 100.8% | 9,146 | 101.5% | ||
NS/U/U | 13,042 | 100.2% | 24,708 | 99.9% | ||
S/1/2 | 2,315 | 98.3% | 5,770 | 97.1% | ||
S/2/2 | 1,857 | 108.6% | 4,721 | 103.9% | ||
S/U/U | 6,588 | 105.5% | 11,934 | 102.9% | ||
U/U/U | 2,626 | 103.1% | 10,161 | 115.1% | ||
AA_Grp | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
0-17 | 67 | 79.2% | 98 | 68.1% | ||
18-25 | 392 | 94.4% | 1,107 | 98.0% | ||
26-30 | 745 | 105.1% | 1,579 | 116.1% | ||
31-35 | 1,494 | 98.8% | 2,531 | 106.8% | ||
36-40 | 2,799 | 88.8% | 4,400 | 102.8% | ||
41-45 | 5,313 | 101.7% | 8,013 | 98.7% | ||
46-50 | 8,274 | 98.7% | 13,364 | 100.6% | ||
51-55 | 11,603 | 99.3% | 20,604 | 100.6% | ||
56-60 | 13,455 | 99.8% | 25,528 | 99.5% | ||
61-65 | 13,390 | 100.5% | 27,971 | 99.4% | ||
66-70 | 10,696 | 101.5% | 24,801 | 99.2% | ||
71-75 | 7,026 | 101.5% | 17,239 | 98.8% | ||
76-80 | 4,117 | 99.9% | 10,927 | 103.6% | ||
81-85 | 2,210 | 118.8% | 4,818 | 103.8% | ||
86-90 | 1,060 | 142.9% | 1,383 | 101.2% | ||
91-95 | 346 | 119.1% | 387 | 105.9% | ||
96-100 | 33 | 41.4% | 45 | 41.7% | ||
101-105 | 0 | 0.0% | 1 | 53.6% | ||
106-110 | 0 | 0.0% | ||||
111-115 | 0 | 0.0% | ||||
Dur_Grp | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
1-1 | 1,698 | 109.9% | 3,799 | 98.6% | ||
2-2 | 2,346 | 101.3% | 4,795 | 102.6% | ||
3-3 | 2,872 | 102.7% | 5,820 | 99.9% | ||
4-5 | 6,545 | 94.9% | 12,875 | 100.9% | ||
6-10 | 21,943 | 100.0% | 43,425 | 99.7% | ||
11-15 | 21,913 | 98.9% | 42,886 | 100.0% | ||
16-20 | 14,433 | 99.9% | 25,114 | 99.2% | ||
21-30 | 8,425 | 103.0% | 15,580 | 101.9% | ||
31-100 | 2,845 | 110.1% | 10,502 | 117.2% | ||
Face_Amount_Band | SOA_Post_Lvl_Ind: WLT | SOA_Post_Lvl_Ind: NLT | SOA_Post_Lvl_Ind: ULT | ||||||
|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||
<10K | 531 | 101.5% | 3,752 | 106.1% | 9,149 | 96.9% | |||
10K - <25K | 5,861 | 100.3% | 1,494 | 99.0% | 4,281 | 100.5% | |||
25K - <50K | 9,075 | 99.9% | 1,500 | 99.4% | 5,784 | 100.2% | |||
50K - <100K | 17,862 | 99.9% | 1,398 | 99.6% | 9,918 | 100.1% | |||
100K - <250K | 72,555 | 102.3% | 1,386 | 94.6% | 15,573 | 105.7% | |||
250K - <500K | 42,303 | 99.8% | 1,167 | 94.9% | 4,284 | 98.8% | |||
500K - <1M | 22,935 | 100.1% | 467 | 93.2% | 1,922 | 96.0% | |||
1M - <2.5M | 12,112 | 100.0% | 150 | 94.4% | 828 | 96.5% | |||
2.5M - <5M | 940 | 97.5% | 5 | 128.0% | 66 | 111.0% | |||
5M - <10M | 393 | 98.2% | 1 | 132.7% | 16 | 110.9% | |||
10M+ | 106 | 96.0% | 0 | 0.0% | 2 | 108.1% | |||
UW | Face_Amount_Band: <10K | Face_Amount_Band: 10K - <25K | Face_Amount_Band: 25K - <50K | Face_Amount_Band: 50K - <100K | Face_Amount_Band: 100K - <250K | Face_Amount_Band: 250K - <500K | Face_Amount_Band: 500K - <1M | Face_Amount_Band: 1M - <2 | Face_Amount_Band: 2 | Face_Amount_Band: 5M - <10M | Face_Amount_Band: 10M+ | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | 5M | 5M - <5M | Deaths | Ratio | Deaths | Ratio | ||||||||||||||
Deaths | Ratio | Deaths | Ratio | ||||||||||||||||||||||||||||||
NS/1/2 | 27 | 204.2% | 44 | 71.5% | 201 | 97.4% | 550 | 96.8% | 6,229 | 97.9% | 2,524 | 93.5% | 1,264 | 88.3% | 565 | 81.0% | 57 | 101.7% | 15 | 97.6% | 6 | 260.9% | |||||||||||
NS/2/2 | 1,363 | 105.1% | 5,851 | 99.6% | 6,081 | 100.1% | 7,582 | 100.1% | 15,125 | 111.8% | 4,444 | 98.6% | 1,201 | 92.9% | 273 | 89.5% | 14 | 90.8% | 3 | 55.4% | 1 | 113.8% | |||||||||||
NS/1/3 | 4 | 59.9% | 13 | 82.0% | 62 | 93.7% | 276 | 99.7% | 4,900 | 100.5% | 4,697 | 99.8% | 2,821 | 101.0% | 1,402 | 97.9% | 76 | 81.2% | 45 | 123.6% | 7 | 71.8% | |||||||||||
NS/2/3 | 5 | 73.1% | 11 | 104.0% | 82 | 110.5% | 616 | 100.0% | 5,154 | 98.5% | 4,152 | 98.8% | 2,129 | 96.9% | 1,212 | 103.5% | 111 | 116.2% | 38 | 106.2% | 9 | 77.7% | |||||||||||
NS/3/3 | 34 | 77.9% | 118 | 112.3% | 457 | 98.9% | 1,775 | 100.2% | 9,179 | 99.9% | 5,924 | 100.2% | 2,715 | 100.3% | 1,331 | 103.4% | 91 | 103.5% | 33 | 84.7% | 6 | 117.9% | |||||||||||
NS/1/4 | 1 | 52.3% | 0 | 0.0% | 19 | 95.8% | 412 | 98.8% | 5,595 | 98.5% | 6,113 | 100.4% | 4,467 | 98.8% | 2,716 | 98.6% | 227 | 94.9% | 99 | 101.2% | 38 | 111.8% | |||||||||||
NS/2/4 | 1 | 1.6% | 3 | 881.7% | 24 | 91.9% | 886 | 99.5% | 6,179 | 97.6% | 4,884 | 101.6% | 3,156 | 102.9% | 1,866 | 102.2% | 140 | 89.7% | 73 | 106.5% | 15 | 74.9% | |||||||||||
NS/3/4 | 3 | 128.6% | 5 | 1632.1% | 12 | 82.1% | 393 | 100.9% | 4,184 | 101.4% | 3,472 | 99.1% | 2,242 | 104.3% | 1,230 | 103.5% | 101 | 99.0% | 43 | 95.5% | 10 | 83.5% | |||||||||||
NS/4/4 | 2 | 235.4% | 8 | 342.1% | 287 | 99.0% | 1,003 | 100.5% | 4,964 | 97.0% | 3,412 | 99.6% | 1,732 | 101.4% | 1,016 | 104.3% | 105 | 118.4% | 40 | 98.0% | 11 | 83.5% | |||||||||||
NS/U/U | 2,918 | 105.2% | 2,093 | 100.7% | 4,110 | 99.8% | 7,950 | 100.0% | 13,004 | 106.7% | 4,353 | 99.4% | 2,256 | 98.4% | 992 | 98.4% | 55 | 89.0% | 14 | 68.9% | 5 | 104.4% | |||||||||||
S/1/2 | 4 | 159.5% | 10 | 414.4% | 60 | 96.3% | 776 | 100.0% | 4,752 | 98.5% | 1,574 | 98.3% | 630 | 101.4% | 258 | 98.9% | 17 | 97.0% | 4 | 64.1% | 0 | 0.0% | |||||||||||
S/2/2 | 6 | 118.4% | 55 | 113.2% | 345 | 101.8% | 975 | 100.0% | 3,556 | 103.1% | 1,046 | 103.8% | 430 | 122.8% | 150 | 105.6% | 13 | 114.7% | 2 | 42.0% | 0 | 0.0% | |||||||||||
S/U/U | 1,018 | 101.7% | 2,271 | 99.3% | 3,623 | 100.1% | 4,774 | 100.1% | 5,460 | 107.2% | 1,030 | 102.6% | 263 | 99.5% | 78 | 107.1% | 4 | 115.2% | 1 | 85.7% | 0 | 0.0% | |||||||||||
U/U/U | 8,046 | 95.4% | 1,154 | 100.9% | 996 | 100.3% | 1,210 | 100.4% | 1,233 | 132.3% | 129 | 143.3% | 18 | 84.5% | 1 | 24.8% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
AA_Grp | Face_Amount_Band: <10K | Face_Amount_Band: 10K - <25K | Face_Amount_Band: 25K - <50K | Face_Amount_Band: 50K - <100K | Face_Amount_Band: 100K - <250K | Face_Amount_Band: 250K - <500K | Face_Amount_Band: 500K - <1M | Face_Amount_Band: 1M - <2 | Face_Amount_Band: 2 | Face_Amount_Band: 5M - <10M | Face_Amount_Band: 10M+ | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | 5M | 5M - <5M | Deaths | Ratio | Deaths | Ratio | ||||||||||||||
Deaths | Ratio | Deaths | Ratio | ||||||||||||||||||||||||||||||
0-17 | 27 | 173.0% | 72 | 111.5% | 42 | 60.3% | 20 | 89.5% | 4 | 79.8% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
18-25 | 51 | 141.1% | 137 | 112.5% | 136 | 93.3% | 469 | 100.9% | 499 | 115.7% | 160 | 92.3% | 37 | 78.0% | 10 | 102.5% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
26-30 | 9 | 70.9% | 47 | 95.2% | 177 | 105.5% | 580 | 100.3% | 753 | 143.8% | 511 | 128.8% | 187 | 99.9% | 57 | 93.6% | 3 | 170.9% | 0 | 0.0% | 0 | 0.0% | |||||||||||
31-35 | 12 | 122.0% | 22 | 64.9% | 224 | 104.3% | 618 | 100.7% | 1,212 | 140.0% | 1,024 | 105.7% | 637 | 105.1% | 257 | 93.1% | 16 | 111.8% | 3 | 97.6% | 0 | 0.0% | |||||||||||
36-40 | 22 | 134.2% | 47 | 84.7% | 264 | 101.1% | 739 | 100.6% | 1,931 | 108.5% | 2,001 | 96.5% | 1,453 | 98.5% | 688 | 94.4% | 39 | 80.1% | 11 | 88.2% | 4 | 258.3% | |||||||||||
41-45 | 29 | 82.1% | 102 | 105.6% | 393 | 102.4% | 986 | 99.9% | 3,792 | 106.7% | 3,811 | 101.9% | 2,698 | 101.9% | 1,387 | 97.2% | 90 | 87.3% | 31 | 104.8% | 7 | 77.6% | |||||||||||
46-50 | 80 | 141.7% | 218 | 105.7% | 647 | 100.9% | 1,696 | 99.7% | 7,105 | 106.3% | 5,872 | 99.7% | 3,778 | 100.0% | 2,015 | 98.1% | 152 | 96.6% | 63 | 114.6% | 12 | 91.8% | |||||||||||
51-55 | 208 | 114.7% | 528 | 102.1% | 1,388 | 100.6% | 2,994 | 99.8% | 11,777 | 103.2% | 8,141 | 102.1% | 4,551 | 100.3% | 2,335 | 98.6% | 202 | 108.1% | 68 | 93.6% | 15 | 81.0% | |||||||||||
56-60 | 374 | 107.5% | 1,056 | 101.6% | 2,241 | 99.6% | 4,448 | 99.9% | 15,609 | 101.7% | 8,389 | 98.0% | 4,316 | 98.0% | 2,250 | 98.8% | 195 | 105.7% | 75 | 92.8% | 30 | 115.0% | |||||||||||
61-65 | 747 | 110.6% | 1,665 | 99.2% | 3,200 | 99.7% | 5,345 | 99.9% | 17,054 | 101.3% | 7,715 | 97.8% | 3,598 | 99.4% | 1,819 | 102.3% | 139 | 97.2% | 62 | 96.8% | 17 | 87.9% | |||||||||||
66-70 | 919 | 108.9% | 2,134 | 100.8% | 3,340 | 99.7% | 5,010 | 99.9% | 14,657 | 100.8% | 5,654 | 97.1% | 2,327 | 96.4% | 1,296 | 103.4% | 92 | 90.3% | 54 | 106.1% | 14 | 105.2% | |||||||||||
71-75 | 1,958 | 95.7% | 2,085 | 100.3% | 2,338 | 100.4% | 3,424 | 100.1% | 9,422 | 98.5% | 3,093 | 99.2% | 1,187 | 98.3% | 655 | 105.2% | 65 | 106.4% | 31 | 100.0% | 7 | 62.3% | |||||||||||
76-80 | 3,733 | 92.5% | 1,779 | 100.0% | 1,300 | 100.5% | 2,011 | 100.2% | 4,412 | 100.6% | 1,097 | 101.1% | 430 | 108.0% | 257 | 116.8% | 12 | 60.2% | 11 | 87.4% | 2 | 137.8% | |||||||||||
81-85 | 3,308 | 99.1% | 1,079 | 98.5% | 497 | 101.2% | 634 | 99.6% | 1,099 | 109.4% | 240 | 119.5% | 108 | 132.5% | 58 | 120.2% | 4 | 92.4% | 1 | 38.8% | 0 | 0.0% | |||||||||||
86-90 | 1,413 | 92.5% | 530 | 101.1% | 130 | 93.5% | 164 | 102.6% | 150 | 101.8% | 36 | 137.0% | 14 | 126.7% | 4 | 90.6% | 2 | 475.5% | |||||||||||||||
91-95 | 491 | 119.7% | 123 | 86.9% | 34 | 92.5% | 35 | 88.3% | 35 | 98.5% | 10 | 97.4% | 3 | 155.7% | 2 | 316.4% | |||||||||||||||||
96-100 | 51 | 88.2% | 12 | 57.8% | 7 | 86.7% | 5 | 76.6% | 3 | 49.8% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||||||
101-105 | 0 | 0.0% | 1 | 179.8% | 0 | 0.0% | |||||||||||||||||||||||||||
106-110 | 0 | 0.0% | |||||||||||||||||||||||||||||||
111-115 | 0 | 0.0% | |||||||||||||||||||||||||||||||
Face_Amount_Band | Dur_Grp: 1-1 | Dur_Grp: 2-2 | Dur_Grp: 3-3 | Dur_Grp: 4-5 | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-100 | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||||||
<10K | 33 | 272.7% | 78 | 171.2% | 70 | 138.9% | 174 | 128.2% | 494 | 117.7% | 545 | 88.8% | 1,777 | 106.9% | 2,367 | 100.4% | 7,894 | 94.1% | |||||||||
10K - <25K | 402 | 126.0% | 520 | 101.4% | 518 | 103.2% | 945 | 98.1% | 2,433 | 99.3% | 1,739 | 99.6% | 1,751 | 98.8% | 2,272 | 99.1% | 1,056 | 101.0% | |||||||||
25K - <50K | 505 | 103.0% | 575 | 98.1% | 576 | 98.4% | 1,132 | 99.2% | 3,095 | 99.7% | 2,771 | 100.3% | 3,186 | 99.7% | 3,413 | 100.2% | 1,106 | 100.9% | |||||||||
50K - <100K | 846 | 102.4% | 894 | 99.3% | 942 | 99.5% | 1,972 | 100.0% | 5,996 | 99.9% | 6,766 | 99.9% | 5,222 | 99.9% | 5,035 | 99.9% | 1,505 | 100.3% | |||||||||
100K - <250K | 1,745 | 116.4% | 2,240 | 112.1% | 2,893 | 120.2% | 6,164 | 101.3% | 22,868 | 102.7% | 26,423 | 99.9% | 16,855 | 103.3% | 8,700 | 99.3% | 1,626 | 128.1% | |||||||||
250K - <500K | 1,028 | 100.8% | 1,425 | 105.2% | 1,829 | 104.9% | 4,398 | 98.5% | 15,613 | 99.5% | 15,074 | 99.6% | 6,734 | 98.4% | 1,518 | 95.2% | 135 | 154.5% | |||||||||
500K - <1M | 554 | 97.7% | 825 | 103.3% | 1,112 | 104.4% | 2,716 | 99.4% | 9,141 | 99.8% | 7,590 | 98.9% | 2,825 | 98.3% | 540 | 102.4% | 21 | 112.5% | |||||||||
1M - <2.5M | 330 | 91.7% | 505 | 102.2% | 666 | 100.2% | 1,651 | 99.7% | 5,092 | 99.3% | 3,563 | 100.1% | 1,138 | 101.6% | 141 | 102.4% | 4 | 61.0% | |||||||||
2.5M - <5M | 34 | 94.2% | 55 | 107.5% | 54 | 78.8% | 177 | 104.3% | 400 | 96.0% | 229 | 101.2% | 48 | 88.0% | 14 | 316.2% | 0 | 0.0% | |||||||||
5M - <10M | 14 | 90.3% | 22 | 99.1% | 26 | 91.8% | 79 | 109.1% | 171 | 95.0% | 87 | 111.3% | 8 | 43.7% | 3 | 209.0% | 0 | 0.0% | |||||||||
10M+ | 6 | 151.7% | 2 | 63.0% | 6 | 68.8% | 12 | 72.0% | 65 | 107.2% | 12 | 80.7% | 3 | 80.1% | 2 | 2853.4% | |||||||||||
UW | SOA_Post_Lvl_Ind: WLT | SOA_Post_Lvl_Ind: NLT | SOA_Post_Lvl_Ind: ULT | ||||||
|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||
NS/1/2 | 7,897 | 92.7% | 327 | 97.4% | 3,258 | 92.1% | |||
NS/2/2 | 35,517 | 101.1% | 479 | 77.4% | 5,942 | 106.3% | |||
NS/1/3 | 12,880 | 98.6% | 1,110 | 97.6% | 313 | 120.0% | |||
NS/2/3 | 12,845 | 100.0% | 355 | 94.3% | 319 | 123.1% | |||
NS/3/3 | 19,350 | 100.9% | 1,566 | 94.6% | 747 | 113.6% | |||
NS/1/4 | 19,621 | 99.5% | 1 | 25.3% | 65 | 101.1% | |||
NS/2/4 | 17,181 | 100.5% | 0 | 0.0% | 46 | 60.8% | |||
NS/3/4 | 11,607 | 101.0% | 0 | 0.0% | 88 | 111.1% | |||
NS/4/4 | 12,474 | 101.6% | 1 | 24.2% | 105 | 84.9% | |||
NS/U/U | 12,376 | 100.2% | 4,649 | 100.3% | 20,725 | 99.8% | |||
S/1/2 | 7,348 | 98.5% | 58 | 88.9% | 679 | 86.7% | |||
S/2/2 | 5,971 | 105.1% | 78 | 111.6% | 529 | 100.5% | |||
S/U/U | 9,106 | 105.0% | 1,902 | 98.1% | 7,514 | 101.8% | |||
U/U/U | 500 | 82.8% | 794 | 101.8% | 11,493 | 117.3% | |||
AA_Grp | SOA_Post_Lvl_Ind: WLT | SOA_Post_Lvl_Ind: NLT | SOA_Post_Lvl_Ind: ULT | ||||||
|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||
0-17 | 24 | 72.3% | 0 | 0.0% | 141 | 71.8% | |||
18-25 | 840 | 101.2% | 7 | 134.2% | 652 | 88.2% | |||
26-30 | 1,533 | 120.5% | 9 | 85.1% | 782 | 91.9% | |||
31-35 | 3,156 | 107.9% | 31 | 131.9% | 838 | 87.0% | |||
36-40 | 6,076 | 100.4% | 89 | 89.2% | 1,034 | 85.0% | |||
41-45 | 11,358 | 99.9% | 253 | 85.7% | 1,715 | 98.7% | |||
46-50 | 18,041 | 100.8% | 564 | 105.0% | 3,033 | 93.1% | |||
51-55 | 25,867 | 100.5% | 1,085 | 108.6% | 5,255 | 96.9% | |||
56-60 | 30,261 | 99.5% | 1,448 | 89.7% | 7,274 | 101.7% | |||
61-65 | 31,335 | 99.2% | 1,824 | 91.9% | 8,202 | 105.0% | |||
66-70 | 27,024 | 98.8% | 1,681 | 94.6% | 6,792 | 108.0% | |||
71-75 | 18,275 | 98.1% | 1,403 | 91.2% | 4,587 | 121.2% | |||
76-80 | 8,762 | 102.0% | 1,199 | 88.9% | 5,083 | 120.1% | |||
81-85 | 1,889 | 105.4% | 880 | 117.3% | 4,259 | 115.0% | |||
86-90 | 228 | 118.3% | 623 | 90.3% | 1,592 | 112.2% | |||
91-95 | 4 | 16.6% | 205 | 88.2% | 524 | 112.6% | |||
96-100 | 19 | 99.2% | 59 | 40.6% | |||||
101-105 | 1 | 51.8% | |||||||
106-110 | 0 | 0.0% | |||||||
111-115 | 0 | 0.0% | |||||||
Dur_Grp | SOA_Post_Lvl_Ind: WLT | SOA_Post_Lvl_Ind: NLT | SOA_Post_Lvl_Ind: ULT | ||||||
|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||
1-1 | 4,645 | 102.8% | 17 | 63.1% | 835 | 78.8% | |||
2-2 | 6,239 | 102.8% | 26 | 369.2% | 876 | 95.2% | |||
3-3 | 7,861 | 101.5% | 9 | 127.0% | 822 | 86.0% | |||
4-5 | 17,919 | 100.1% | 32 | 93.9% | 1,469 | 90.4% | |||
6-10 | 61,422 | 100.0% | 585 | 105.2% | 3,361 | 93.7% | |||
11-15 | 58,582 | 99.8% | 2,561 | 93.7% | 3,656 | 102.5% | |||
16-20 | 27,730 | 98.7% | 3,853 | 91.9% | 7,964 | 104.3% | |||
21-30 | 275 | 98.5% | 3,413 | 97.0% | 20,317 | 102.4% | |||
31-100 | 824 | 97.6% | 12,523 | 115.9% | |||||
AA_Grp | UW: NS/U/U | UW: S/U/U | UW: U/U/U | UW: NS/1/2 | UW: NS/2/2 | UW: NS/1/3 | UW: NS/2/3 | UW: NS/3/3 | UW: NS/1/4 | UW: NS/2/4 | UW: NS/3/4 | UW: NS/4/4 | UW: S/1/2 | UW: S/2/2 | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | |||||||||||||||
0-17 | 5 | 58.3% | 14 | 63.2% | 146 | 74.8% | ||||||||||||||||||||||||||||||||||||
18-25 | 188 | 118.0% | 156 | 138.5% | 404 | 100.0% | 51 | 91.9% | 264 | 82.7% | 54 | 84.9% | 35 | 85.5% | 114 | 119.2% | 51 | 70.7% | 23 | 75.6% | 16 | 65.1% | 31 | 86.2% | 58 | 185.9% | 54 | 160.6% | ||||||||||||||
26-30 | 217 | 135.0% | 284 | 144.8% | 131 | 158.2% | 101 | 62.6% | 711 | 124.7% | 148 | 130.3% | 84 | 142.0% | 155 | 119.1% | 132 | 94.4% | 55 | 97.3% | 48 | 103.0% | 82 | 113.2% | 100 | 152.3% | 76 | 115.2% | ||||||||||||||
31-35 | 277 | 84.2% | 391 | 111.7% | 123 | 122.2% | 250 | 85.0% | 986 | 104.3% | 294 | 108.4% | 213 | 133.8% | 360 | 128.4% | 375 | 101.1% | 157 | 98.3% | 137 | 108.4% | 180 | 117.3% | 139 | 77.3% | 143 | 99.3% | ||||||||||||||
36-40 | 623 | 92.9% | 501 | 88.9% | 125 | 201.5% | 456 | 69.3% | 1,560 | 98.2% | 548 | 96.2% | 372 | 89.6% | 636 | 119.8% | 744 | 94.4% | 430 | 120.9% | 314 | 102.3% | 381 | 119.7% | 278 | 84.7% | 231 | 96.2% | ||||||||||||||
41-45 | 1,364 | 99.5% | 843 | 99.9% | 106 | 111.6% | 906 | 96.6% | 2,435 | 98.6% | 1,112 | 99.0% | 777 | 101.6% | 1,270 | 108.9% | 1,538 | 99.1% | 759 | 99.7% | 669 | 95.2% | 665 | 99.6% | 485 | 88.4% | 397 | 105.5% | ||||||||||||||
46-50 | 2,739 | 93.7% | 1,534 | 99.8% | 162 | 95.5% | 1,390 | 88.2% | 3,701 | 98.9% | 1,707 | 101.6% | 1,257 | 100.4% | 1,801 | 97.2% | 2,366 | 103.2% | 1,433 | 102.8% | 1,017 | 102.8% | 1,082 | 109.9% | 799 | 91.5% | 650 | 107.7% | ||||||||||||||
51-55 | 4,844 | 95.4% | 2,644 | 102.1% | 300 | 90.9% | 1,914 | 88.8% | 5,303 | 102.4% | 2,256 | 103.0% | 1,715 | 98.9% | 2,520 | 102.4% | 3,124 | 97.1% | 2,118 | 102.3% | 1,615 | 105.1% | 1,532 | 106.9% | 1,355 | 99.5% | 967 | 111.4% | ||||||||||||||
56-60 | 6,504 | 99.3% | 3,499 | 106.8% | 707 | 108.2% | 2,001 | 91.5% | 6,339 | 103.9% | 2,217 | 95.3% | 2,090 | 100.9% | 3,054 | 97.9% | 3,340 | 102.7% | 2,705 | 96.3% | 1,943 | 104.8% | 1,919 | 97.0% | 1,543 | 99.7% | 1,122 | 98.4% | ||||||||||||||
61-65 | 6,981 | 100.3% | 3,558 | 102.0% | 1,351 | 116.2% | 1,783 | 107.3% | 6,408 | 101.1% | 2,143 | 94.9% | 2,232 | 97.2% | 3,488 | 95.8% | 3,132 | 96.5% | 3,122 | 103.9% | 2,198 | 102.0% | 2,300 | 101.7% | 1,500 | 94.8% | 1,165 | 100.0% | ||||||||||||||
66-70 | 5,880 | 101.8% | 2,728 | 106.4% | 1,341 | 121.3% | 1,252 | 104.6% | 5,538 | 100.9% | 1,756 | 96.2% | 2,064 | 100.7% | 3,398 | 103.5% | 2,518 | 99.3% | 2,935 | 95.2% | 1,934 | 96.4% | 2,066 | 92.1% | 1,101 | 107.7% | 986 | 112.9% | ||||||||||||||
71-75 | 3,521 | 111.2% | 1,377 | 114.2% | 1,606 | 117.7% | 750 | 88.1% | 3,924 | 100.5% | 1,264 | 99.5% | 1,612 | 103.5% | 2,558 | 97.4% | 1,600 | 98.1% | 2,209 | 94.0% | 1,263 | 92.9% | 1,521 | 97.3% | 532 | 110.0% | 528 | 104.5% | ||||||||||||||
76-80 | 2,241 | 122.2% | 586 | 104.7% | 2,888 | 111.5% | 376 | 145.3% | 2,747 | 108.6% | 633 | 102.4% | 849 | 94.7% | 1,570 | 90.4% | 638 | 108.3% | 1,016 | 99.9% | 474 | 99.3% | 651 | 91.2% | 176 | 112.2% | 199 | 102.1% | ||||||||||||||
81-85 | 1,337 | 113.7% | 289 | 75.8% | 2,263 | 107.4% | 152 | 90.6% | 1,366 | 102.1% | 157 | 119.5% | 195 | 129.3% | 623 | 107.6% | 120 | 89.2% | 243 | 118.3% | 63 | 79.1% | 154 | 94.4% | 16 | 98.3% | 50 | 84.7% | ||||||||||||||
86-90 | 787 | 91.5% | 96 | 78.1% | 749 | 93.2% | 79 | 144.3% | 526 | 107.8% | 11 | 131.0% | 23 | 209.5% | 110 | 94.2% | 9 | 124.3% | 22 | 198.6% | 4 | 67.4% | 15 | 95.2% | 3 | 569.0% | 9 | 97.8% | ||||||||||||||
91-95 | 236 | 122.4% | 21 | 84.2% | 326 | 98.0% | 20 | 179.9% | 120 | 82.5% | 3 | 46.1% | 0 | 0.0% | 5 | 15.9% | 0 | 0.0% | 1 | 111.6% | 0 | 0.0% | 1 | 49.0% | ||||||||||||||||||
96-100 | 6 | 21.1% | 1 | 10.1% | 58 | 50.6% | 1 | 118.7% | 10 | 70.5% | 1 | 198.1% | 1 | 1.8% | 0 | 0.0% | 0 | 0.0% | ||||||||||||||||||||||||
101-105 | 1 | 51.8% | ||||||||||||||||||||||||||||||||||||||||
106-110 | 0 | 0.0% | ||||||||||||||||||||||||||||||||||||||||
111-115 | 0 | 0.0% | ||||||||||||||||||||||||||||||||||||||||
UW | Dur_Grp: 1-1 | Dur_Grp: 2-2 | Dur_Grp: 3-3 | Dur_Grp: 4-5 | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-100 | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||||||
NS/1/2 | 115 | 63.2% | 182 | 88.5% | 248 | 78.7% | 581 | 77.7% | 2,543 | 90.5% | 2,878 | 93.5% | 3,165 | 98.0% | 1,560 | 120.9% | 210 | 137.4% | |||||||||
NS/2/2 | 1,379 | 98.4% | 1,846 | 92.8% | 2,039 | 108.9% | 4,047 | 105.0% | 11,815 | 97.9% | 10,482 | 101.4% | 8,703 | 105.6% | 1,519 | 101.3% | 108 | 93.4% | |||||||||
NS/1/3 | 182 | 84.2% | 246 | 110.7% | 341 | 106.0% | 856 | 92.2% | 3,619 | 99.7% | 5,756 | 99.1% | 3,270 | 98.5% | 30 | 304.6% | 3 | 114.1% | |||||||||
NS/2/3 | 177 | 82.5% | 202 | 87.6% | 325 | 103.8% | 779 | 99.7% | 3,923 | 102.1% | 5,492 | 102.5% | 2,590 | 93.9% | 31 | 87.4% | 0 | 0.0% | |||||||||
NS/3/3 | 470 | 124.5% | 646 | 106.3% | 850 | 104.2% | 1,931 | 97.7% | 7,612 | 101.9% | 7,498 | 100.0% | 2,487 | 94.3% | 163 | 80.2% | 6 | 58.2% | |||||||||
NS/1/4 | 403 | 115.7% | 614 | 93.8% | 894 | 97.3% | 2,206 | 103.4% | 7,317 | 99.0% | 6,572 | 98.2% | 1,681 | 97.9% | 0 | 0.0% | |||||||||||
NS/2/4 | 282 | 110.5% | 511 | 103.8% | 714 | 100.3% | 1,727 | 100.4% | 6,770 | 100.2% | 6,059 | 100.0% | 1,164 | 95.9% | 0 | 0.0% | |||||||||||
NS/3/4 | 288 | 79.9% | 490 | 120.5% | 642 | 93.1% | 1,541 | 97.8% | 4,781 | 101.0% | 3,417 | 104.3% | 536 | 103.6% | 0 | 0.0% | |||||||||||
NS/4/4 | 437 | 106.4% | 605 | 106.9% | 809 | 106.4% | 1,777 | 100.9% | 5,206 | 102.4% | 3,046 | 98.3% | 676 | 85.7% | 14 | 59.0% | 10 | 104.3% | |||||||||
NS/U/U | 528 | 83.2% | 636 | 96.5% | 682 | 116.2% | 1,462 | 121.3% | 3,588 | 101.0% | 5,667 | 97.0% | 8,985 | 99.6% | 14,258 | 98.6% | 1,944 | 117.4% | |||||||||
S/1/2 | 167 | 82.7% | 233 | 96.0% | 291 | 93.9% | 739 | 96.6% | 2,512 | 92.6% | 2,629 | 101.7% | 1,242 | 108.2% | 254 | 103.7% | 18 | 98.7% | |||||||||
S/2/2 | 231 | 130.5% | 244 | 113.5% | 318 | 102.6% | 689 | 93.8% | 2,272 | 102.3% | 1,883 | 107.5% | 720 | 111.5% | 187 | 120.1% | 34 | 137.3% | |||||||||
S/U/U | 459 | 117.9% | 449 | 110.8% | 476 | 111.2% | 974 | 104.5% | 3,218 | 99.8% | 3,278 | 100.5% | 4,104 | 112.3% | 4,758 | 100.5% | 806 | 103.7% | |||||||||
U/U/U | 379 | 129.7% | 237 | 148.7% | 63 | 76.9% | 111 | 83.7% | 192 | 70.7% | 142 | 51.3% | 224 | 101.4% | 1,231 | 118.9% | 10,208 | 117.0% | |||||||||
AA_Grp | Dur_Grp: 1-1 | Dur_Grp: 2-2 | Dur_Grp: 3-3 | Dur_Grp: 4-5 | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-100 | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||||||
0-17 | 29 | 65.7% | 15 | 53.7% | 12 | 59.1% | 17 | 73.1% | 42 | 102.3% | 27 | 70.5% | 23 | 115.9% | |||||||||||||
18-25 | 525 | 97.5% | 251 | 89.1% | 184 | 112.3% | 221 | 92.4% | 167 | 103.2% | 38 | 90.8% | 71 | 81.9% | 42 | 86.0% | |||||||||||
26-30 | 372 | 106.2% | 410 | 89.3% | 367 | 134.1% | 565 | 124.1% | 498 | 111.0% | 73 | 132.3% | 13 | 80.3% | 26 | 111.7% | 0 | 0.0% | |||||||||
31-35 | 389 | 94.4% | 424 | 99.5% | 441 | 103.1% | 788 | 107.0% | 1,461 | 105.2% | 410 | 121.8% | 86 | 124.6% | 19 | 128.3% | 7 | 153.3% | |||||||||
36-40 | 399 | 131.0% | 525 | 114.9% | 593 | 105.3% | 1,135 | 92.5% | 2,691 | 95.7% | 1,410 | 88.3% | 370 | 112.1% | 62 | 105.4% | 14 | 54.0% | |||||||||
41-45 | 531 | 116.9% | 642 | 96.1% | 733 | 104.9% | 1,659 | 97.7% | 4,702 | 98.4% | 3,326 | 99.1% | 1,471 | 103.7% | 247 | 102.9% | 15 | 66.5% | |||||||||
46-50 | 609 | 78.3% | 773 | 102.6% | 950 | 98.6% | 2,194 | 104.9% | 6,546 | 100.0% | 6,097 | 100.5% | 3,360 | 100.4% | 1,029 | 95.3% | 80 | 145.6% | |||||||||
51-55 | 696 | 114.7% | 1,037 | 99.6% | 1,262 | 103.2% | 2,693 | 95.6% | 8,778 | 101.3% | 8,866 | 100.7% | 5,758 | 100.7% | 2,843 | 89.3% | 274 | 112.9% | |||||||||
56-60 | 668 | 96.1% | 1,067 | 100.6% | 1,399 | 90.9% | 3,123 | 101.8% | 10,254 | 101.3% | 9,999 | 98.5% | 6,943 | 99.0% | 4,603 | 96.9% | 927 | 120.5% | |||||||||
61-65 | 541 | 74.2% | 849 | 115.4% | 1,182 | 97.5% | 2,968 | 105.2% | 10,706 | 98.4% | 11,195 | 99.1% | 6,915 | 96.7% | 5,041 | 106.5% | 1,964 | 114.9% | |||||||||
66-70 | 368 | 117.5% | 586 | 102.5% | 852 | 100.2% | 2,142 | 94.3% | 8,996 | 98.1% | 10,589 | 99.4% | 6,086 | 100.0% | 3,946 | 107.3% | 1,932 | 117.7% | |||||||||
71-75 | 163 | 84.6% | 284 | 91.7% | 384 | 82.0% | 1,213 | 88.5% | 6,068 | 101.6% | 7,575 | 97.8% | 4,473 | 100.0% | 2,334 | 115.6% | 1,771 | 125.0% | |||||||||
76-80 | 158 | 105.8% | 148 | 92.6% | 170 | 140.9% | 402 | 81.5% | 3,179 | 100.3% | 3,852 | 107.2% | 2,627 | 97.9% | 1,494 | 122.4% | 3,014 | 101.3% | |||||||||
81-85 | 27 | 152.0% | 114 | 125.4% | 140 | 154.3% | 256 | 86.6% | 1,001 | 93.4% | 1,108 | 123.3% | 892 | 90.1% | 1,190 | 118.8% | 2,300 | 109.2% | |||||||||
86-90 | 22 | 226.3% | 11 | 114.0% | 19 | 107.0% | 36 | 102.9% | 249 | 121.7% | 195 | 124.5% | 388 | 111.8% | 825 | 109.6% | 698 | 100.0% | |||||||||
91-95 | 0 | 0.0% | 5 | 51.6% | 4 | 139.8% | 7 | 43.9% | 27 | 58.7% | 38 | 79.5% | 67 | 48.7% | 285 | 123.3% | 300 | 102.2% | |||||||||
96-100 | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 1 | 126.3% | 3 | 81.1% | 1 | 197.3% | 4 | 381.2% | 19 | 19.3% | 50 | 56.6% | |||||||||
101-105 | 0 | 0.0% | 1 | 53.1% | |||||||||||||||||||||||
106-110 | 0 | 0.0% | |||||||||||||||||||||||||
111-115 | 0 | 0.0% | |||||||||||||||||||||||||
For the bivariate fit checks, the fit can be great in some cases and poor in others. This could be due to a need for higher level interactions.
7.2 PLT Only
Code
dat.term.plt <- readRDS("dat.term.plt.rds")
dat.term.plt <- dat.term.plt[Policies_Exposed > 0]
bUseAllInteractions <- FALSE
AA.brks <- c(-1,17,
seq(25,115,5))
AA.lbls <- paste0(
AA.brks[1:(length(AA.brks)-1)]+1,
"-",
AA.brks[2:length(AA.brks)]
)
Dur.brks <- c(0,1,2,3,5,10,15,20,30,100)
Dur.lbls <- paste0(
Dur.brks[1:(length(Dur.brks)-1)]+1,
"-",
Dur.brks[2:length(Dur.brks)]
)
dat.term.plt[,`:=`(
AA_Grp=cut(Attained_Age,
breaks=AA.brks,
labels=AA.lbls),
Dur_Grp=cut(Duration,
breaks=Dur.brks,
labels=Dur.lbls)
)]
pred.cols <- names(dat.term.plt)[c(1,5,9,16:18)]
factor.cols <- c("Sex",
"Face_Amount_Band",
"SOA_Antp_Lvl_TP",
"UW",
"AA_Grp",
"Dur_Grp")
dat.term.plt[,
(factor.cols):=lapply(.SD,factor),
.SDcols=factor.cols]
UW.levels<-data.table(UW.levels=dat.term.plt[,levels(UW)])
UW.levels[,c("NS","Pref_Class","NClasses"):=tstrsplit(UW.levels,"/")]
setkeyv(UW.levels,c("NS","NClasses","Pref_Class"))
set.seed(traintest.seed)
dat.term.plt %>%
mutate(
IsTraining = (runif(nrow(.)) < training.fraction),
Noise = rnorm(nrow(.)),
.before = 1
) %>%
mutate(Face_Amount_Band=fct_relabel(
Face_Amount_Band,
#function(.) sub(":"," -",.,fixed=T)
function(.) fa.remap[Face_Amount_Band.Old==.,Face_Amount_Band.New]
),
AE_Count=Death_Count/ExpDth_Cnt_VBT2015,
AE_Amount=Death_Claim_Amount/ExpDth_Amt_VBT2015,
UW=factor(UW,levels=UW.levels$UW.levels)
) ->
dat.term.plt
gbm.pred.cols <- c("Noise",pred.cols)Here is a data preview.
Code
dat.term.plt %>%
head(10) %>%
flextable()IsTraining | Noise | Sex | Smoker_Status | Attained_Age | Duration | Face_Amount_Band | SOA_Post_Lvl_Ind | Number_of_Pfd_Classes | Preferred_Class | SOA_Antp_Lvl_TP | Death_Count | Policies_Exposed | ExpDth_Cnt_VBT2015 | Death_Claim_Amount | Amount_Exposed | ExpDth_Amt_VBT2015 | UW | AA_Grp | Dur_Grp | AE_Count | AE_Amount |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
TRUE | 0.1278386 | F | NS | 55 | 8 | 500K - <1M | PLT | U | U | Unknown | 0 | 0.796549 | 0.001099238 | 0 | 398,274.5 | 549.6188 | NS/U/U | 51-55 | 6-10 | 0 | 0 |
TRUE | -0.1518745 | F | NS | 56 | 9 | 50K - <100K | PLT | 2 | 2 | Unknown | 0 | 8.847863 | 0.013624558 | 0 | 491,198.0 | 756.3875 | NS/2/2 | 56-60 | 6-10 | 0 | 0 |
TRUE | -0.0547556 | F | NS | 56 | 9 | 100K - <250K | PLT | 3 | 1 | Unknown | 0 | 2.627397 | 0.003993918 | 0 | 262,739.7 | 399.3917 | NS/1/3 | 56-60 | 6-10 | 0 | 0 |
TRUE | -1.6323762 | F | NS | 56 | 9 | 100K - <250K | PLT | U | U | Unknown | 0 | 21.468803 | 0.033037792 | 0 | 2,438,239.4 | 3,752.4723 | NS/U/U | 56-60 | 6-10 | 0 | 0 |
TRUE | 1.5316881 | F | NS | 56 | 9 | 100K - <250K | PLT | 3 | 3 | Unknown | 0 | 33.395670 | 0.049664452 | 0 | 4,304,540.0 | 6,412.5258 | NS/3/3 | 56-60 | 6-10 | 0 | 0 |
TRUE | -1.7326077 | F | NS | 56 | 9 | 250K - <500K | PLT | 3 | 3 | Unknown | 0 | 15.885403 | 0.023630075 | 0 | 4,442,986.5 | 6,606.8924 | NS/3/3 | 56-60 | 6-10 | 0 | 0 |
FALSE | -0.8680619 | F | NS | 56 | 9 | 250K - <500K | PLT | 3 | 1 | Unknown | 0 | 2.824276 | 0.004231874 | 0 | 733,773.9 | 1,098.9717 | NS/1/3 | 56-60 | 6-10 | 0 | 0 |
TRUE | 1.0450097 | F | NS | 57 | 10 | 50K - <100K | PLT | 2 | 2 | Unknown | 0 | 16.856679 | 0.029410194 | 0 | 888,904.2 | 1,551.5934 | NS/2/2 | 56-60 | 6-10 | 0 | 0 |
TRUE | -0.6840765 | F | NS | 57 | 10 | 100K - <250K | PLT | 2 | 1 | Unknown | 0 | 10.063515 | 0.017114580 | 0 | 1,218,666.6 | 2,070.2707 | NS/1/2 | 56-60 | 6-10 | 0 | 0 |
TRUE | -1.8073461 | F | NS | 57 | 10 | 100K - <250K | PLT | 3 | 1 | Unknown | 0 | 5.295008 | 0.009276088 | 0 | 614,610.4 | 1,077.4017 | NS/1/3 | 56-60 | 6-10 | 0 | 0 |
7.2.1 Feature Discovery with Catboost
As in the predictive analytics framework, gradient boosted machines as implemented with Catboost are used for exploratory data analysis. The framework uses LightGBM, while Catboost is used here. It is easier to use Catboost with GPUs.
Code
dat.term.plt %>%
filter(IsTraining == TRUE) %>%
select(all_of(gbm.pred.cols)) %>%
mutate(Sex = as.numeric(Sex)) %>%
catboost.load_pool(
data=.,
label = dat.term.plt[IsTraining==TRUE,AE_Amount],
weight = dat.term.plt[IsTraining==TRUE,ExpDth_Amt_VBT2015]) ->
train_pool_plt
dat.term.plt %>%
filter(IsTraining == FALSE) %>%
select(all_of(gbm.pred.cols)) %>%
mutate(Sex = as.numeric(Sex)) %>%
catboost.load_pool(
data=.,
label = dat.term.plt[IsTraining==FALSE,AE_Amount],
weight = dat.term.plt[IsTraining==FALSE,ExpDth_Amt_VBT2015]) ->
test_pool_plt
set.seed(catboost.seed)
if(bUseCache & file.exists(
'dat.term.mod.plt.cbm'
) & !bInvalidateCaches)
{
cb.model.plt <- catboost.load_model(model_path = 'dat.term.mod.plt.cbm')
} else {
cb.model.plt <- catboost.train(learn_pool=train_pool_plt,
test_pool = test_pool_plt,
params=fit_params)
catboost.save_model(cb.model.plt,
model_path = 'dat.term.mod.plt.cbm')
}7.2.2 Feature Importance
Next is to check for the variables with most variability. Attained age and underwriting are prominent.
Code
shp.plt <- shapviz(
cb.model.plt,
X=as.data.frame(dat.term.plt[IsTraining==TRUE,..gbm.pred.cols]),
X_pred=train_pool_plt
)
setDT(shp.plt$X)
shp.plt$X[,c("NS","Pref_Class","NClasses"):=tstrsplit(UW,"/")]
sv_importance(shp.plt) + theme_minimal()
7.2.3 Feature Interactions
The top three interactions are face amount band with each of underwriting, attained age, and level term period.
Code
imp.int.plt <- catboost.get_feature_importance(
cb.model.plt,
type="Interaction"
)
mod.ft.map.plt <- data.table(
FeatureNames=names(dat.term.plt[IsTraining==TRUE,..gbm.pred.cols])
)
mod.ft.map.plt[,ID:=1:nrow(.SD)-1]
imp.int.plt %>%
merge(mod.ft.map.plt,
by.x="feature1_index",
by.y="ID") %>%
merge(mod.ft.map.plt,
by.x="feature2_index",
by.y="ID") %>%
setnames(
old=c("FeatureNames.x","FeatureNames.y"),
new=c("Feature1","Feature2")
) %>%
mutate(feature1_index=NULL,feature2_index=NULL) %>%
as.data.table() %>%
setcolorder(c("Feature1","Feature2","score")) ->
imp.int.plt
imp.int.plt[order(-score)] %>%
filter(Feature1 != "Noise") %>%
flextable() %>%
colformat_double(j="score",digits=2)Feature1 | Feature2 | score |
|---|---|---|
Face_Amount_Band | UW | 15.75 |
Sex | Face_Amount_Band | 9.68 |
Face_Amount_Band | AA_Grp | 9.31 |
Face_Amount_Band | SOA_Antp_Lvl_TP | 6.10 |
Sex | UW | 4.64 |
Face_Amount_Band | Dur_Grp | 4.46 |
Sex | AA_Grp | 4.21 |
UW | AA_Grp | 4.08 |
SOA_Antp_Lvl_TP | UW | 2.95 |
Sex | SOA_Antp_Lvl_TP | 2.70 |
SOA_Antp_Lvl_TP | AA_Grp | 1.84 |
UW | Dur_Grp | 1.40 |
Sex | Dur_Grp | 1.01 |
SOA_Antp_Lvl_TP | Dur_Grp | 0.72 |
AA_Grp | Dur_Grp | 0.46 |
7.2.4 Feature Interaction Plots
Each of the interactions are discussed below with plots using SHAP values from both sides of the interaction.
7.2.4.1 UW
7.2.4.1.1 Face Amount Band SHAPs
To the extent that an interaction is present, it appears to be occurring at face amounts 2.5 million and above.
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"Face_Amount_Band"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"Face_Amount_Band"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"Face_Amount_Band"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '3') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, 3 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"Face_Amount_Band"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '4') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, 4 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"Face_Amount_Band"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"Face_Amount_Band"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"Face_Amount_Band"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for unismokers")) +
theme_minimal()
7.2.4.1.2 UW SHAPs
On the UW SHAP side, there appears to be little to no interaction, except at face amounts 2.5 million and above.
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"UW"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"UW"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"UW"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '3') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 3 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"UW"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '4') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 4 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"UW"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"UW"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.plt$S[,"UW"]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for unismokers")) +
theme_minimal()
7.2.4.2 Attained Age Group
7.2.4.2.1 Face Amount Band SHAPs
For face amount SHAPS by attained age, any interaction is once again a high face phenomenon, if it indeed exists. One can see that for the 10M+ band at least, there is a cluster of nearly 0% factors, suggesting that there may be some challenges around sparse data. Additionally, for the 5M-<10M face amounts, there is some evidence of multi-modality across attained ages. Again, this may be due to thin data.
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
AA_Grp)],
shap=shp.plt$S[,"Face_Amount_Band"]
)
) %>%
ggplot(aes(y=AA_Grp, x=exp(shap),color=Face_Amount_Band,fill=Face_Amount_Band)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,2)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("by attained age")) +
theme_minimal()
7.2.4.2.2 Attained Age SHAPs
On the other hand, the attained age SHAPs do exhibit a clear interaction with face amount band.
In the first plot, it is clear that there is a separation in SHAP value distributions with higher attained ages separating from lower attained ages. The approximate breakpoint is most evident in the second plot, at about attained age 66+ or so.
The other interesting phenomenon is the shifts in the SHAP distributions for each of the face amount bands of 5M - < 10M and 10M+. In the second plot, if one’s eyes follows the distributions from bottom to top, one sees that starting at attained age group 18-25, the distribution starts low, shifts rightward through about age group 61-65, then shifts leftward again through age group 81-85. Given the claim count, this is arguably weak evidence for anti-selection at the high face amounts for middle attained ages.
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
AA_Grp)],
shap=shp.plt$S[,"AA_Grp"]
)
) %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=AA_Grp,fill=AA_Grp)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,2)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect AA_Grp"),
subtitle = paste0("by face amount band")) +
theme_minimal()
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
AA_Grp)],
shap=shp.plt$S[,"AA_Grp"]
)
) %>%
ggplot(aes(y=AA_Grp, x=exp(shap),color=Face_Amount_Band,fill=Face_Amount_Band)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,2)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect AA_Grp"),
subtitle = paste0("by attained age")) +
theme_minimal()
7.2.4.3 Sex and Face Amount Band
7.2.4.3.1 Face Amount Band SHAPs
As with the other groups, the interaction, if any, is a high face amount phenomenon.
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
Sex)],
shap=shp.plt$S[,"Face_Amount_Band"]
)
) %>%
ggplot(aes(y=Sex, x=exp(shap),color=Face_Amount_Band,fill=Face_Amount_Band)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,2)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("by sex")) +
theme_minimal()
7.2.4.3.2 Sex SHAPs
There appears to be an interaction at the highest face amounts for Sex.
Code
data.table(
cbind(
shp.plt$X[,.(Face_Amount_Band,
Sex)],
shap=shp.plt$S[,"Sex"]
)
) %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Sex,fill=Sex)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,2)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Sex"),
subtitle = paste0("by face amount band")) +
theme_minimal()
7.2.5 Next Steps in Modeling
The catboost modeling is informative here for exploratory analytics. We next build an elastic net model which includes the main effects plus the top eight interactions from the catboost analysis. This cutoff is chosen arbitrarily. The top three are stronger than the others, while the next five seem to cluster in the middle. These interactions may turn out to be unneeded. Elastic net modeling will reveal which is truly important in a mortality model.
7.2.6 Elastic Net Models
The following formula is used for the PLT model.
Code
if(bUseAllInteractions) {
glmnetFormula <- as.formula(
paste0(
"~ -1 + (",
paste(pred.cols,collapse=" + "),
")^2"
)
)
} else {
glmnetFormula <- as.formula(
paste(c("~ -1",
pred.cols,
imp.int.plt[order(-score)][Feature1 != "Noise",
paste0(Feature1,":",Feature2)]),
collapse=" + ")
)
}
print(glmnetFormula)~-1 + Sex + Face_Amount_Band + SOA_Antp_Lvl_TP + UW + AA_Grp +
Dur_Grp + Face_Amount_Band:UW + Sex:Face_Amount_Band + Face_Amount_Band:AA_Grp +
Face_Amount_Band:SOA_Antp_Lvl_TP + Sex:UW + Face_Amount_Band:Dur_Grp +
Sex:AA_Grp + UW:AA_Grp + SOA_Antp_Lvl_TP:UW + Sex:SOA_Antp_Lvl_TP +
SOA_Antp_Lvl_TP:AA_Grp + UW:Dur_Grp + Sex:Dur_Grp + SOA_Antp_Lvl_TP:Dur_Grp +
AA_Grp:Dur_GrpThe interactions included in the model are as follows:
Code
data.table(Interaction=imp.int.plt[order(-score)][Feature1 != "Noise",
paste0(Feature1,":",Feature2)]) %>%
flextable()Interaction |
|---|
Face_Amount_Band:UW |
Sex:Face_Amount_Band |
Face_Amount_Band:AA_Grp |
Face_Amount_Band:SOA_Antp_Lvl_TP |
Sex:UW |
Face_Amount_Band:Dur_Grp |
Sex:AA_Grp |
UW:AA_Grp |
SOA_Antp_Lvl_TP:UW |
Sex:SOA_Antp_Lvl_TP |
SOA_Antp_Lvl_TP:AA_Grp |
UW:Dur_Grp |
Sex:Dur_Grp |
SOA_Antp_Lvl_TP:Dur_Grp |
AA_Grp:Dur_Grp |
7.2.6.1 Model Fit
Code
dat.term.el.plt <- prepELData(
formula=glmnetFormula,
data=dat.term.plt,
predictors = pred.cols,
response = "AE_Amount",
weights = "ExpDth_Amt_VBT2015",
useSparse = T
)
set.seed(cvfit.seed)
if(bUseCache & file.exists(
'term.model.el.plt.rds'
) & !bInvalidateCaches)
{
cvfit.term.plt <- readRDS('term.model.el.plt.rds')
} else
{
cvfit.term.plt <- fitCVGLMNet(
dat.term.el.plt,
nfolds = nFolds
)
if(bUseCache)
saveRDS(cvfit.term.plt, 'term.model.el.plt.rds')
}7.2.6.1.1 Usual plots for Elastic Net Models
When presenting elastic net models, the cross validation plot for \(\lambda\) and the coefficient shrinkage plots are provided.
At the minimum \(\lambda\) of 0.002387, the model has 266 parameters.
Code
plot(cvfit.term.plt)
Code
plot(cvfit.term.plt$glmnet.fit,xvar="lambda")
7.2.6.1.2 Factor Table
The exponentiated coefficients are as follows:
Code
reformatCoefs(cvfit.term.plt, pred.cols) %>%
filter(Coef != 0) %>%
select(Feature1Name,
Feature1Level,
Feature2Name,
Feature2Level,
Coef) %>%
mutate(Coef=exp(Coef)) %>%
flextable() %>%
set_formatter(
Coef=function(x) paste0(sprintf("%.01f", 100*x),"%")
) %>%
theme_vanilla()Feature1Name | Feature1Level | Feature2Name | Feature2Level | Coef |
|---|---|---|---|---|
(Intercept) | (Intercept) | 104.2% | ||
Sex | F | 101.6% | ||
Sex | M | 99.8% | ||
Face_Amount_Band | 10K - <25K | 97.3% | ||
Face_Amount_Band | 100K - <250K | 97.0% | ||
Face_Amount_Band | 250K - <500K | 97.3% | ||
Face_Amount_Band | 2.5M - <5M | 119.7% | ||
Face_Amount_Band | 10M+ | 138.4% | ||
SOA_Antp_Lvl_TP | 10 yr anticipated | 113.5% | ||
SOA_Antp_Lvl_TP | 15 yr anticipated | 107.6% | ||
SOA_Antp_Lvl_TP | 20 yr anticipated | 114.2% | ||
SOA_Antp_Lvl_TP | Unknown | 101.5% | ||
UW | NS/2/2 | 118.7% | ||
UW | NS/1/3 | 96.0% | ||
UW | NS/2/3 | 103.8% | ||
UW | NS/3/3 | 100.8% | ||
UW | NS/3/4 | 123.4% | ||
UW | NS/4/4 | 144.6% | ||
UW | S/1/2 | 87.3% | ||
UW | S/2/2 | 110.4% | ||
UW | S/U/U | 109.2% | ||
UW | U/U/U | 112.6% | ||
AA_Grp | 31-35 | 92.6% | ||
AA_Grp | 36-40 | 96.0% | ||
AA_Grp | 41-45 | 87.1% | ||
AA_Grp | 46-50 | 97.2% | ||
AA_Grp | 66-70 | 101.4% | ||
AA_Grp | 71-75 | 107.4% | ||
AA_Grp | 76-80 | 133.0% | ||
AA_Grp | 81-85 | 127.4% | ||
Dur_Grp | 11-15 | 106.5% | ||
Dur_Grp | 16-20 | 109.3% | ||
Face_Amount_Band | 10K - <25K | UW | NS/2/2 | 96.0% |
Face_Amount_Band | 50K - <100K | UW | NS/2/2 | 110.0% |
Face_Amount_Band | 100K - <250K | UW | NS/2/2 | 108.5% |
Face_Amount_Band | 250K - <500K | UW | NS/2/2 | 102.4% |
Face_Amount_Band | 1M - <2.5M | UW | NS/2/2 | 87.5% |
Face_Amount_Band | 500K - <1M | UW | NS/1/3 | 102.8% |
Face_Amount_Band | 2.5M - <5M | UW | NS/1/3 | 151.8% |
Face_Amount_Band | 100K - <250K | UW | NS/2/3 | 94.8% |
Face_Amount_Band | 1M - <2.5M | UW | NS/2/3 | 100.1% |
Face_Amount_Band | 2.5M - <5M | UW | NS/2/3 | 125.3% |
Face_Amount_Band | 100K - <250K | UW | NS/3/3 | 95.6% |
Face_Amount_Band | 500K - <1M | UW | NS/3/3 | 89.8% |
Face_Amount_Band | 1M - <2.5M | UW | NS/3/3 | 120.9% |
Face_Amount_Band | 2.5M - <5M | UW | NS/3/3 | 65.0% |
Face_Amount_Band | 5M - <10M | UW | NS/3/3 | 228.9% |
Face_Amount_Band | 10M+ | UW | NS/3/3 | 433.0% |
Face_Amount_Band | 500K - <1M | UW | NS/1/4 | 127.6% |
Face_Amount_Band | 1M - <2.5M | UW | NS/1/4 | 145.4% |
Face_Amount_Band | 2.5M - <5M | UW | NS/1/4 | 83.7% |
Face_Amount_Band | 500K - <1M | UW | NS/2/4 | 102.4% |
Face_Amount_Band | 2.5M - <5M | UW | NS/2/4 | 100.4% |
Face_Amount_Band | 5M - <10M | UW | NS/2/4 | 69.4% |
Face_Amount_Band | 100K - <250K | UW | NS/3/4 | 92.0% |
Face_Amount_Band | 1M - <2.5M | UW | NS/3/4 | 109.2% |
Face_Amount_Band | 2.5M - <5M | UW | NS/3/4 | 165.2% |
Face_Amount_Band | 5M - <10M | UW | NS/3/4 | 158.4% |
Face_Amount_Band | 250K - <500K | UW | NS/4/4 | 100.8% |
Face_Amount_Band | 500K - <1M | UW | NS/4/4 | 114.7% |
Face_Amount_Band | 25K - <50K | UW | NS/U/U | 107.8% |
Face_Amount_Band | 50K - <100K | UW | NS/U/U | 114.8% |
Face_Amount_Band | 500K - <1M | UW | NS/U/U | 98.4% |
Face_Amount_Band | 2.5M - <5M | UW | NS/U/U | 138.9% |
Face_Amount_Band | 100K - <250K | UW | S/1/2 | 114.8% |
Face_Amount_Band | 100K - <250K | UW | S/2/2 | 110.8% |
Face_Amount_Band | 250K - <500K | UW | S/2/2 | 105.7% |
Face_Amount_Band | 100K - <250K | UW | S/U/U | 98.3% |
Face_Amount_Band | 5M - <10M | UW | S/U/U | 123.4% |
Face_Amount_Band | 10M+ | UW | S/U/U | 774.6% |
Sex | M | Face_Amount_Band | 25K - <50K | 103.5% |
Sex | M | Face_Amount_Band | 50K - <100K | 105.8% |
Sex | M | Face_Amount_Band | 100K - <250K | 100.8% |
Sex | M | Face_Amount_Band | 2.5M - <5M | 117.2% |
Sex | M | Face_Amount_Band | 5M - <10M | 81.1% |
Sex | M | Face_Amount_Band | 10M+ | 25.6% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 41-45 | 109.9% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 41-45 | 88.2% |
Face_Amount_Band | 250K - <500K | AA_Grp | 46-50 | 93.0% |
Face_Amount_Band | 500K - <1M | AA_Grp | 46-50 | 98.8% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 46-50 | 93.1% |
Face_Amount_Band | 5M - <10M | AA_Grp | 46-50 | 109.2% |
Face_Amount_Band | 25K - <50K | AA_Grp | 51-55 | 100.9% |
Face_Amount_Band | 50K - <100K | AA_Grp | 51-55 | 105.4% |
Face_Amount_Band | 250K - <500K | AA_Grp | 51-55 | 93.0% |
Face_Amount_Band | 500K - <1M | AA_Grp | 51-55 | 96.3% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 51-55 | 128.0% |
Face_Amount_Band | 50K - <100K | AA_Grp | 56-60 | 106.6% |
Face_Amount_Band | 100K - <250K | AA_Grp | 56-60 | 97.9% |
Face_Amount_Band | 250K - <500K | AA_Grp | 56-60 | 96.4% |
Face_Amount_Band | 500K - <1M | AA_Grp | 56-60 | 94.9% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 56-60 | 91.7% |
Face_Amount_Band | 5M - <10M | AA_Grp | 56-60 | 210.2% |
Face_Amount_Band | 10M+ | AA_Grp | 56-60 | 196.4% |
Face_Amount_Band | 100K - <250K | AA_Grp | 61-65 | 99.2% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 61-65 | 90.7% |
Face_Amount_Band | 5M - <10M | AA_Grp | 61-65 | 52.9% |
Face_Amount_Band | 10M+ | AA_Grp | 61-65 | 447.9% |
Face_Amount_Band | 100K - <250K | AA_Grp | 66-70 | 101.0% |
Face_Amount_Band | 250K - <500K | AA_Grp | 66-70 | 100.3% |
Face_Amount_Band | 500K - <1M | AA_Grp | 66-70 | 108.6% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 66-70 | 103.0% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 66-70 | 64.4% |
Face_Amount_Band | 5M - <10M | AA_Grp | 66-70 | 99.1% |
Face_Amount_Band | 10M+ | AA_Grp | 66-70 | 97.8% |
Face_Amount_Band | 50K - <100K | AA_Grp | 71-75 | 88.0% |
Face_Amount_Band | 500K - <1M | AA_Grp | 71-75 | 116.1% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 71-75 | 107.2% |
Face_Amount_Band | 5M - <10M | AA_Grp | 71-75 | 100.4% |
Face_Amount_Band | 25K - <50K | AA_Grp | 76-80 | 89.1% |
Face_Amount_Band | 50K - <100K | AA_Grp | 76-80 | 88.5% |
Face_Amount_Band | 250K - <500K | AA_Grp | 76-80 | 116.1% |
Face_Amount_Band | 500K - <1M | AA_Grp | 76-80 | 111.3% |
Face_Amount_Band | 100K - <250K | AA_Grp | 81-85 | 106.6% |
Face_Amount_Band | 100K - <250K | SOA_Antp_Lvl_TP | 10 yr anticipated | 98.8% |
Face_Amount_Band | 5M - <10M | SOA_Antp_Lvl_TP | 10 yr anticipated | 131.2% |
Face_Amount_Band | 10M+ | SOA_Antp_Lvl_TP | 10 yr anticipated | 112.0% |
Face_Amount_Band | 50K - <100K | SOA_Antp_Lvl_TP | 15 yr anticipated | 97.4% |
Face_Amount_Band | 100K - <250K | SOA_Antp_Lvl_TP | 15 yr anticipated | 94.7% |
Face_Amount_Band | 500K - <1M | SOA_Antp_Lvl_TP | 15 yr anticipated | 115.0% |
Face_Amount_Band | 1M - <2.5M | SOA_Antp_Lvl_TP | 15 yr anticipated | 110.3% |
Face_Amount_Band | 2.5M - <5M | SOA_Antp_Lvl_TP | 15 yr anticipated | 104.1% |
Face_Amount_Band | 5M - <10M | SOA_Antp_Lvl_TP | 15 yr anticipated | 99.7% |
Face_Amount_Band | 10M+ | SOA_Antp_Lvl_TP | 15 yr anticipated | 234.5% |
Face_Amount_Band | 100K - <250K | SOA_Antp_Lvl_TP | Unknown | 95.8% |
Face_Amount_Band | 500K - <1M | SOA_Antp_Lvl_TP | Unknown | 98.7% |
Face_Amount_Band | 1M - <2.5M | SOA_Antp_Lvl_TP | Unknown | 101.4% |
Face_Amount_Band | 2.5M - <5M | SOA_Antp_Lvl_TP | Unknown | 146.5% |
Face_Amount_Band | 5M - <10M | SOA_Antp_Lvl_TP | Unknown | 111.9% |
Sex | M | UW | NS/2/2 | 101.2% |
Sex | M | UW | NS/3/3 | 104.1% |
Sex | M | UW | NS/1/4 | 91.3% |
Sex | M | UW | NS/2/4 | 123.0% |
Sex | M | UW | NS/U/U | 108.0% |
Sex | M | UW | S/1/2 | 95.8% |
Sex | M | UW | S/U/U | 97.7% |
Sex | M | UW | U/U/U | 116.6% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 11-15 | 91.9% |
Face_Amount_Band | 100K - <250K | Dur_Grp | 11-15 | 96.8% |
Face_Amount_Band | 2.5M - <5M | Dur_Grp | 11-15 | 100.1% |
Face_Amount_Band | 5M - <10M | Dur_Grp | 11-15 | 133.2% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 16-20 | 99.8% |
Face_Amount_Band | 100K - <250K | Dur_Grp | 16-20 | 96.4% |
Face_Amount_Band | 250K - <500K | Dur_Grp | 16-20 | 106.3% |
Face_Amount_Band | 1M - <2.5M | Dur_Grp | 16-20 | 105.3% |
Face_Amount_Band | 10M+ | Dur_Grp | 16-20 | 141.0% |
Face_Amount_Band | 100K - <250K | Dur_Grp | 21-30 | 105.3% |
Face_Amount_Band | 500K - <1M | Dur_Grp | 21-30 | 105.6% |
Face_Amount_Band | 1M - <2.5M | Dur_Grp | 21-30 | 97.0% |
Face_Amount_Band | 5M - <10M | Dur_Grp | 21-30 | 85.3% |
Sex | M | AA_Grp | 51-55 | 98.0% |
Sex | M | AA_Grp | 56-60 | 101.5% |
Sex | M | AA_Grp | 71-75 | 103.4% |
UW | NS/2/3 | AA_Grp | 36-40 | 109.9% |
UW | NS/2/2 | AA_Grp | 41-45 | 116.9% |
UW | NS/U/U | AA_Grp | 41-45 | 123.3% |
UW | NS/2/3 | AA_Grp | 46-50 | 88.1% |
UW | NS/3/4 | AA_Grp | 46-50 | 104.6% |
UW | NS/2/2 | AA_Grp | 51-55 | 104.1% |
UW | NS/1/3 | AA_Grp | 51-55 | 94.6% |
UW | NS/2/2 | AA_Grp | 56-60 | 100.6% |
UW | NS/2/3 | AA_Grp | 56-60 | 105.4% |
UW | NS/3/3 | AA_Grp | 56-60 | 104.4% |
UW | NS/1/4 | AA_Grp | 56-60 | 103.4% |
UW | NS/3/4 | AA_Grp | 56-60 | 118.0% |
UW | NS/U/U | AA_Grp | 56-60 | 94.6% |
UW | S/U/U | AA_Grp | 56-60 | 116.6% |
UW | NS/3/3 | AA_Grp | 61-65 | 120.9% |
UW | NS/1/4 | AA_Grp | 61-65 | 93.0% |
UW | NS/4/4 | AA_Grp | 61-65 | 102.1% |
UW | NS/U/U | AA_Grp | 61-65 | 95.9% |
UW | NS/3/3 | AA_Grp | 66-70 | 87.9% |
UW | NS/1/3 | AA_Grp | 71-75 | 67.5% |
UW | NS/2/3 | AA_Grp | 71-75 | 96.6% |
UW | NS/1/4 | AA_Grp | 71-75 | 111.6% |
UW | NS/U/U | AA_Grp | 71-75 | 125.6% |
UW | S/U/U | AA_Grp | 71-75 | 103.0% |
UW | NS/2/2 | AA_Grp | 76-80 | 89.4% |
UW | NS/1/3 | AA_Grp | 76-80 | 101.7% |
UW | NS/3/3 | AA_Grp | 76-80 | 85.6% |
UW | NS/2/4 | AA_Grp | 76-80 | 124.6% |
UW | NS/U/U | AA_Grp | 76-80 | 110.8% |
UW | NS/2/2 | AA_Grp | 81-85 | 87.5% |
UW | NS/3/3 | AA_Grp | 81-85 | 101.8% |
UW | NS/U/U | AA_Grp | 81-85 | 106.3% |
UW | NS/2/2 | AA_Grp | 86-90 | 99.8% |
SOA_Antp_Lvl_TP | 10 yr anticipated | UW | NS/2/2 | 101.9% |
SOA_Antp_Lvl_TP | 15 yr anticipated | UW | NS/2/2 | 97.6% |
SOA_Antp_Lvl_TP | 20 yr anticipated | UW | NS/2/2 | 105.6% |
SOA_Antp_Lvl_TP | Unknown | UW | NS/2/2 | 99.1% |
SOA_Antp_Lvl_TP | Unknown | UW | NS/1/3 | 120.7% |
SOA_Antp_Lvl_TP | 10 yr anticipated | UW | NS/2/3 | 97.4% |
SOA_Antp_Lvl_TP | 15 yr anticipated | UW | NS/2/3 | 97.8% |
SOA_Antp_Lvl_TP | Unknown | UW | NS/2/3 | 115.6% |
SOA_Antp_Lvl_TP | 10 yr anticipated | UW | NS/3/3 | 120.5% |
SOA_Antp_Lvl_TP | 15 yr anticipated | UW | NS/3/3 | 133.1% |
SOA_Antp_Lvl_TP | Unknown | UW | NS/3/3 | 96.2% |
SOA_Antp_Lvl_TP | 10 yr anticipated | UW | NS/1/4 | 115.4% |
SOA_Antp_Lvl_TP | 15 yr anticipated | UW | NS/1/4 | 87.2% |
SOA_Antp_Lvl_TP | 10 yr anticipated | UW | NS/2/4 | 116.2% |
SOA_Antp_Lvl_TP | 15 yr anticipated | UW | NS/2/4 | 87.4% |
SOA_Antp_Lvl_TP | Unknown | UW | NS/3/4 | 136.1% |
SOA_Antp_Lvl_TP | 10 yr anticipated | UW | NS/4/4 | 107.4% |
SOA_Antp_Lvl_TP | 10 yr anticipated | UW | NS/U/U | 77.7% |
SOA_Antp_Lvl_TP | 15 yr anticipated | UW | NS/U/U | 138.4% |
SOA_Antp_Lvl_TP | 20 yr anticipated | UW | NS/U/U | 86.5% |
SOA_Antp_Lvl_TP | Unknown | UW | NS/U/U | 94.2% |
SOA_Antp_Lvl_TP | 10 yr anticipated | UW | S/1/2 | 105.2% |
SOA_Antp_Lvl_TP | Unknown | UW | S/U/U | 90.8% |
Sex | M | SOA_Antp_Lvl_TP | 15 yr anticipated | 114.2% |
Sex | M | SOA_Antp_Lvl_TP | 20 yr anticipated | 108.5% |
Sex | M | SOA_Antp_Lvl_TP | Unknown | 108.1% |
SOA_Antp_Lvl_TP | 10 yr anticipated | AA_Grp | 41-45 | 86.4% |
SOA_Antp_Lvl_TP | 10 yr anticipated | AA_Grp | 46-50 | 98.4% |
SOA_Antp_Lvl_TP | 20 yr anticipated | AA_Grp | 51-55 | 97.4% |
SOA_Antp_Lvl_TP | Unknown | AA_Grp | 56-60 | 103.7% |
SOA_Antp_Lvl_TP | 10 yr anticipated | AA_Grp | 61-65 | 101.7% |
SOA_Antp_Lvl_TP | 20 yr anticipated | AA_Grp | 61-65 | 106.8% |
SOA_Antp_Lvl_TP | 15 yr anticipated | AA_Grp | 66-70 | 112.8% |
SOA_Antp_Lvl_TP | 20 yr anticipated | AA_Grp | 66-70 | 108.2% |
SOA_Antp_Lvl_TP | 10 yr anticipated | AA_Grp | 71-75 | 113.7% |
SOA_Antp_Lvl_TP | 15 yr anticipated | AA_Grp | 71-75 | 116.5% |
SOA_Antp_Lvl_TP | 20 yr anticipated | AA_Grp | 71-75 | 108.2% |
SOA_Antp_Lvl_TP | 15 yr anticipated | AA_Grp | 76-80 | 106.4% |
SOA_Antp_Lvl_TP | Unknown | AA_Grp | 76-80 | 124.2% |
SOA_Antp_Lvl_TP | 15 yr anticipated | AA_Grp | 81-85 | 129.0% |
SOA_Antp_Lvl_TP | 20 yr anticipated | AA_Grp | 81-85 | 86.0% |
UW | NS/3/3 | Dur_Grp | 11-15 | 116.4% |
UW | NS/3/4 | Dur_Grp | 11-15 | 155.5% |
UW | NS/4/4 | Dur_Grp | 11-15 | 115.7% |
UW | NS/U/U | Dur_Grp | 11-15 | 103.2% |
UW | S/1/2 | Dur_Grp | 11-15 | 101.2% |
UW | NS/2/3 | Dur_Grp | 16-20 | 92.5% |
UW | NS/3/3 | Dur_Grp | 16-20 | 100.2% |
UW | S/1/2 | Dur_Grp | 16-20 | 117.0% |
UW | S/U/U | Dur_Grp | 16-20 | 111.4% |
UW | NS/U/U | Dur_Grp | 21-30 | 99.1% |
UW | S/1/2 | Dur_Grp | 21-30 | 103.4% |
UW | S/U/U | Dur_Grp | 21-30 | 101.8% |
UW | U/U/U | Dur_Grp | 21-30 | 103.9% |
Sex | M | Dur_Grp | 16-20 | 102.9% |
Sex | M | Dur_Grp | 21-30 | 107.4% |
Sex | M | Dur_Grp | 31-100 | 100.3% |
SOA_Antp_Lvl_TP | 10 yr anticipated | Dur_Grp | 11-15 | 132.6% |
SOA_Antp_Lvl_TP | Unknown | Dur_Grp | 11-15 | 123.6% |
SOA_Antp_Lvl_TP | 15 yr anticipated | Dur_Grp | 16-20 | 131.3% |
SOA_Antp_Lvl_TP | Unknown | Dur_Grp | 16-20 | 106.9% |
SOA_Antp_Lvl_TP | 15 yr anticipated | Dur_Grp | 21-30 | 87.5% |
SOA_Antp_Lvl_TP | 20 yr anticipated | Dur_Grp | 21-30 | 101.7% |
SOA_Antp_Lvl_TP | Unknown | Dur_Grp | 21-30 | 106.9% |
SOA_Antp_Lvl_TP | 15 yr anticipated | Dur_Grp | 31-100 | 106.1% |
AA_Grp | 36-40 | Dur_Grp | 11-15 | 82.0% |
AA_Grp | 41-45 | Dur_Grp | 11-15 | 91.3% |
AA_Grp | 56-60 | Dur_Grp | 11-15 | 97.8% |
AA_Grp | 76-80 | Dur_Grp | 11-15 | 114.2% |
AA_Grp | 81-85 | Dur_Grp | 11-15 | 102.9% |
AA_Grp | 46-50 | Dur_Grp | 16-20 | 93.0% |
AA_Grp | 56-60 | Dur_Grp | 16-20 | 98.8% |
AA_Grp | 61-65 | Dur_Grp | 16-20 | 98.5% |
AA_Grp | 66-70 | Dur_Grp | 16-20 | 106.1% |
AA_Grp | 71-75 | Dur_Grp | 16-20 | 106.5% |
AA_Grp | 81-85 | Dur_Grp | 16-20 | 102.4% |
AA_Grp | 51-55 | Dur_Grp | 21-30 | 97.0% |
AA_Grp | 61-65 | Dur_Grp | 21-30 | 108.5% |
AA_Grp | 66-70 | Dur_Grp | 21-30 | 117.6% |
AA_Grp | 71-75 | Dur_Grp | 21-30 | 107.8% |
In the plots and tables that follow, we fix all of the other variables at their middle values when extracting final factors.
We generate some supporting tables: a factor grid for attaching to the experience, and a list of interactions present in the model
Code
dat.term.plt[,..pred.cols] %>%
lapply(levels) %>%
expand.grid() %>%
setDT() ->
dat.term.plt.grid
dat.term.plt.grid %>%
model.Matrix(
object=glmnetFormula,
data=.,
sparse=T
) %>%
predict(
cvfit.term.plt,
newx=.,
s="lambda.min"
) %>%
as.vector() ->
newCoef
dat.term.plt.grid %>%
add_column(
Factor=exp(newCoef)
) %>%
setDT() ->
dat.term.plt.grid
write.xlsx(dat.term.plt.grid,
file="dat.term.plt.grid.xlsx")
reformatCoefs(cvfit.term.plt, pred.cols) %>%
filter(Coef != 0 & !is.na(Feature2Name)) %>%
select(Feature1Name,Feature2Name) %>%
distinct() %>%
as.list() %>%
purrr::list_transpose() ->
term.plt.int.list7.2.6.1.3 Plots of Terms
Below are plots of the 2-way interaction terms, with external factors fixed at their middle values.
One thing to note in these plots is the upward sloping mortality from attained age 65 or so through attained age 85. Otherwise, effects can be subtle except as called out below.
- Face Amount Band x UW: There is a general increase in mortality with increasing face amount band above 2.5 million, with the increase more pronounced at certain UW combinations.
- Face Amount Band x UW: The increase above 2.5 million is more pronounced for females.
- Face Amount Band x Attained Age: The increases above 2.5 million appear predominantly in the ages 60-85.
- Face Amount Band x Term Length: The increase above 2.5 million is more pronounced for the 15-year term length.
- Duration x Term Length: The 10- and 15-year term lengths exhibit bumps in their first post-level durations.
7.2.6.1.4 Tables of Terms
Below are tables of the 2-way interaction terms, with external factors fixed at their middle values.
Face_Amount_Band | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
<10K | 118.6% | 138.3% | 113.9% | 127.1% | 193.3% | 107.1% | 103.6% | 268.6% | 198.5% | 160.4% | 104.7% | 131.0% | 151.1% | 133.6% |
10K - <25K | 115.5% | 129.1% | 110.8% | 123.6% | 188.1% | 104.2% | 100.9% | 261.4% | 193.1% | 156.0% | 101.9% | 127.5% | 147.1% | 130.0% |
25K - <50K | 118.6% | 138.3% | 113.9% | 127.1% | 193.3% | 107.1% | 103.6% | 268.6% | 198.5% | 172.8% | 104.7% | 131.0% | 151.1% | 133.6% |
50K - <100K | 113.2% | 145.1% | 108.6% | 121.2% | 184.4% | 102.1% | 98.9% | 256.2% | 189.3% | 175.5% | 99.9% | 125.0% | 144.2% | 127.5% |
100K - <250K | 103.2% | 130.4% | 99.0% | 104.8% | 160.7% | 93.1% | 90.1% | 214.8% | 172.6% | 139.4% | 104.6% | 126.2% | 129.1% | 116.2% |
250K - <500K | 111.3% | 132.9% | 106.8% | 119.2% | 181.4% | 100.5% | 97.3% | 252.0% | 187.8% | 150.5% | 98.3% | 130.0% | 141.8% | 125.4% |
500K - <1M | 129.5% | 150.9% | 127.8% | 138.7% | 189.4% | 149.1% | 115.8% | 293.1% | 248.5% | 172.3% | 114.3% | 143.0% | 164.9% | 145.8% |
1M - <2.5M | 120.1% | 122.4% | 115.2% | 128.7% | 236.5% | 157.5% | 104.9% | 296.9% | 200.8% | 162.3% | 106.0% | 132.6% | 152.9% | 135.2% |
2.5M - <5M | 147.9% | 172.4% | 215.4% | 198.4% | 156.7% | 111.8% | 129.7% | 553.2% | 247.5% | 277.8% | 130.6% | 163.4% | 188.4% | 166.6% |
5M - <10M | 331.2% | 386.0% | 317.9% | 354.7% | 1235.5% | 298.9% | 200.8% | 1188.1% | 554.2% | 447.7% | 292.4% | 365.8% | 520.8% | 373.1% |
10M+ | 756.3% | 881.3% | 725.8% | 809.9% | 5335.2% | 682.4% | 660.7% | 1712.1% | 1265.2% | 1022.2% | 667.7% | 835.1% | 7461.7% | 851.7% |
Face_Amount_Band | F | M |
|---|---|---|
<10K | 103.6% | 145.2% |
10K - <25K | 100.9% | 141.3% |
25K - <50K | 103.6% | 150.3% |
50K - <100K | 98.9% | 146.6% |
100K - <250K | 90.1% | 127.2% |
250K - <500K | 97.3% | 136.3% |
500K - <1M | 115.8% | 162.3% |
1M - <2.5M | 104.9% | 147.0% |
2.5M - <5M | 129.7% | 212.9% |
5M - <10M | 200.8% | 228.2% |
10M+ | 660.7% | 236.7% |
AA_Grp | <10K | 10K - <25K | 25K - <50K | 50K - <100K | 100K - <250K | 250K - <500K | 500K - <1M | 1M - <2.5M | 2.5M - <5M | 5M - <10M | 10M+ |
|---|---|---|---|---|---|---|---|---|---|---|---|
0-17 | 105.9% | 103.1% | 105.9% | 94.8% | 94.1% | 103.1% | 124.7% | 116.9% | 132.6% | 97.6% | 343.8% |
18-25 | 105.9% | 103.1% | 105.9% | 94.8% | 94.1% | 103.1% | 124.7% | 116.9% | 132.6% | 97.6% | 343.8% |
26-30 | 105.9% | 103.1% | 105.9% | 94.8% | 94.1% | 103.1% | 124.7% | 116.9% | 132.6% | 97.6% | 343.8% |
31-35 | 98.1% | 95.5% | 98.1% | 87.9% | 87.2% | 95.5% | 115.5% | 108.3% | 122.8% | 90.4% | 318.5% |
36-40 | 83.5% | 81.2% | 83.5% | 74.7% | 74.1% | 81.2% | 98.2% | 92.1% | 104.4% | 76.9% | 270.8% |
41-45 | 84.3% | 82.0% | 84.3% | 75.4% | 74.9% | 82.0% | 99.2% | 102.2% | 93.0% | 77.6% | 273.5% |
46-50 | 103.0% | 100.3% | 103.0% | 92.2% | 91.5% | 93.3% | 119.8% | 105.8% | 128.9% | 103.6% | 334.4% |
51-55 | 105.9% | 103.1% | 106.9% | 100.0% | 94.1% | 95.9% | 120.1% | 116.9% | 169.7% | 97.6% | 343.8% |
56-60 | 103.6% | 100.9% | 103.6% | 98.9% | 90.1% | 97.3% | 115.8% | 104.9% | 129.7% | 200.8% | 660.7% |
61-65 | 105.9% | 103.1% | 105.9% | 94.8% | 93.4% | 103.1% | 124.7% | 106.0% | 132.6% | 51.6% | 1539.9% |
66-70 | 121.1% | 117.9% | 121.1% | 108.5% | 108.7% | 118.3% | 154.9% | 137.7% | 97.7% | 110.6% | 384.6% |
71-75 | 132.6% | 129.0% | 132.6% | 104.5% | 117.8% | 129.1% | 181.2% | 156.8% | 165.9% | 122.7% | 430.3% |
76-80 | 213.5% | 207.8% | 190.3% | 169.2% | 189.7% | 241.3% | 279.7% | 235.5% | 267.2% | 196.7% | 692.9% |
81-85 | 179.3% | 174.4% | 179.3% | 160.5% | 169.7% | 174.5% | 211.0% | 197.7% | 224.3% | 165.2% | 581.8% |
86-90 | 105.9% | 103.1% | 105.9% | 94.8% | 94.1% | 103.1% | 124.7% | 116.9% | 132.6% | 97.6% | 343.8% |
91-95 | 105.9% | 103.1% | 105.9% | 94.8% | 94.1% | 103.1% | 124.7% | 116.9% | 132.6% | 97.6% | 343.8% |
96-100 | 105.9% | 103.1% | 105.9% | 94.8% | 94.1% | 103.1% | 124.7% | 116.9% | 132.6% | 97.6% | 343.8% |
106-110 | 105.9% | 103.1% | 105.9% | 94.8% | 94.1% | 103.1% | 124.7% | 116.9% | 132.6% | 97.6% | 343.8% |
111-115 | 105.9% | 103.1% | 105.9% | 94.8% | 94.1% | 103.1% | 124.7% | 116.9% | 132.6% | 97.6% | 343.8% |
Face_Amount_Band | 5 yr anticipated | 10 yr anticipated | 15 yr anticipated | 20 yr anticipated | 25 yr anticipated | 30 yr anticipated | Unknown |
|---|---|---|---|---|---|---|---|
<10K | 110.2% | 192.9% | 103.6% | 125.9% | 110.2% | 110.2% | 143.4% |
10K - <25K | 107.3% | 187.7% | 100.9% | 122.5% | 107.3% | 107.3% | 139.5% |
25K - <50K | 110.2% | 192.9% | 103.6% | 125.9% | 110.2% | 110.2% | 143.4% |
50K - <100K | 107.9% | 188.9% | 98.9% | 123.3% | 107.9% | 107.9% | 140.4% |
100K - <250K | 101.2% | 175.0% | 90.1% | 115.6% | 101.2% | 101.2% | 126.1% |
250K - <500K | 103.4% | 181.0% | 97.3% | 118.2% | 103.4% | 103.4% | 134.5% |
500K - <1M | 107.2% | 187.5% | 115.8% | 122.4% | 107.2% | 107.2% | 137.5% |
1M - <2.5M | 101.1% | 176.9% | 104.9% | 115.5% | 101.1% | 101.1% | 133.3% |
2.5M - <5M | 132.5% | 231.9% | 129.7% | 151.4% | 132.5% | 132.5% | 252.5% |
5M - <10M | 214.2% | 491.7% | 200.8% | 244.6% | 214.2% | 214.2% | 311.8% |
10M+ | 299.6% | 587.0% | 660.7% | 342.2% | 299.6% | 299.6% | 389.7% |
Sex | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
F | 103.2% | 130.4% | 99.0% | 104.8% | 160.7% | 93.1% | 90.1% | 214.8% | 172.6% | 139.4% | 104.6% | 126.2% | 129.1% | 116.2% |
M | 118.4% | 151.5% | 113.6% | 120.3% | 192.0% | 97.5% | 127.2% | 246.6% | 198.1% | 172.8% | 115.0% | 144.9% | 144.8% | 155.5% |
Dur_Grp | <10K | 10K - <25K | 25K - <50K | 50K - <100K | 100K - <250K | 250K - <500K | 500K - <1M | 1M - <2.5M | 2.5M - <5M | 5M - <10M | 10M+ |
|---|---|---|---|---|---|---|---|---|---|---|---|
6-10 | 99.5% | 96.8% | 99.5% | 103.3% | 89.4% | 93.4% | 111.2% | 100.7% | 124.5% | 144.7% | 634.4% |
11-15 | 103.6% | 100.9% | 103.6% | 98.9% | 90.1% | 97.3% | 115.8% | 104.9% | 129.7% | 200.8% | 660.7% |
16-20 | 141.3% | 137.5% | 141.3% | 146.3% | 122.4% | 140.9% | 157.9% | 150.6% | 176.7% | 205.4% | 1269.5% |
21-30 | 87.0% | 84.7% | 87.0% | 90.4% | 82.4% | 81.7% | 102.7% | 85.4% | 108.8% | 108.0% | 554.8% |
31-100 | 105.6% | 102.8% | 105.6% | 109.7% | 94.9% | 99.1% | 118.0% | 106.9% | 132.1% | 153.6% | 673.3% |
AA_Grp | F | M |
|---|---|---|
0-17 | 94.1% | 130.9% |
18-25 | 94.1% | 130.9% |
26-30 | 94.1% | 130.9% |
31-35 | 87.2% | 121.3% |
36-40 | 74.1% | 103.1% |
41-45 | 74.9% | 104.1% |
46-50 | 91.5% | 127.3% |
51-55 | 94.1% | 128.3% |
56-60 | 90.1% | 127.2% |
61-65 | 93.4% | 129.9% |
66-70 | 108.7% | 151.1% |
71-75 | 117.8% | 169.3% |
76-80 | 189.7% | 263.8% |
81-85 | 169.7% | 236.0% |
86-90 | 94.1% | 130.9% |
91-95 | 94.1% | 130.9% |
96-100 | 94.1% | 130.9% |
106-110 | 94.1% | 130.9% |
111-115 | 94.1% | 130.9% |
AA_Grp | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0-17 | 107.7% | 135.4% | 103.4% | 103.8% | 160.9% | 94.0% | 94.1% | 190.1% | 180.2% | 153.9% | 109.2% | 131.8% | 115.6% | 121.3% |
18-25 | 107.7% | 135.4% | 103.4% | 103.8% | 160.9% | 94.0% | 94.1% | 190.1% | 180.2% | 153.9% | 109.2% | 131.8% | 115.6% | 121.3% |
26-30 | 107.7% | 135.4% | 103.4% | 103.8% | 160.9% | 94.0% | 94.1% | 190.1% | 180.2% | 153.9% | 109.2% | 131.8% | 115.6% | 121.3% |
31-35 | 99.8% | 125.4% | 95.8% | 96.2% | 149.0% | 87.1% | 87.2% | 176.1% | 167.0% | 142.6% | 101.2% | 122.1% | 107.1% | 112.4% |
36-40 | 84.9% | 106.7% | 81.4% | 89.8% | 126.7% | 74.0% | 74.1% | 149.8% | 142.0% | 121.2% | 86.0% | 103.9% | 91.1% | 95.6% |
41-45 | 85.7% | 125.9% | 82.2% | 82.6% | 128.0% | 74.8% | 74.9% | 151.2% | 143.4% | 150.9% | 86.9% | 104.9% | 92.0% | 96.5% |
46-50 | 104.8% | 131.7% | 100.5% | 89.0% | 156.4% | 91.4% | 91.5% | 193.3% | 175.3% | 149.7% | 106.2% | 128.2% | 112.4% | 118.0% |
51-55 | 107.7% | 140.9% | 97.8% | 103.8% | 160.9% | 94.0% | 94.1% | 190.1% | 180.2% | 153.9% | 109.2% | 131.8% | 115.6% | 121.3% |
56-60 | 103.2% | 130.4% | 99.0% | 104.8% | 160.7% | 93.1% | 90.1% | 214.8% | 172.6% | 139.4% | 104.6% | 126.2% | 129.1% | 116.2% |
61-65 | 106.9% | 134.4% | 102.6% | 103.0% | 192.9% | 86.8% | 93.4% | 188.7% | 182.6% | 146.5% | 108.4% | 130.8% | 114.7% | 120.4% |
66-70 | 124.4% | 156.3% | 119.4% | 119.8% | 163.3% | 108.5% | 108.7% | 219.5% | 208.1% | 177.7% | 126.1% | 152.2% | 133.5% | 140.1% |
71-75 | 134.8% | 169.4% | 87.4% | 125.5% | 201.3% | 131.2% | 117.8% | 237.9% | 225.5% | 241.8% | 136.7% | 165.0% | 149.0% | 151.8% |
76-80 | 174.2% | 195.7% | 170.1% | 167.8% | 222.6% | 152.0% | 189.7% | 307.4% | 291.4% | 275.8% | 176.6% | 213.2% | 187.0% | 196.2% |
81-85 | 194.3% | 213.6% | 186.4% | 187.2% | 295.3% | 169.5% | 169.7% | 342.9% | 325.0% | 295.0% | 196.9% | 237.7% | 208.5% | 218.8% |
86-90 | 107.7% | 135.1% | 103.4% | 103.8% | 160.9% | 94.0% | 94.1% | 190.1% | 180.2% | 153.9% | 109.2% | 131.8% | 115.6% | 121.3% |
91-95 | 107.7% | 135.4% | 103.4% | 103.8% | 160.9% | 94.0% | 94.1% | 190.1% | 180.2% | 153.9% | 109.2% | 131.8% | 115.6% | 121.3% |
96-100 | 107.7% | 135.4% | 103.4% | 103.8% | 160.9% | 94.0% | 94.1% | 190.1% | 180.2% | 153.9% | 109.2% | 131.8% | 115.6% | 121.3% |
106-110 | 107.7% | 135.4% | 103.4% | 103.8% | 160.9% | 94.0% | 94.1% | 190.1% | 180.2% | 153.9% | 109.2% | 131.8% | 115.6% | 121.3% |
111-115 | 107.7% | 135.4% | 103.4% | 103.8% | 160.9% | 94.0% | 94.1% | 190.1% | 180.2% | 153.9% | 109.2% | 131.8% | 115.6% | 121.3% |
SOA_Antp_Lvl_TP | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
5 yr anticipated | 101.2% | 131.1% | 97.1% | 105.1% | 118.5% | 104.7% | 101.2% | 210.7% | 169.3% | 98.9% | 102.6% | 123.9% | 126.7% | 114.0% |
10 yr anticipated | 150.6% | 198.8% | 144.5% | 152.2% | 212.3% | 179.7% | 175.0% | 313.5% | 270.6% | 114.3% | 160.6% | 184.2% | 188.4% | 169.6% |
15 yr anticipated | 103.2% | 130.4% | 99.0% | 104.8% | 160.7% | 93.1% | 90.1% | 214.8% | 172.6% | 139.4% | 104.6% | 126.2% | 129.1% | 116.2% |
20 yr anticipated | 115.6% | 158.2% | 111.0% | 120.0% | 135.3% | 119.6% | 115.6% | 240.7% | 193.4% | 97.6% | 117.2% | 141.5% | 144.7% | 130.2% |
25 yr anticipated | 101.2% | 131.1% | 97.1% | 105.1% | 118.5% | 104.7% | 101.2% | 210.7% | 169.3% | 98.9% | 102.6% | 123.9% | 126.7% | 114.0% |
30 yr anticipated | 101.2% | 131.1% | 97.1% | 105.1% | 118.5% | 104.7% | 101.2% | 210.7% | 169.3% | 98.9% | 102.6% | 123.9% | 126.7% | 114.0% |
Unknown | 126.1% | 161.8% | 146.1% | 151.3% | 142.0% | 130.4% | 126.1% | 357.4% | 211.0% | 116.0% | 127.8% | 154.3% | 143.3% | 142.0% |
SOA_Antp_Lvl_TP | F | M |
|---|---|---|
5 yr anticipated | 101.2% | 125.1% |
10 yr anticipated | 175.0% | 216.3% |
15 yr anticipated | 90.1% | 127.2% |
20 yr anticipated | 115.6% | 155.0% |
25 yr anticipated | 101.2% | 125.1% |
30 yr anticipated | 101.2% | 125.1% |
Unknown | 126.1% | 168.5% |
AA_Grp | 5 yr anticipated | 10 yr anticipated | 15 yr anticipated | 20 yr anticipated | 25 yr anticipated | 30 yr anticipated | Unknown |
|---|---|---|---|---|---|---|---|
0-17 | 105.7% | 182.8% | 94.1% | 120.8% | 105.7% | 105.7% | 127.0% |
18-25 | 105.7% | 182.8% | 94.1% | 120.8% | 105.7% | 105.7% | 127.0% |
26-30 | 105.7% | 182.8% | 94.1% | 120.8% | 105.7% | 105.7% | 127.0% |
31-35 | 97.9% | 169.3% | 87.2% | 111.9% | 97.9% | 97.9% | 117.7% |
36-40 | 83.3% | 144.0% | 74.1% | 95.1% | 83.3% | 83.3% | 100.1% |
41-45 | 84.1% | 125.6% | 74.9% | 96.0% | 84.1% | 84.1% | 101.0% |
46-50 | 102.8% | 174.9% | 91.5% | 117.4% | 102.8% | 102.8% | 123.5% |
51-55 | 105.7% | 182.8% | 94.1% | 117.6% | 105.7% | 105.7% | 127.0% |
56-60 | 101.2% | 175.0% | 90.1% | 115.6% | 101.2% | 101.2% | 126.1% |
61-65 | 104.9% | 184.5% | 93.4% | 128.0% | 104.9% | 104.9% | 126.1% |
66-70 | 108.2% | 187.1% | 108.7% | 133.8% | 108.2% | 108.2% | 130.1% |
71-75 | 113.5% | 223.3% | 117.8% | 140.4% | 113.5% | 113.5% | 136.4% |
76-80 | 200.3% | 346.3% | 189.7% | 228.7% | 200.3% | 200.3% | 298.9% |
81-85 | 147.8% | 255.5% | 169.7% | 145.1% | 147.8% | 147.8% | 177.6% |
86-90 | 105.7% | 182.8% | 94.1% | 120.8% | 105.7% | 105.7% | 127.0% |
91-95 | 105.7% | 182.8% | 94.1% | 120.8% | 105.7% | 105.7% | 127.0% |
96-100 | 105.7% | 182.8% | 94.1% | 120.8% | 105.7% | 105.7% | 127.0% |
106-110 | 105.7% | 182.8% | 94.1% | 120.8% | 105.7% | 105.7% | 127.0% |
111-115 | 105.7% | 182.8% | 94.1% | 120.8% | 105.7% | 105.7% | 127.0% |
Dur_Grp | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6-10 | 102.4% | 129.4% | 98.2% | 103.9% | 137.0% | 92.4% | 89.4% | 137.0% | 148.0% | 134.0% | 102.5% | 125.3% | 128.1% | 115.3% |
11-15 | 103.2% | 130.4% | 99.0% | 104.8% | 160.7% | 93.1% | 90.1% | 214.8% | 172.6% | 139.4% | 104.6% | 126.2% | 129.1% | 116.2% |
16-20 | 140.1% | 177.2% | 134.5% | 131.7% | 188.0% | 126.4% | 122.4% | 187.6% | 202.6% | 183.5% | 164.2% | 171.5% | 195.4% | 157.8% |
21-30 | 94.3% | 119.2% | 90.5% | 95.7% | 126.2% | 85.1% | 82.4% | 126.2% | 136.3% | 122.4% | 97.7% | 115.4% | 120.1% | 110.3% |
31-100 | 108.6% | 137.4% | 104.3% | 110.3% | 145.4% | 98.0% | 94.9% | 145.4% | 157.1% | 142.2% | 108.8% | 132.9% | 136.0% | 122.3% |
Dur_Grp | F | M |
|---|---|---|
6-10 | 89.4% | 126.2% |
11-15 | 90.1% | 127.2% |
16-20 | 122.4% | 177.9% |
21-30 | 82.4% | 124.9% |
31-100 | 94.9% | 134.3% |
Dur_Grp | 5 yr anticipated | 10 yr anticipated | 15 yr anticipated | 20 yr anticipated | 25 yr anticipated | 30 yr anticipated | Unknown |
|---|---|---|---|---|---|---|---|
6-10 | 100.4% | 130.9% | 89.4% | 114.7% | 100.4% | 100.4% | 101.2% |
11-15 | 101.2% | 175.0% | 90.1% | 115.6% | 101.2% | 101.2% | 126.1% |
16-20 | 104.7% | 136.5% | 122.4% | 119.6% | 104.7% | 104.7% | 112.8% |
21-30 | 105.8% | 137.9% | 82.4% | 122.9% | 105.8% | 105.8% | 113.9% |
31-100 | 100.4% | 130.9% | 94.9% | 114.7% | 100.4% | 100.4% | 101.2% |
AA_Grp | 6-10 | 11-15 | 16-20 | 21-30 | 31-100 |
|---|---|---|---|---|---|
0-17 | 91.4% | 94.1% | 126.5% | 84.2% | 97.0% |
18-25 | 91.4% | 94.1% | 126.5% | 84.2% | 97.0% |
26-30 | 91.4% | 94.1% | 126.5% | 84.2% | 97.0% |
31-35 | 84.6% | 87.2% | 117.2% | 78.0% | 89.8% |
36-40 | 87.7% | 74.1% | 121.5% | 80.8% | 93.1% |
41-45 | 79.6% | 74.9% | 110.3% | 73.3% | 84.5% |
46-50 | 88.8% | 91.5% | 114.5% | 81.8% | 94.3% |
51-55 | 91.4% | 94.1% | 126.5% | 81.6% | 97.0% |
56-60 | 89.4% | 90.1% | 122.4% | 82.4% | 94.9% |
61-65 | 90.7% | 93.4% | 123.7% | 90.6% | 96.2% |
66-70 | 105.5% | 108.7% | 155.0% | 114.2% | 112.0% |
71-75 | 114.3% | 117.8% | 168.6% | 113.5% | 121.3% |
76-80 | 161.2% | 189.7% | 223.2% | 148.4% | 171.1% |
81-85 | 160.1% | 169.7% | 226.9% | 147.4% | 169.9% |
86-90 | 91.4% | 94.1% | 126.5% | 84.2% | 97.0% |
91-95 | 91.4% | 94.1% | 126.5% | 84.2% | 97.0% |
96-100 | 91.4% | 94.1% | 126.5% | 84.2% | 97.0% |
106-110 | 91.4% | 94.1% | 126.5% | 84.2% | 97.0% |
111-115 | 91.4% | 94.1% | 126.5% | 84.2% | 97.0% |
7.2.6.2 Goodness-of-Fit
Next comes checking goodness-of-fit, on both a univariate and bivariate basis. Tables are provided which show the ratio of the actual to model predicted deaths and show the associated death counts.
Code
dat.term.plt.grid %>%
right_join(dat.term.plt) %>%
mutate(ExpDth_Amt_GLMNet=ExpDth_Amt_VBT2015*Factor) %>%
mutate(Factor=NULL) ->
dat.term.plt7.2.6.2.1 Univariate Fit Checks
Sex | Death Count | Actual-to-Model |
|---|---|---|
F | 17,571 | 100.3% |
M | 24,955 | 99.9% |
Face_Amount_Band | Death Count | Actual-to-Model |
|---|---|---|
<10K | 903 | 86.4% |
10K - <25K | 6,652 | 95.4% |
25K - <50K | 7,682 | 101.7% |
50K - <100K | 8,892 | 100.6% |
100K - <250K | 12,915 | 99.8% |
250K - <500K | 3,439 | 99.6% |
500K - <1M | 1,415 | 99.6% |
1M - <2.5M | 563 | 99.7% |
2.5M - <5M | 45 | 103.0% |
5M - <10M | 17 | 101.4% |
10M+ | 3 | 111.6% |
SOA_Antp_Lvl_TP | Death Count | Actual-to-Model |
|---|---|---|
5 yr anticipated | 9,885 | 98.4% |
10 yr anticipated | 11,750 | 100.2% |
15 yr anticipated | 5,440 | 100.5% |
20 yr anticipated | 10,861 | 100.8% |
25 yr anticipated | 0 | 0.0% |
30 yr anticipated | 0 | 0.0% |
Unknown | 4,590 | 100.6% |
UW | Death Count | Actual-to-Model |
|---|---|---|
NS/1/2 | 3,872 | 95.9% |
NS/2/2 | 14,000 | 100.6% |
NS/1/3 | 1,016 | 98.8% |
NS/2/3 | 1,263 | 101.1% |
NS/3/3 | 1,685 | 100.8% |
NS/1/4 | 789 | 100.8% |
NS/2/4 | 905 | 99.1% |
NS/3/4 | 452 | 102.8% |
NS/4/4 | 536 | 104.3% |
NS/U/U | 7,755 | 100.3% |
S/1/2 | 1,354 | 98.0% |
S/2/2 | 664 | 104.1% |
S/U/U | 5,935 | 101.1% |
U/U/U | 2,300 | 104.8% |
AA_Grp | Death Count | Actual-to-Model |
|---|---|---|
0-17 | 1 | 293.9% |
18-25 | 29 | 67.1% |
26-30 | 90 | 89.7% |
31-35 | 208 | 81.6% |
36-40 | 416 | 94.7% |
41-45 | 1,068 | 97.8% |
46-50 | 2,195 | 99.1% |
51-55 | 4,236 | 99.9% |
56-60 | 5,910 | 100.3% |
61-65 | 6,974 | 100.2% |
66-70 | 6,547 | 100.5% |
71-75 | 4,658 | 100.8% |
76-80 | 4,751 | 101.3% |
81-85 | 3,582 | 102.5% |
86-90 | 1,487 | 100.3% |
91-95 | 359 | 78.4% |
96-100 | 15 | 64.4% |
106-110 | 0 | 0.0% |
111-115 | 0 | 0.0% |
Dur_Grp | Death Count | Actual-to-Model |
|---|---|---|
6-10 | 1,273 | 95.0% |
11-15 | 9,129 | 100.2% |
16-20 | 10,770 | 100.2% |
21-30 | 18,917 | 100.2% |
31-100 | 2,437 | 102.0% |
7.2.6.2.2 Bivariate Fit Checks
Face_Amount_Band | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
<10K | 629 | 88.1% | 274 | 83.9% | ||
10K - <25K | 3,926 | 94.9% | 2,726 | 95.9% | ||
25K - <50K | 3,557 | 99.6% | 4,125 | 103.2% | ||
50K - <100K | 3,731 | 99.4% | 5,161 | 101.3% | ||
100K - <250K | 4,504 | 98.7% | 8,411 | 100.4% | ||
250K - <500K | 888 | 98.2% | 2,551 | 100.1% | ||
500K - <1M | 253 | 99.3% | 1,162 | 99.7% | ||
1M - <2.5M | 72 | 100.5% | 491 | 99.6% | ||
2.5M - <5M | 4 | 100.2% | 41 | 103.3% | ||
5M - <10M | 5 | 127.8% | 12 | 93.7% | ||
10M+ | 2 | 210.2% | 1 | 70.4% | ||
SOA_Antp_Lvl_TP | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
5 yr anticipated | 3,880 | 99.8% | 6,005 | 97.8% | ||
10 yr anticipated | 4,537 | 100.8% | 7,213 | 100.0% | ||
15 yr anticipated | 2,137 | 100.0% | 3,303 | 100.7% | ||
20 yr anticipated | 5,461 | 100.2% | 5,400 | 101.0% | ||
25 yr anticipated | 0 | 0.0% | 0 | 0.0% | ||
30 yr anticipated | 0 | 0.0% | 0 | 0.0% | ||
Unknown | 1,556 | 99.7% | 3,034 | 100.8% | ||
UW | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
NS/1/2 | 1,447 | 95.1% | 2,425 | 96.3% | ||
NS/2/2 | 7,291 | 100.4% | 6,709 | 100.7% | ||
NS/1/3 | 386 | 93.3% | 630 | 101.2% | ||
NS/2/3 | 417 | 105.4% | 846 | 99.8% | ||
NS/3/3 | 564 | 99.8% | 1,121 | 101.1% | ||
NS/1/4 | 275 | 109.0% | 514 | 97.9% | ||
NS/2/4 | 223 | 83.7% | 682 | 102.3% | ||
NS/3/4 | 125 | 108.0% | 327 | 101.7% | ||
NS/4/4 | 162 | 109.3% | 374 | 102.9% | ||
NS/U/U | 2,770 | 99.5% | 4,985 | 100.6% | ||
S/1/2 | 456 | 99.4% | 898 | 97.4% | ||
S/2/2 | 212 | 119.8% | 452 | 99.5% | ||
S/U/U | 2,418 | 106.6% | 3,517 | 98.5% | ||
U/U/U | 825 | 99.2% | 1,475 | 106.4% | ||
AA_Grp | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
0-17 | 0 | 0.0% | 1 | 442.9% | ||
18-25 | 7 | 67.0% | 22 | 67.1% | ||
26-30 | 24 | 69.9% | 66 | 98.5% | ||
31-35 | 72 | 70.0% | 136 | 88.7% | ||
36-40 | 169 | 89.8% | 247 | 97.6% | ||
41-45 | 440 | 98.9% | 628 | 97.2% | ||
46-50 | 842 | 95.1% | 1,353 | 100.8% | ||
51-55 | 1,716 | 101.3% | 2,520 | 99.3% | ||
56-60 | 2,332 | 99.5% | 3,578 | 100.6% | ||
61-65 | 2,701 | 100.3% | 4,273 | 100.1% | ||
66-70 | 2,559 | 101.8% | 3,988 | 100.1% | ||
71-75 | 1,944 | 100.1% | 2,714 | 101.0% | ||
76-80 | 2,062 | 102.9% | 2,689 | 100.7% | ||
81-85 | 1,672 | 108.6% | 1,910 | 99.6% | ||
86-90 | 804 | 119.6% | 683 | 89.8% | ||
91-95 | 216 | 93.8% | 143 | 72.8% | ||
96-100 | 11 | 87.4% | 4 | 38.5% | ||
106-110 | 0 | 0.0% | ||||
111-115 | 0 | 0.0% | ||||
Dur_Grp | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
6-10 | 546 | 106.8% | 727 | 90.1% | ||
11-15 | 3,391 | 100.0% | 5,738 | 100.3% | ||
16-20 | 4,224 | 100.0% | 6,546 | 100.3% | ||
21-30 | 8,568 | 99.8% | 10,349 | 100.4% | ||
31-100 | 842 | 95.3% | 1,595 | 104.1% | ||
Face_Amount_Band | SOA_Antp_Lvl_TP: 5 yr anticipated | SOA_Antp_Lvl_TP: 10 yr anticipated | SOA_Antp_Lvl_TP: 15 yr anticipated | SOA_Antp_Lvl_TP: 20 yr anticipated | SOA_Antp_Lvl_TP: 25 yr anticipated | SOA_Antp_Lvl_TP: 30 yr anticipated | SOA_Antp_Lvl_TP: Unknown | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||||
<10K | 48 | 87.4% | 207 | 92.7% | 65 | 91.3% | 559 | 83.7% | 0 | 0.0% | 0 | 0.0% | 24 | 84.6% | |||||||
10K - <25K | 331 | 107.5% | 1,734 | 94.3% | 533 | 88.6% | 3,793 | 94.3% | 0 | 0.0% | 0 | 0.0% | 261 | 115.1% | |||||||
25K - <50K | 2,537 | 111.1% | 1,194 | 96.2% | 734 | 90.7% | 2,149 | 97.3% | 0 | 0.0% | 0 | 0.0% | 1,068 | 103.9% | |||||||
50K - <100K | 2,792 | 105.2% | 1,851 | 99.7% | 1,096 | 93.9% | 2,007 | 101.0% | 0 | 0.0% | 1,146 | 97.2% | |||||||||
100K - <250K | 3,183 | 101.7% | 4,223 | 99.3% | 1,993 | 98.5% | 2,040 | 101.0% | 0 | 0.0% | 0 | 0.0% | 1,476 | 97.9% | |||||||
250K - <500K | 694 | 98.2% | 1,504 | 99.5% | 616 | 99.7% | 221 | 102.6% | 0 | 0.0% | 404 | 100.9% | |||||||||
500K - <1M | 212 | 96.1% | 706 | 99.8% | 289 | 102.7% | 70 | 105.7% | 138 | 95.4% | |||||||||||
1M - <2.5M | 82 | 86.3% | 294 | 100.7% | 105 | 103.2% | 20 | 110.9% | 62 | 105.5% | |||||||||||
2.5M - <5M | 5 | 68.1% | 23 | 104.2% | 7 | 119.7% | 2 | 97.2% | 8 | 124.4% | |||||||||||
5M - <10M | 1 | 58.1% | 12 | 108.0% | 1 | 58.4% | 0 | 0.0% | 3 | 136.0% | |||||||||||
10M+ | 0 | 0.0% | 2 | 118.9% | 1 | 149.2% | 0 | 0.0% | 0 | 0.0% | |||||||||||
UW | Face_Amount_Band: <10K | Face_Amount_Band: 10K - <25K | Face_Amount_Band: 25K - <50K | Face_Amount_Band: 50K - <100K | Face_Amount_Band: 100K - <250K | Face_Amount_Band: 250K - <500K | Face_Amount_Band: 500K - <1M | Face_Amount_Band: 1M - <2 | Face_Amount_Band: 2 | Face_Amount_Band: 5M - <10M | Face_Amount_Band: 10M+ | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | 5M | 5M - <5M | Deaths | Ratio | Deaths | Ratio | ||||||||||||||
Deaths | Ratio | Deaths | Ratio | ||||||||||||||||||||||||||||||
NS/1/2 | 16 | 67.4% | 144 | 79.9% | 350 | 86.9% | 611 | 100.0% | 1,804 | 100.6% | 676 | 95.3% | 197 | 91.0% | 69 | 95.7% | 4 | 100.4% | 1 | 66.7% | 0 | 0.0% | |||||||||||
NS/2/2 | 600 | 83.3% | 4,492 | 93.0% | 2,822 | 102.4% | 2,641 | 103.2% | 2,828 | 101.3% | 489 | 102.9% | 108 | 105.6% | 19 | 84.0% | 1 | 64.7% | 0 | 0.0% | 0 | 0.0% | |||||||||||
NS/1/3 | 0 | 0.0% | 0 | 0.0% | 19 | 60.5% | 72 | 78.9% | 453 | 95.1% | 242 | 97.9% | 161 | 104.4% | 60 | 96.0% | 8 | 121.9% | 1 | 69.2% | 0 | 0.0% | |||||||||||
NS/2/3 | 0 | 0.0% | 1 | 153.3% | 31 | 64.4% | 146 | 108.3% | 551 | 95.0% | 302 | 101.4% | 157 | 100.0% | 66 | 104.8% | 7 | 124.0% | 2 | 118.5% | 0 | 0.0% | |||||||||||
NS/3/3 | 3 | 58.0% | 26 | 100.4% | 117 | 75.4% | 233 | 88.3% | 752 | 96.1% | 314 | 99.7% | 142 | 95.1% | 87 | 104.3% | 2 | 51.9% | 7 | 122.2% | 2 | 141.3% | |||||||||||
NS/1/4 | 17 | 53.8% | 80 | 72.3% | 336 | 102.3% | 166 | 101.6% | 123 | 107.1% | 65 | 106.6% | 1 | 47.5% | 1 | 80.5% | 0 | 0.0% | |||||||||||||||
NS/2/4 | 3 | 862.1% | 20 | 48.6% | 148 | 77.3% | 407 | 93.4% | 175 | 106.4% | 105 | 107.0% | 42 | 100.1% | 5 | 129.9% | 0 | 0.0% | 0 | 0.0% | |||||||||||||
NS/3/4 | 8 | 40.0% | 48 | 51.7% | 202 | 86.4% | 95 | 92.3% | 60 | 98.4% | 30 | 111.5% | 6 | 140.5% | 3 | 153.1% | 0 | 0.0% | |||||||||||||||
NS/4/4 | 1 | 1006.2% | 22 | 50.6% | 101 | 81.4% | 245 | 102.9% | 96 | 115.4% | 52 | 116.7% | 18 | 103.9% | 1 | 88.7% | 0 | 0.0% | 0 | 0.0% | |||||||||||||
NS/U/U | 21 | 82.2% | 341 | 124.4% | 1,598 | 109.4% | 2,216 | 103.5% | 2,822 | 100.6% | 487 | 99.1% | 190 | 96.7% | 69 | 96.6% | 10 | 118.3% | 1 | 78.5% | 0 | 0.0% | |||||||||||
S/1/2 | 1 | 83.3% | 1 | 424.2% | 97 | 101.7% | 302 | 106.3% | 716 | 105.0% | 160 | 97.2% | 55 | 94.7% | 22 | 95.4% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
S/2/2 | 0 | 0.0% | 0 | 0.0% | 44 | 110.6% | 133 | 94.0% | 355 | 110.6% | 95 | 117.0% | 29 | 106.1% | 8 | 81.9% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
S/U/U | 157 | 108.9% | 962 | 98.4% | 1,796 | 104.6% | 1,621 | 102.3% | 1,235 | 97.5% | 126 | 90.7% | 30 | 83.3% | 6 | 67.3% | 0 | 0.0% | 1 | 723.3% | 1 | 361.5% | |||||||||||
U/U/U | 105 | 82.0% | 681 | 96.8% | 741 | 104.8% | 540 | 108.4% | 209 | 107.2% | 16 | 97.1% | 6 | 134.0% | 2 | 104.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
AA_Grp | Face_Amount_Band: <10K | Face_Amount_Band: 10K - <25K | Face_Amount_Band: 25K - <50K | Face_Amount_Band: 50K - <100K | Face_Amount_Band: 100K - <250K | Face_Amount_Band: 250K - <500K | Face_Amount_Band: 500K - <1M | Face_Amount_Band: 1M - <2 | Face_Amount_Band: 2 | Face_Amount_Band: 10M+ | Face_Amount_Band: 5M - <10M | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | 5M | 5M - <5M | Deaths | Ratio | Deaths | Ratio | ||||||||||||||
Deaths | Ratio | Deaths | Ratio | ||||||||||||||||||||||||||||||
0-17 | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 1 | 773.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||||||||||
18-25 | 0 | 0.0% | 0 | 0.0% | 3 | 162.3% | 23 | 82.9% | 3 | 59.9% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||||
26-30 | 0 | 0.0% | 2 | 239.3% | 17 | 78.8% | 51 | 98.4% | 17 | 111.0% | 3 | 107.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
31-35 | 2 | 2106.3% | 2 | 174.8% | 71 | 127.8% | 69 | 131.9% | 49 | 84.9% | 11 | 67.7% | 3 | 58.5% | 1 | 53.3% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
36-40 | 1 | 0.0% | 9 | 136.1% | 76 | 109.7% | 101 | 140.0% | 135 | 86.7% | 58 | 86.9% | 28 | 110.0% | 7 | 72.0% | 1 | 207.2% | 0 | 0.0% | 0 | 0.0% | |||||||||||
41-45 | 3 | 91.1% | 50 | 240.6% | 140 | 130.4% | 206 | 123.5% | 415 | 95.0% | 164 | 99.3% | 60 | 94.0% | 30 | 112.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
46-50 | 6 | 181.1% | 80 | 147.6% | 238 | 136.6% | 399 | 112.1% | 958 | 99.6% | 318 | 95.9% | 138 | 95.3% | 52 | 94.0% | 4 | 112.9% | 0 | 0.0% | 2 | 163.4% | |||||||||||
51-55 | 21 | 158.9% | 186 | 183.6% | 507 | 137.7% | 870 | 109.0% | 1,802 | 99.1% | 531 | 97.4% | 218 | 97.0% | 88 | 98.1% | 11 | 116.5% | 0 | 0.0% | 2 | 96.1% | |||||||||||
56-60 | 25 | 55.1% | 260 | 114.0% | 791 | 105.1% | 1,463 | 105.4% | 2,341 | 98.7% | 659 | 98.0% | 257 | 97.4% | 100 | 96.7% | 7 | 101.5% | 1 | 166.0% | 6 | 124.2% | |||||||||||
61-65 | 50 | 68.5% | 466 | 109.8% | 1,309 | 110.6% | 1,672 | 99.1% | 2,484 | 98.8% | 649 | 101.5% | 247 | 98.2% | 88 | 96.1% | 7 | 113.3% | 2 | 142.2% | 0 | 0.0% | |||||||||||
66-70 | 72 | 87.1% | 557 | 103.4% | 1,398 | 105.8% | 1,646 | 98.8% | 2,096 | 101.5% | 490 | 102.7% | 209 | 103.5% | 76 | 104.2% | 2 | 57.7% | 0 | 0.0% | 1 | 58.3% | |||||||||||
71-75 | 86 | 80.6% | 768 | 93.7% | 1,101 | 95.2% | 995 | 92.8% | 1,245 | 100.5% | 260 | 96.6% | 135 | 105.9% | 59 | 105.8% | 7 | 111.9% | 0 | 0.0% | 2 | 148.3% | |||||||||||
76-80 | 163 | 69.3% | 1,438 | 84.9% | 1,098 | 88.1% | 843 | 91.9% | 876 | 101.7% | 204 | 107.7% | 85 | 109.7% | 38 | 107.4% | 4 | 123.4% | 0 | 0.0% | 2 | 106.0% | |||||||||||
81-85 | 226 | 98.9% | 1,675 | 97.5% | 717 | 87.5% | 436 | 94.1% | 399 | 109.2% | 76 | 117.5% | 32 | 112.0% | 18 | 98.4% | 1 | 108.6% | 0 | 0.0% | 2 | 108.6% | |||||||||||
86-90 | 184 | 91.5% | 901 | 88.3% | 190 | 84.8% | 104 | 100.7% | 84 | 138.3% | 16 | 135.2% | 2 | 63.1% | 6 | 122.5% | 0 | 0.0% | 0 | 0.0% | |||||||||||||
91-95 | 60 | 82.8% | 248 | 83.8% | 25 | 87.0% | 13 | 122.9% | 11 | 143.2% | 0 | 0.0% | 1 | 95.0% | 0 | 0.0% | 1 | 61.0% | |||||||||||||||
96-100 | 4 | 75.9% | 10 | 85.5% | 1 | 41.4% | 0 | 0.0% | |||||||||||||||||||||||||
106-110 | 0 | 0.0% | |||||||||||||||||||||||||||||||
111-115 | 0 | 0.0% | |||||||||||||||||||||||||||||||
Face_Amount_Band | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-100 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||
<10K | 0 | 0.0% | 65 | 90.0% | 87 | 92.6% | 647 | 85.3% | 104 | 86.0% | |||||
10K - <25K | 44 | 221.5% | 617 | 87.9% | 655 | 88.6% | 4,731 | 96.0% | 605 | 102.5% | |||||
25K - <50K | 100 | 180.0% | 1,052 | 103.0% | 1,761 | 98.3% | 3,985 | 101.5% | 784 | 102.7% | |||||
50K - <100K | 426 | 137.1% | 1,491 | 95.3% | 2,316 | 97.2% | 4,136 | 101.6% | 523 | 103.2% | |||||
100K - <250K | 420 | 96.5% | 3,504 | 99.1% | 3,977 | 99.2% | 4,635 | 100.7% | 379 | 107.2% | |||||
250K - <500K | 149 | 83.8% | 1,393 | 99.9% | 1,293 | 101.1% | 570 | 101.6% | 34 | 88.3% | |||||
500K - <1M | 81 | 95.2% | 667 | 99.7% | 487 | 99.2% | 175 | 104.1% | 5 | 69.8% | |||||
1M - <2.5M | 46 | 92.0% | 299 | 100.7% | 180 | 101.8% | 36 | 91.7% | 2 | 103.0% | |||||
2.5M - <5M | 6 | 109.2% | 26 | 104.5% | 10 | 99.6% | 2 | 83.2% | 1 | 105.5% | |||||
5M - <10M | 1 | 70.9% | 13 | 107.2% | 3 | 123.0% | 0 | 0.0% | |||||||
10M+ | 0 | 0.0% | 2 | 112.1% | 1 | 131.5% | 0 | 0.0% | |||||||
UW | SOA_Antp_Lvl_TP: 5 yr anticipated | SOA_Antp_Lvl_TP: 10 yr anticipated | SOA_Antp_Lvl_TP: 15 yr anticipated | SOA_Antp_Lvl_TP: 20 yr anticipated | SOA_Antp_Lvl_TP: Unknown | SOA_Antp_Lvl_TP: 30 yr anticipated | SOA_Antp_Lvl_TP: 25 yr anticipated | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||||
NS/1/2 | 881 | 92.7% | 1,065 | 92.9% | 643 | 102.9% | 783 | 97.8% | 500 | 98.7% | |||||||||||
NS/2/2 | 1,415 | 103.0% | 3,080 | 102.0% | 1,091 | 95.7% | 7,878 | 101.4% | 536 | 94.7% | 0 | 0.0% | |||||||||
NS/1/3 | 117 | 89.6% | 441 | 99.9% | 321 | 100.1% | 29 | 78.0% | 108 | 112.8% | |||||||||||
NS/2/3 | 148 | 107.8% | 569 | 97.9% | 360 | 95.6% | 68 | 118.6% | 118 | 112.1% | |||||||||||
NS/3/3 | 235 | 96.2% | 985 | 101.7% | 288 | 105.7% | 20 | 139.8% | 157 | 88.5% | |||||||||||
NS/1/4 | 19 | 97.6% | 465 | 102.6% | 225 | 94.0% | 2 | 201.5% | 78 | 109.5% | |||||||||||
NS/2/4 | 15 | 40.3% | 594 | 102.7% | 220 | 92.8% | 1 | 178.0% | 75 | 99.7% | |||||||||||
NS/3/4 | 5 | 44.9% | 312 | 99.8% | 81 | 102.5% | 0 | 0.0% | 54 | 126.2% | |||||||||||
NS/4/4 | 16 | 95.1% | 343 | 105.1% | 124 | 100.5% | 0 | 0.0% | 53 | 116.3% | |||||||||||
NS/U/U | 3,674 | 103.8% | 1,551 | 98.3% | 575 | 104.8% | 456 | 93.7% | 1,499 | 97.5% | 0 | 0.0% | 0 | 0.0% | |||||||
S/1/2 | 337 | 79.1% | 543 | 104.5% | 249 | 98.9% | 65 | 160.3% | 160 | 109.1% | |||||||||||
S/2/2 | 164 | 91.5% | 288 | 108.4% | 125 | 106.6% | 15 | 132.1% | 72 | 112.2% | |||||||||||
S/U/U | 2,126 | 103.0% | 1,251 | 101.0% | 291 | 110.4% | 1,470 | 101.6% | 797 | 91.6% | 0 | 0.0% | 0 | 0.0% | |||||||
U/U/U | 733 | 104.4% | 263 | 94.2% | 847 | 112.7% | 74 | 93.1% | 383 | 105.8% | 0 | 0.0% | 0 | 0.0% | |||||||
AA_Grp | SOA_Antp_Lvl_TP: 5 yr anticipated | SOA_Antp_Lvl_TP: 10 yr anticipated | SOA_Antp_Lvl_TP: 15 yr anticipated | SOA_Antp_Lvl_TP: Unknown | SOA_Antp_Lvl_TP: 20 yr anticipated | SOA_Antp_Lvl_TP: 25 yr anticipated | SOA_Antp_Lvl_TP: 30 yr anticipated | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||||
0-17 | 0 | 0.0% | 1 | 399.9% | 0 | 0.0% | 0 | 0.0% | |||||||||||||
18-25 | 17 | 66.1% | 2 | 51.3% | 0 | 0.0% | 9 | 70.5% | 1 | 3643.5% | 0 | 0.0% | |||||||||
26-30 | 47 | 90.1% | 9 | 66.1% | 1 | 25.9% | 33 | 107.1% | 0 | 0.0% | 0 | 0.0% | |||||||||
31-35 | 124 | 92.1% | 40 | 72.8% | 3 | 68.0% | 41 | 72.6% | 0 | 0.0% | 0 | 0.0% | |||||||||
36-40 | 193 | 103.5% | 121 | 90.6% | 4 | 37.5% | 89 | 90.3% | 9 | 120.4% | 0 | 0.0% | |||||||||
41-45 | 407 | 104.5% | 310 | 94.5% | 38 | 62.7% | 201 | 98.3% | 112 | 122.4% | 0 | 0.0% | |||||||||
46-50 | 782 | 104.1% | 602 | 97.9% | 159 | 90.8% | 367 | 94.8% | 285 | 109.2% | 0 | 0.0% | |||||||||
51-55 | 1,374 | 100.2% | 1,164 | 101.1% | 423 | 96.9% | 684 | 102.0% | 591 | 92.5% | 0 | 0.0% | 0 | 0.0% | |||||||
56-60 | 1,777 | 100.1% | 1,548 | 100.3% | 707 | 98.0% | 798 | 103.4% | 1,080 | 100.1% | 0 | 0.0% | 0 | 0.0% | |||||||
61-65 | 2,014 | 96.2% | 1,829 | 101.1% | 842 | 98.8% | 927 | 103.4% | 1,362 | 103.8% | 0 | 0.0% | 0 | 0.0% | |||||||
66-70 | 1,728 | 95.6% | 1,677 | 101.2% | 1,040 | 102.8% | 655 | 98.1% | 1,447 | 104.4% | 0 | 0.0% | 0 | 0.0% | |||||||
71-75 | 709 | 90.0% | 1,448 | 102.0% | 914 | 103.6% | 347 | 94.3% | 1,240 | 106.7% | 0 | 0.0% | 0 | 0.0% | |||||||
76-80 | 416 | 85.4% | 1,441 | 100.0% | 910 | 103.8% | 273 | 111.4% | 1,711 | 103.3% | 0 | 0.0% | |||||||||
81-85 | 237 | 103.9% | 1,171 | 102.8% | 334 | 111.9% | 127 | 113.1% | 1,713 | 89.6% | 0 | 0.0% | |||||||||
86-90 | 56 | 139.1% | 376 | 97.6% | 58 | 143.1% | 33 | 109.8% | 964 | 84.4% | 0 | 0.0% | |||||||||
91-95 | 4 | 269.7% | 11 | 114.9% | 7 | 85.0% | 5 | 11.6% | 332 | 89.7% | |||||||||||
96-100 | 0 | 0.0% | 1 | 7.7% | 14 | 72.8% | |||||||||||||||
106-110 | 0 | 0.0% | |||||||||||||||||||
111-115 | 0 | 0.0% | |||||||||||||||||||
SOA_Antp_Lvl_TP | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-100 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||
5 yr anticipated | 949 | 97.9% | 1,577 | 97.2% | 3,033 | 98.8% | 3,339 | 99.8% | 987 | 95.6% | |||||
10 yr anticipated | 5,922 | 100.3% | 3,018 | 99.8% | 2,496 | 100.1% | 314 | 104.7% | |||||||
15 yr anticipated | 3,407 | 100.7% | 1,462 | 96.9% | 571 | 122.5% | |||||||||
20 yr anticipated | 10,571 | 100.7% | 290 | 102.1% | |||||||||||
25 yr anticipated | 0 | 0.0% | 0 | 0.0% | |||||||||||
30 yr anticipated | 0 | 0.0% | |||||||||||||
Unknown | 324 | 84.3% | 1,630 | 101.5% | 1,312 | 102.6% | 1,049 | 105.4% | 275 | 98.0% | |||||
AA_Grp | UW: NS/U/U | UW: S/U/U | UW: U/U/U | UW: NS/1/2 | UW: NS/2/2 | UW: NS/1/3 | UW: NS/2/3 | UW: NS/3/3 | UW: NS/1/4 | UW: NS/4/4 | UW: S/1/2 | UW: S/2/2 | UW: NS/2/4 | UW: NS/3/4 | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | |||||||||||||||
0-17 | 1 | 299.9% | 0 | 0.0% | 0 | 0.0% | ||||||||||||||||||||||||||||||||||||
18-25 | 5 | 81.6% | 1 | 50.2% | 22 | 73.8% | 0 | 0.0% | 1 | 606.7% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | ||||||||||||||||||
26-30 | 24 | 113.5% | 10 | 103.3% | 42 | 87.1% | 2 | 287.7% | 2 | 51.4% | 3 | 58.6% | 1 | 41.0% | 1 | 26.4% | 1 | 69.4% | 0 | 0.0% | 2 | 65.6% | 2 | 428.1% | 0 | 0.0% | 0 | 0.0% | ||||||||||||||
31-35 | 62 | 101.4% | 32 | 73.6% | 47 | 115.7% | 9 | 74.4% | 11 | 63.5% | 11 | 73.6% | 8 | 101.2% | 9 | 62.2% | 2 | 61.7% | 0 | 0.0% | 9 | 84.4% | 6 | 118.6% | 1 | 15.8% | 1 | 114.8% | ||||||||||||||
36-40 | 99 | 88.0% | 68 | 73.4% | 14 | 103.3% | 46 | 91.5% | 71 | 121.5% | 28 | 95.7% | 21 | 144.4% | 28 | 94.8% | 7 | 32.5% | 2 | 42.2% | 15 | 73.8% | 8 | 72.3% | 5 | 96.0% | 4 | 86.4% | ||||||||||||||
41-45 | 269 | 116.0% | 159 | 87.8% | 31 | 221.5% | 114 | 103.8% | 256 | 117.5% | 43 | 104.9% | 43 | 99.8% | 62 | 92.4% | 15 | 71.7% | 5 | 65.3% | 41 | 89.8% | 18 | 60.6% | 9 | 48.4% | 3 | 19.8% | ||||||||||||||
46-50 | 529 | 96.3% | 354 | 91.9% | 51 | 173.1% | 290 | 100.9% | 479 | 99.5% | 81 | 99.3% | 63 | 85.7% | 109 | 106.7% | 37 | 98.2% | 24 | 150.6% | 83 | 84.1% | 56 | 85.2% | 20 | 104.3% | 19 | 139.3% | ||||||||||||||
51-55 | 1,036 | 97.2% | 748 | 101.0% | 168 | 153.8% | 475 | 94.1% | 940 | 103.7% | 113 | 92.5% | 136 | 106.6% | 136 | 93.9% | 75 | 95.8% | 34 | 117.3% | 186 | 106.2% | 96 | 119.4% | 64 | 108.7% | 29 | 92.2% | ||||||||||||||
56-60 | 1,366 | 97.7% | 1,043 | 104.9% | 347 | 117.7% | 602 | 89.5% | 1,369 | 102.9% | 141 | 105.2% | 168 | 105.7% | 221 | 105.5% | 113 | 109.2% | 47 | 93.3% | 236 | 91.8% | 116 | 99.0% | 84 | 89.6% | 57 | 116.6% | ||||||||||||||
61-65 | 1,536 | 97.9% | 1,179 | 100.0% | 571 | 99.0% | 643 | 97.8% | 1,661 | 102.4% | 173 | 97.2% | 195 | 101.7% | 262 | 104.8% | 122 | 89.3% | 68 | 122.1% | 257 | 92.6% | 136 | 108.6% | 112 | 104.0% | 59 | 105.6% | ||||||||||||||
66-70 | 1,320 | 100.3% | 994 | 101.4% | 500 | 99.8% | 576 | 100.4% | 1,692 | 100.1% | 142 | 92.0% | 206 | 100.9% | 262 | 92.8% | 125 | 106.5% | 90 | 111.7% | 281 | 111.6% | 117 | 115.9% | 158 | 92.3% | 84 | 106.9% | ||||||||||||||
71-75 | 673 | 106.0% | 594 | 115.4% | 222 | 93.2% | 389 | 94.9% | 1,613 | 102.5% | 97 | 77.0% | 181 | 90.9% | 237 | 105.1% | 103 | 112.3% | 92 | 81.1% | 141 | 106.5% | 62 | 109.8% | 169 | 106.1% | 85 | 95.4% | ||||||||||||||
76-80 | 460 | 110.0% | 402 | 106.9% | 165 | 95.7% | 329 | 102.2% | 2,322 | 94.3% | 116 | 115.2% | 152 | 86.4% | 202 | 87.4% | 115 | 102.7% | 115 | 94.9% | 77 | 116.8% | 39 | 134.4% | 184 | 111.4% | 73 | 104.5% | ||||||||||||||
81-85 | 257 | 118.3% | 257 | 122.4% | 97 | 84.3% | 280 | 91.5% | 2,163 | 91.7% | 58 | 133.3% | 73 | 121.5% | 129 | 113.8% | 66 | 132.9% | 51 | 111.0% | 24 | 97.2% | 5 | 38.5% | 87 | 73.7% | 35 | 59.7% | ||||||||||||||
86-90 | 93 | 123.9% | 80 | 100.0% | 20 | 160.0% | 95 | 81.1% | 1,114 | 82.4% | 9 | 176.6% | 15 | 128.3% | 26 | 158.3% | 8 | 44.7% | 8 | 145.2% | 2 | 166.5% | 2 | 284.2% | 12 | 58.4% | 3 | 161.7% | ||||||||||||||
91-95 | 24 | 68.5% | 14 | 123.7% | 2 | 80.7% | 22 | 108.6% | 293 | 85.1% | 1 | 74.1% | 1 | 893.4% | 1 | 44.3% | 0 | 0.0% | 0 | 0.0% | 1 | 137.2% | 0 | 0.0% | ||||||||||||||||||
96-100 | 1 | 44.7% | 1 | 27.2% | 0 | 0.0% | 13 | 82.7% | ||||||||||||||||||||||||||||||||||
106-110 | 0 | 0.0% | ||||||||||||||||||||||||||||||||||||||||
111-115 | 0 | 0.0% | ||||||||||||||||||||||||||||||||||||||||
UW | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-100 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||
NS/1/2 | 24 | 87.1% | 558 | 84.3% | 1,377 | 98.8% | 1,892 | 99.3% | 21 | 84.4% | |||||
NS/2/2 | 104 | 150.3% | 2,054 | 101.1% | 2,578 | 100.0% | 9,110 | 99.4% | 154 | 132.1% | |||||
NS/1/3 | 88 | 98.6% | 413 | 100.3% | 445 | 99.1% | 70 | 85.3% | 0 | 0.0% | |||||
NS/2/3 | 119 | 112.7% | 490 | 100.6% | 528 | 96.7% | 126 | 102.0% | 0 | 0.0% | |||||
NS/3/3 | 218 | 95.1% | 804 | 101.6% | 454 | 103.3% | 204 | 93.5% | 5 | 116.5% | |||||
NS/1/4 | 7 | 34.1% | 488 | 101.2% | 289 | 100.8% | 5 | 291.8% | |||||||
NS/2/4 | 8 | 46.1% | 621 | 100.4% | 274 | 97.5% | 2 | 253.6% | |||||||
NS/3/4 | 4 | 54.0% | 354 | 104.0% | 94 | 98.3% | 0 | 0.0% | |||||||
NS/4/4 | 5 | 69.7% | 380 | 105.2% | 151 | 104.8% | 0 | 0.0% | |||||||
NS/U/U | 268 | 140.3% | 1,182 | 101.9% | 2,296 | 99.6% | 3,562 | 98.8% | 447 | 98.8% | |||||
S/1/2 | 118 | 58.1% | 473 | 104.6% | 508 | 106.3% | 251 | 117.5% | 4 | 219.3% | |||||
S/2/2 | 65 | 88.0% | 296 | 106.5% | 230 | 105.2% | 72 | 119.9% | 1 | 267.7% | |||||
S/U/U | 213 | 109.8% | 963 | 96.7% | 1,498 | 103.7% | 2,991 | 102.8% | 270 | 90.7% | |||||
U/U/U | 32 | 80.3% | 53 | 72.9% | 48 | 101.0% | 632 | 114.2% | 1,535 | 103.1% | |||||
AA_Grp | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-100 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||
0-17 | 0 | 0.0% | 1 | 426.1% | 0 | 0.0% | |||||||||
18-25 | 25 | 66.0% | 1 | 34.4% | 2 | 106.9% | 1 | 302.7% | |||||||
26-30 | 39 | 87.2% | 49 | 96.2% | 2 | 29.3% | 0 | 0.0% | 0 | 0.0% | |||||
31-35 | 38 | 68.3% | 124 | 86.1% | 45 | 111.4% | 1 | 14.0% | 0 | 0.0% | |||||
36-40 | 85 | 102.7% | 197 | 89.6% | 103 | 100.9% | 30 | 97.4% | 1 | 64.6% | |||||
41-45 | 113 | 100.3% | 426 | 96.1% | 300 | 96.1% | 223 | 113.8% | 6 | 259.6% | |||||
46-50 | 152 | 88.5% | 697 | 100.6% | 690 | 96.8% | 627 | 105.4% | 29 | 126.3% | |||||
51-55 | 193 | 91.9% | 1,082 | 101.1% | 1,259 | 100.7% | 1,550 | 97.4% | 152 | 127.5% | |||||
56-60 | 184 | 117.3% | 1,199 | 98.9% | 1,598 | 98.7% | 2,523 | 100.2% | 406 | 117.1% | |||||
61-65 | 170 | 94.5% | 1,364 | 101.0% | 1,736 | 98.7% | 3,014 | 101.6% | 690 | 101.0% | |||||
66-70 | 129 | 84.7% | 1,207 | 100.3% | 1,694 | 101.6% | 2,870 | 102.1% | 647 | 94.5% | |||||
71-75 | 67 | 68.4% | 1,072 | 100.5% | 1,267 | 102.3% | 2,030 | 103.4% | 222 | 98.7% | |||||
76-80 | 55 | 84.8% | 1,064 | 103.3% | 1,242 | 101.6% | 2,234 | 99.0% | 156 | 110.2% | |||||
81-85 | 23 | 141.3% | 583 | 107.1% | 649 | 106.4% | 2,233 | 94.7% | 94 | 67.4% | |||||
86-90 | 63 | 118.3% | 179 | 112.0% | 1,222 | 89.8% | 23 | 137.1% | |||||||
91-95 | 0 | 0.0% | 4 | 77.0% | 346 | 71.7% | 9 | 96.7% | |||||||
96-100 | 13 | 64.6% | 2 | 63.5% | |||||||||||
106-110 | 0 | 0.0% | |||||||||||||
111-115 | 0 | 0.0% | |||||||||||||
8 Perm Modeling by Amount
8.1 Perm Model, Unknown Smoker
Code
dat.perm.unk <- readRDS("dat.perm.rds")
dat.perm.unk <- dat.perm.unk[Policies_Exposed > 0]
dat.perm.unk <- dat.perm.unk[UW == "U/U/U" &
Insurance_Plan == "Perm"]
bUseAllInteractions <- FALSE
AA.brks <- c(-1,17,
seq(25,120,5))
AA.lbls <- paste0(
AA.brks[1:(length(AA.brks)-1)]+1,
"-",
AA.brks[2:length(AA.brks)]
)
Dur.brks <- c(0,1,2,3,5,10,15,20,30,120)
Dur.lbls <- paste0(
Dur.brks[1:(length(Dur.brks)-1)]+1,
"-",
Dur.brks[2:length(Dur.brks)]
)
dat.perm.unk[,`:=`(
AA_Grp=cut(Attained_Age,
breaks=AA.brks,
labels=AA.lbls),
Dur_Grp=cut(Duration,
breaks=Dur.brks,
labels=Dur.lbls)
)]
pred.cols <- names(dat.perm.unk)[c(1,5,16:17)]
factor.cols <- pred.cols
dat.perm.unk[,
(factor.cols):=lapply(.SD,factor),
.SDcols=factor.cols]
set.seed(traintest.seed)
dat.perm.unk %>%
mutate(
IsTraining = (runif(nrow(.)) < training.fraction),
Noise = rnorm(nrow(.)),
.before = 1
) %>%
mutate(Face_Amount_Band=fct_relabel(
Face_Amount_Band,
#function(.) sub(":"," -",.,fixed=T)
function(.) fa.remap[Face_Amount_Band.Old==.,Face_Amount_Band.New]
),
AE_Count=Death_Count/ExpDth_Cnt_VBT2015,
AE_Amount=Death_Claim_Amount/ExpDth_Amt_VBT2015
) ->
dat.perm.unk
gbm.pred.cols <- c("Noise",pred.cols)Here is a data preview.
Code
dat.perm.unk %>%
head(10) %>%
flextable()IsTraining | Noise | Sex | Smoker_Status | Attained_Age | Duration | Face_Amount_Band | Insurance_Plan | Number_of_Pfd_Classes | Preferred_Class | Death_Count | Policies_Exposed | ExpDth_Cnt_VBT2015 | Death_Claim_Amount | Amount_Exposed | ExpDth_Amt_VBT2015 | UW | AA_Grp | Dur_Grp | AE_Count | AE_Amount |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
TRUE | -1.31531994 | M | U | 72 | 56 | 250K - <500K | Perm | U | U | 0 | 5.465753 | 0.1014444 | 0 | 1,745,572 | 32,397.82 | U/U/U | 71-75 | 31-120 | 0.0000000 | 0.0000000 |
TRUE | -0.65764994 | M | U | 73 | 57 | 10K - <25K | Perm | U | U | 151 | 7,161.337555 | 150.0379591 | 1,979,552 | 95,811,011 | 2,007,923.42 | U/U/U | 71-75 | 31-120 | 1.0064120 | 0.9858703 |
TRUE | 0.78905215 | M | U | 73 | 57 | 25K - <50K | Perm | U | U | 26 | 1,271.731550 | 26.6477580 | 938,930 | 42,122,230 | 882,099.08 | U/U/U | 71-75 | 31-120 | 0.9756918 | 1.0644269 |
TRUE | -1.52205566 | M | U | 73 | 57 | 100K - <250K | Perm | U | U | 2 | 75.895890 | 1.5842799 | 295,327 | 10,165,449 | 212,139.10 | U/U/U | 71-75 | 31-120 | 1.2624032 | 1.3921385 |
TRUE | 0.07196495 | M | U | 74 | 58 | 50K - <100K | Perm | U | U | 4 | 328.650822 | 7.7000963 | 270,364 | 21,161,507 | 495,822.79 | U/U/U | 71-75 | 31-120 | 0.5194740 | 0.5452835 |
TRUE | -0.18478717 | M | U | 74 | 58 | 250K - <500K | Perm | U | U | 0 | 6.336987 | 0.1482855 | 0 | 2,052,935 | 48,038.67 | U/U/U | 71-75 | 31-120 | 0.0000000 | 0.0000000 |
FALSE | 0.47450347 | M | U | 75 | 59 | <10K | Perm | U | U | 469 | 19,436.460915 | 511.1919127 | 1,892,560 | 81,348,082 | 2,137,055.46 | U/U/U | 71-75 | 31-120 | 0.9174637 | 0.8855924 |
TRUE | -1.04162923 | M | U | 75 | 59 | 250K - <500K | Perm | U | U | 0 | 6.361337 | 0.1667943 | 0 | 2,021,135 | 52,994.16 | U/U/U | 71-75 | 31-120 | 0.0000000 | 0.0000000 |
TRUE | 0.40207422 | M | U | 76 | 60 | <10K | Perm | U | U | 523 | 18,052.611237 | 529.5150148 | 2,156,603 | 74,124,703 | 2,171,516.43 | U/U/U | 76-80 | 31-120 | 0.9876963 | 0.9931323 |
TRUE | 1.01522821 | M | U | 76 | 60 | 10K - <25K | Perm | U | U | 97 | 3,605.502399 | 105.6160386 | 1,358,119 | 49,470,772 | 1,448,978.11 | U/U/U | 76-80 | 31-120 | 0.9184211 | 0.9372944 |
8.1.1 Feature Discovery with Catboost
As in the predictive analytics framework, gradient boosted machines as implemented with Catboost are used for exploratory data analysis. The framework uses LightGBM, while Catboost is used here. LightGBM does not currently support GPUs under Windows Subsystem for Linux 2, which is why Catboost is used here.
Code
dat.perm.unk %>%
filter(IsTraining == TRUE) %>%
select(all_of(gbm.pred.cols)) %>%
mutate(Sex = as.numeric(Sex)) %>%
catboost.load_pool(
data=.,
label = dat.perm.unk[IsTraining==TRUE,AE_Amount],
weight = dat.perm.unk[IsTraining==TRUE,ExpDth_Amt_VBT2015]) ->
train_pool_perm_unk
dat.perm.unk %>%
filter(IsTraining == FALSE) %>%
select(all_of(gbm.pred.cols)) %>%
mutate(Sex = as.numeric(Sex)) %>%
catboost.load_pool(
data=.,
label = dat.perm.unk[IsTraining==FALSE,AE_Amount],
weight = dat.perm.unk[IsTraining==FALSE,ExpDth_Amt_VBT2015]) ->
test_pool_perm_unk
if(bUseCache & file.exists(
'dat.term.mod.perm.unk.cbm'
) & !bInvalidateCaches)
{
cb.model.perm.unk <- catboost.load_model(model_path = 'dat.term.mod.perm.unk.cbm')
} else {
cb.model.perm.unk <- catboost.train(learn_pool=train_pool_perm_unk,
test_pool = test_pool_perm_unk,
params=fit_params)
catboost.save_model(cb.model.perm.unk,
model_path = 'dat.term.mod.perm.unk.cbm')
}8.1.2 Feature Importance
Next is to check for the variables with most variability. Duration, face amount, and attained age top the importance chart.
Code
shp.perm.unk <- shapviz(
cb.model.perm.unk,
X=as.data.frame(dat.perm.unk[IsTraining==TRUE,..gbm.pred.cols]),
X_pred=train_pool_perm_unk
)
setDT(shp.perm.unk$X)
sv_importance(shp.perm.unk) + theme_minimal()
8.1.3 Feature Interactions
Code
imp.int.perm.unk <- catboost.get_feature_importance(
cb.model.perm.unk,
type="Interaction"
)
mod.ft.map.perm.unk <- data.table(
FeatureNames=names(dat.perm.unk[IsTraining==TRUE,..gbm.pred.cols])
)
mod.ft.map.perm.unk[,ID:=1:nrow(.SD)-1]
imp.int.perm.unk %>%
merge(mod.ft.map.perm.unk,
by.x="feature1_index",
by.y="ID") %>%
merge(mod.ft.map.perm.unk,
by.x="feature2_index",
by.y="ID") %>%
setnames(
old=c("FeatureNames.x","FeatureNames.y"),
new=c("Feature1","Feature2")
) %>%
mutate(feature1_index=NULL,feature2_index=NULL) %>%
as.data.table() %>%
setcolorder(c("Feature1","Feature2","score")) ->
imp.int.perm.unk
imp.int.perm.unk[order(-score)] %>%
filter(Feature1 != "Noise") %>%
flextable() %>%
colformat_double(j="score",digits=2)Feature1 | Feature2 | score |
|---|---|---|
Face_Amount_Band | AA_Grp | 23.49 |
Face_Amount_Band | Dur_Grp | 19.03 |
AA_Grp | Dur_Grp | 12.30 |
Sex | Face_Amount_Band | 3.54 |
Sex | AA_Grp | 2.79 |
Sex | Dur_Grp | 1.96 |
8.1.4 Feature Interaction Plots
Each of the interactions are discussed below with plots using SHAP values from both sides of the interaction.
8.1.4.1 Attained Age Group
8.1.4.1.1 Face Amount Band SHAPs
Several things are apparent in the following ridge plot:
- The two lowest face amount bands, <10K and 10k - <25K, tend to be strongly separated rightward from the others.
- Starting at about attained age 61 or so, the difference between those two low bands and the others narrows.
- This suggests the potential that the slope of the 2015 VBT above attained age 65 for unknown perm business is generally off.
Code
data.table(
cbind(
shp.perm.unk$X[,.(Face_Amount_Band,
AA_Grp)],
shap=shp.perm.unk$S[,"Face_Amount_Band"]
)
) %>%
ggplot(aes(y=AA_Grp, x=exp(shap),color=Face_Amount_Band,fill=Face_Amount_Band)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,NA)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("by attained age")) +
theme_minimal()
8.1.4.1.2 Attained Age SHAPs
The interaction within attained age group SHAPs is harder to trace out. Higher attained ages 61+ exhibit different locations of the SHAP distribution for lower face amounts than higher. This is borne out in both views below.
Code
plot.lbls.aa <- dat.perm.unk[,levels(AA_Grp)]
plot.lbls.aa[-(1:5)*4] <- ""
data.table(
cbind(
shp.perm.unk$X[,.(Face_Amount_Band,
AA_Grp)],
shap=shp.perm.unk$S[,"AA_Grp"]
)
) %>%
ggplot(aes(y=AA_Grp, x=exp(shap),color=Face_Amount_Band,fill=Face_Amount_Band)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,NA)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
scale_y_discrete(labels=plot.lbls.aa) +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect AA_Grp"),
subtitle = paste0("by attained age")) +
theme_minimal() +
facet_wrap(vars(Face_Amount_Band))
Code
plot.lbls.fa <- dat.perm.unk[,levels(Face_Amount_Band)]
plot.lbls.fa[-c(1,6,11)] <- ""
data.table(
cbind(
shp.perm.unk$X[,.(Face_Amount_Band,
AA_Grp)],
shap=shp.perm.unk$S[,"AA_Grp"]
)
) %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=AA_Grp,fill=AA_Grp)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,NA)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
scale_y_discrete(labels=plot.lbls.fa) +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect AA_Grp"),
subtitle = paste0("by face amount band")) +
theme_minimal() +
facet_wrap(vars(AA_Grp))
8.1.4.2 Duration Group
8.1.4.2.1 Face Amount Band SHAPs
There is some suggestion of differing slope by duration across face amount bands.
Code
data.table(
cbind(
shp.perm.unk$X[,.(Face_Amount_Band,
Dur_Grp)],
shap=shp.perm.unk$S[,"Face_Amount_Band"]
)
) %>%
ggplot(aes(y=Dur_Grp, x=exp(shap),color=Face_Amount_Band,fill=Face_Amount_Band)) +
stat_density_ridges(alpha=0.9,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,NA)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("by face amount and duration")) +
theme_minimal() +
facet_wrap(vars(Face_Amount_Band))
8.1.4.2.2 Duration Group SHAPs
There are at least two sources of interaction here:
- Early duration and low face amount
- Multimodal distributions, with a diversity in the number and location of modes
Code
data.table(
cbind(
shp.perm.unk$X[,.(Face_Amount_Band,
Dur_Grp)],
shap=shp.perm.unk$S[,"Dur_Grp"]
)
) %>%
ggplot(aes(y=Dur_Grp, x=exp(shap),color=Face_Amount_Band,fill=Face_Amount_Band)) +
stat_density_ridges(alpha=0.9,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,NA)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Dur_Grp"),
subtitle = paste0("by face amount and duration")) +
theme_minimal() +
facet_wrap(vars(Face_Amount_Band))
8.1.4.3 Attained Age vs Duration
8.1.4.3.1 Attained Age SHAPs
There appears to be an interaction for durations 16+, attained ages 61+, where the attained age SHAP is lower than for others.
Code
data.table(
cbind(
shp.perm.unk$X[,.(AA_Grp,
Dur_Grp)],
shap=shp.perm.unk$S[,"AA_Grp"]
)
) %>%
ggplot(aes(y=AA_Grp, x=exp(shap),color=Dur_Grp,fill=Dur_Grp)) +
stat_density_ridges(alpha=0.9,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,NA)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
scale_y_discrete(labels=plot.lbls.aa) +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect AA_Grp")) +
theme_minimal() +
facet_wrap(vars(Dur_Grp))
8.1.4.3.2 Duration SHAPs
The opposite is true within the duration SHAPs. Here, there is an interaction for early durations <16 for attained ages 61+.
Code
data.table(
cbind(
shp.perm.unk$X[,.(AA_Grp,
Dur_Grp)],
shap=shp.perm.unk$S[,"Dur_Grp"]
)
) %>%
ggplot(aes(y=AA_Grp, x=exp(shap),color=Dur_Grp,fill=Dur_Grp)) +
stat_density_ridges(alpha=0.9,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,NA)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
scale_y_discrete(labels=plot.lbls.aa) +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Dur_Grp")) +
theme_minimal() +
facet_wrap(vars(Dur_Grp))
Overall, this suggests that the current dataset and 2015 VBT may not have slopes in sync at older ages.
8.1.5 Next Steps in Modeling
The catboost modeling is informative here for exploratory analytics. We next build an elastic net model which includes the main effects plus the top eight interactions from the catboost analysis. This cutoff is chosen arbitrarily. The top three are stronger than the others, while the next five seem to cluster in the middle. These interactions may turn out to be unneeded. Elastic net modeling will reveal which is truly important in a mortality model.
While the work for supporting this is omitted here, it became clear that separate models should be fit for above and below 100K face amounts. A unified model had difficulty adequately fitting face amounts below 100K.
8.1.6 Elastic Net Models
The following formula is used below:
Code
if(bUseAllInteractions) {
glmnetFormula <- as.formula(
paste0(
"~ -1 + (",
paste(pred.cols,collapse=" + "),
")^2"
)
)
} else {
glmnetFormula <- as.formula(
paste(c("~ -1",
pred.cols,
imp.int.perm.unk[order(-score)][Feature1 != "Noise",
paste0(Feature1,":",Feature2)]),
collapse=" + ")
)
}
print(glmnetFormula)~-1 + Sex + Face_Amount_Band + AA_Grp + Dur_Grp + Face_Amount_Band:AA_Grp +
Face_Amount_Band:Dur_Grp + AA_Grp:Dur_Grp + Sex:Face_Amount_Band +
Sex:AA_Grp + Sex:Dur_GrpThe interactions included in the model are as follows:
Code
data.table(Interaction=imp.int.perm.unk[order(-score)][Feature1 != "Noise",
paste0(Feature1,":",Feature2)]) %>%
flextable()Interaction |
|---|
Face_Amount_Band:AA_Grp |
Face_Amount_Band:Dur_Grp |
AA_Grp:Dur_Grp |
Sex:Face_Amount_Band |
Sex:AA_Grp |
Sex:Dur_Grp |
8.1.6.1 Model Fit
Code
dat.perm.unk.el <- prepELData(
formula=glmnetFormula,
data=dat.perm.unk,
predictors = pred.cols,
response = "AE_Amount",
weights = "ExpDth_Amt_VBT2015",
useSparse = T
)
set.seed(cvfit.seed)
if(bUseCache & file.exists(
'perm.model.unk.el.rds'
) & !bInvalidateCaches)
{
cvfit.perm.unk <- readRDS('perm.model.unk.el.rds')
} else
{
cvfit.perm.unk <- fitCVGLMNet(
dat.perm.unk.el,
nfolds = nFolds
)
if(bUseCache)
saveRDS(cvfit.perm.unk, 'perm.model.unk.el.rds')
}8.1.6.1.1 Usual plots for Elastic Net Models
When presenting elastic net models, the cross validation plot for \(\lambda\) and the coefficient shrinkage plots are provided.
At the minimum \(\lambda\) of 0.0001798, the model has 174 parameters.
Code
plot(cvfit.perm.unk)
Code
plot(cvfit.perm.unk$glmnet.fit,xvar="lambda")
8.1.6.1.2 Factor Table
The exponentiated coefficients are as follows:
Code
reformatCoefs(cvfit.perm.unk, pred.cols) %>%
filter(Coef != 0) %>%
select(Feature1Name,
Feature1Level,
Feature2Name,
Feature2Level,
Coef) %>%
mutate(Coef=exp(Coef)) %>%
flextable() %>%
set_formatter(
Coef=function(x) paste0(sprintf("%.01f", 100*x),"%")
) %>%
theme_vanilla()Feature1Name | Feature1Level | Feature2Name | Feature2Level | Coef |
|---|---|---|---|---|
(Intercept) | (Intercept) | 133.8% | ||
Sex | F | 99.7% | ||
Sex | M | 101.2% | ||
Face_Amount_Band | 25K - <50K | 83.8% | ||
Face_Amount_Band | 50K - <100K | 79.2% | ||
Face_Amount_Band | 100K - <250K | 67.6% | ||
Face_Amount_Band | 250K - <500K | 76.1% | ||
Face_Amount_Band | 500K - <1M | 64.8% | ||
Face_Amount_Band | 1M - <2.5M | 57.0% | ||
AA_Grp | 18-25 | 95.9% | ||
AA_Grp | 26-30 | 104.2% | ||
AA_Grp | 31-35 | 107.1% | ||
AA_Grp | 41-45 | 108.2% | ||
AA_Grp | 46-50 | 127.8% | ||
AA_Grp | 51-55 | 133.6% | ||
AA_Grp | 56-60 | 127.1% | ||
AA_Grp | 61-65 | 122.5% | ||
AA_Grp | 66-70 | 112.7% | ||
AA_Grp | 71-75 | 109.8% | ||
AA_Grp | 76-80 | 103.6% | ||
AA_Grp | 81-85 | 99.1% | ||
AA_Grp | 86-90 | 95.5% | ||
AA_Grp | 91-95 | 93.3% | ||
AA_Grp | 96-100 | 96.3% | ||
AA_Grp | 101-105 | 100.2% | ||
Dur_Grp | 6-10 | 115.2% | ||
Dur_Grp | 11-15 | 117.1% | ||
Dur_Grp | 16-20 | 106.5% | ||
Dur_Grp | 21-30 | 97.9% | ||
Dur_Grp | 31-120 | 81.1% | ||
Face_Amount_Band | 10K - <25K | AA_Grp | 18-25 | 97.8% |
Face_Amount_Band | 10M+ | AA_Grp | 18-25 | 163.3% |
Face_Amount_Band | 25K - <50K | AA_Grp | 31-35 | 102.5% |
Face_Amount_Band | 50K - <100K | AA_Grp | 31-35 | 101.6% |
Face_Amount_Band | 250K - <500K | AA_Grp | 31-35 | 95.1% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 36-40 | 107.8% |
Face_Amount_Band | 10K - <25K | AA_Grp | 46-50 | 102.3% |
Face_Amount_Band | 50K - <100K | AA_Grp | 46-50 | 96.0% |
Face_Amount_Band | 25K - <50K | AA_Grp | 51-55 | 85.4% |
Face_Amount_Band | 50K - <100K | AA_Grp | 51-55 | 87.6% |
Face_Amount_Band | 100K - <250K | AA_Grp | 51-55 | 86.3% |
Face_Amount_Band | 10K - <25K | AA_Grp | 56-60 | 99.7% |
Face_Amount_Band | 25K - <50K | AA_Grp | 56-60 | 87.1% |
Face_Amount_Band | 50K - <100K | AA_Grp | 56-60 | 77.4% |
Face_Amount_Band | 100K - <250K | AA_Grp | 56-60 | 87.0% |
Face_Amount_Band | 25K - <50K | AA_Grp | 61-65 | 94.5% |
Face_Amount_Band | 50K - <100K | AA_Grp | 61-65 | 85.6% |
Face_Amount_Band | 100K - <250K | AA_Grp | 61-65 | 91.4% |
Face_Amount_Band | 250K - <500K | AA_Grp | 61-65 | 96.9% |
Face_Amount_Band | 500K - <1M | AA_Grp | 61-65 | 79.6% |
Face_Amount_Band | 25K - <50K | AA_Grp | 66-70 | 98.3% |
Face_Amount_Band | 50K - <100K | AA_Grp | 66-70 | 90.5% |
Face_Amount_Band | 100K - <250K | AA_Grp | 66-70 | 97.6% |
Face_Amount_Band | 250K - <500K | AA_Grp | 66-70 | 85.2% |
Face_Amount_Band | 500K - <1M | AA_Grp | 66-70 | 85.9% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 66-70 | 58.9% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 66-70 | 75.9% |
Face_Amount_Band | 10K - <25K | AA_Grp | 71-75 | 99.3% |
Face_Amount_Band | 25K - <50K | AA_Grp | 71-75 | 97.8% |
Face_Amount_Band | 50K - <100K | AA_Grp | 71-75 | 93.3% |
Face_Amount_Band | 100K - <250K | AA_Grp | 71-75 | 98.6% |
Face_Amount_Band | 250K - <500K | AA_Grp | 71-75 | 88.2% |
Face_Amount_Band | 500K - <1M | AA_Grp | 71-75 | 102.4% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 71-75 | 95.1% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 71-75 | 59.7% |
Face_Amount_Band | 10K - <25K | AA_Grp | 76-80 | 97.4% |
Face_Amount_Band | 25K - <50K | AA_Grp | 76-80 | 99.0% |
Face_Amount_Band | 100K - <250K | AA_Grp | 76-80 | 107.0% |
Face_Amount_Band | 500K - <1M | AA_Grp | 76-80 | 92.2% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 76-80 | 89.7% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 76-80 | 82.2% |
Face_Amount_Band | 10M+ | AA_Grp | 76-80 | 88.0% |
Face_Amount_Band | 10K - <25K | AA_Grp | 81-85 | 97.9% |
Face_Amount_Band | 25K - <50K | AA_Grp | 81-85 | 101.3% |
Face_Amount_Band | 50K - <100K | AA_Grp | 81-85 | 106.0% |
Face_Amount_Band | 100K - <250K | AA_Grp | 81-85 | 117.4% |
Face_Amount_Band | 250K - <500K | AA_Grp | 81-85 | 100.0% |
Face_Amount_Band | 500K - <1M | AA_Grp | 81-85 | 105.1% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 81-85 | 93.5% |
Face_Amount_Band | 10K - <25K | AA_Grp | 86-90 | 100.1% |
Face_Amount_Band | 25K - <50K | AA_Grp | 86-90 | 106.8% |
Face_Amount_Band | 50K - <100K | AA_Grp | 86-90 | 112.9% |
Face_Amount_Band | 100K - <250K | AA_Grp | 86-90 | 126.9% |
Face_Amount_Band | 250K - <500K | AA_Grp | 86-90 | 113.1% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 86-90 | 133.4% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 86-90 | 152.0% |
Face_Amount_Band | 10K - <25K | AA_Grp | 91-95 | 104.3% |
Face_Amount_Band | 25K - <50K | AA_Grp | 91-95 | 113.8% |
Face_Amount_Band | 50K - <100K | AA_Grp | 91-95 | 124.4% |
Face_Amount_Band | 100K - <250K | AA_Grp | 91-95 | 138.9% |
Face_Amount_Band | 250K - <500K | AA_Grp | 91-95 | 126.5% |
Face_Amount_Band | 500K - <1M | AA_Grp | 91-95 | 125.8% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 91-95 | 111.1% |
Face_Amount_Band | 10K - <25K | AA_Grp | 96-100 | 104.6% |
Face_Amount_Band | 25K - <50K | AA_Grp | 96-100 | 115.9% |
Face_Amount_Band | 50K - <100K | AA_Grp | 96-100 | 129.0% |
Face_Amount_Band | 100K - <250K | AA_Grp | 96-100 | 138.9% |
Face_Amount_Band | 250K - <500K | AA_Grp | 96-100 | 128.4% |
Face_Amount_Band | 500K - <1M | AA_Grp | 96-100 | 109.4% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 96-100 | 159.7% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 96-100 | 151.2% |
Face_Amount_Band | 5M - <10M | AA_Grp | 96-100 | 323.2% |
Face_Amount_Band | 500K - <1M | AA_Grp | 101-105 | 100.6% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 101-105 | 105.9% |
Face_Amount_Band | 2.5M - <5M | Dur_Grp | 2-2 | 112.9% |
Face_Amount_Band | 10K - <25K | Dur_Grp | 6-10 | 102.5% |
Face_Amount_Band | 100K - <250K | Dur_Grp | 11-15 | 88.4% |
Face_Amount_Band | 250K - <500K | Dur_Grp | 11-15 | 87.6% |
Face_Amount_Band | 10M+ | Dur_Grp | 11-15 | 267.1% |
Face_Amount_Band | 250K - <500K | Dur_Grp | 16-20 | 97.2% |
Face_Amount_Band | 1M - <2.5M | Dur_Grp | 16-20 | 97.2% |
Face_Amount_Band | 10M+ | Dur_Grp | 16-20 | 263.7% |
Face_Amount_Band | 10K - <25K | Dur_Grp | 21-30 | 90.7% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 21-30 | 94.5% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 21-30 | 93.9% |
Face_Amount_Band | 250K - <500K | Dur_Grp | 21-30 | 101.5% |
Face_Amount_Band | 500K - <1M | Dur_Grp | 21-30 | 99.4% |
Face_Amount_Band | 2.5M - <5M | Dur_Grp | 21-30 | 71.6% |
Face_Amount_Band | 10K - <25K | Dur_Grp | 31-120 | 93.2% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 31-120 | 100.3% |
Face_Amount_Band | 100K - <250K | Dur_Grp | 31-120 | 109.9% |
Face_Amount_Band | 250K - <500K | Dur_Grp | 31-120 | 104.3% |
Face_Amount_Band | 500K - <1M | Dur_Grp | 31-120 | 119.6% |
Face_Amount_Band | 1M - <2.5M | Dur_Grp | 31-120 | 140.2% |
Face_Amount_Band | 10M+ | Dur_Grp | 31-120 | 59.5% |
AA_Grp | 18-25 | Dur_Grp | 6-10 | 96.4% |
AA_Grp | 71-75 | Dur_Grp | 6-10 | 114.9% |
AA_Grp | 76-80 | Dur_Grp | 6-10 | 101.4% |
AA_Grp | 81-85 | Dur_Grp | 6-10 | 107.7% |
AA_Grp | 18-25 | Dur_Grp | 11-15 | 103.4% |
AA_Grp | 66-70 | Dur_Grp | 11-15 | 102.3% |
AA_Grp | 71-75 | Dur_Grp | 11-15 | 110.2% |
AA_Grp | 76-80 | Dur_Grp | 11-15 | 101.3% |
AA_Grp | 18-25 | Dur_Grp | 16-20 | 88.9% |
AA_Grp | 26-30 | Dur_Grp | 16-20 | 99.9% |
AA_Grp | 66-70 | Dur_Grp | 16-20 | 105.1% |
AA_Grp | 71-75 | Dur_Grp | 16-20 | 103.6% |
AA_Grp | 91-95 | Dur_Grp | 16-20 | 99.1% |
AA_Grp | 18-25 | Dur_Grp | 21-30 | 114.7% |
AA_Grp | 26-30 | Dur_Grp | 21-30 | 120.3% |
AA_Grp | 56-60 | Dur_Grp | 21-30 | 100.3% |
AA_Grp | 66-70 | Dur_Grp | 21-30 | 99.8% |
AA_Grp | 71-75 | Dur_Grp | 21-30 | 99.6% |
AA_Grp | 81-85 | Dur_Grp | 21-30 | 94.6% |
AA_Grp | 86-90 | Dur_Grp | 21-30 | 89.7% |
AA_Grp | 31-35 | Dur_Grp | 31-120 | 117.6% |
AA_Grp | 46-50 | Dur_Grp | 31-120 | 105.1% |
AA_Grp | 56-60 | Dur_Grp | 31-120 | 92.6% |
AA_Grp | 61-65 | Dur_Grp | 31-120 | 83.5% |
AA_Grp | 66-70 | Dur_Grp | 31-120 | 84.3% |
AA_Grp | 71-75 | Dur_Grp | 31-120 | 88.6% |
AA_Grp | 76-80 | Dur_Grp | 31-120 | 95.8% |
Sex | M | Face_Amount_Band | 10K - <25K | 108.1% |
Sex | M | Face_Amount_Band | 25K - <50K | 106.1% |
Sex | M | Face_Amount_Band | 50K - <100K | 104.7% |
Sex | M | Face_Amount_Band | 100K - <250K | 102.4% |
Sex | M | Face_Amount_Band | 250K - <500K | 98.7% |
Sex | M | Face_Amount_Band | 1M - <2.5M | 93.0% |
Sex | M | Face_Amount_Band | 2.5M - <5M | 69.4% |
Sex | M | Face_Amount_Band | 5M - <10M | 57.7% |
Sex | M | Face_Amount_Band | 10M+ | 150.4% |
Sex | M | AA_Grp | 31-35 | 104.0% |
Sex | M | AA_Grp | 51-55 | 111.4% |
Sex | M | AA_Grp | 56-60 | 111.2% |
Sex | M | AA_Grp | 61-65 | 105.7% |
Sex | M | AA_Grp | 66-70 | 108.8% |
Sex | M | AA_Grp | 71-75 | 102.5% |
Sex | M | AA_Grp | 81-85 | 99.7% |
Sex | M | AA_Grp | 86-90 | 96.1% |
Sex | M | AA_Grp | 91-95 | 96.4% |
Sex | M | AA_Grp | 96-100 | 100.3% |
Sex | M | AA_Grp | 101-105 | 107.6% |
Sex | M | Dur_Grp | 16-20 | 101.1% |
Sex | M | Dur_Grp | 21-30 | 102.9% |
Note that interaction terms must be considered together, as noted in prior sections. Since penalization is roughly equivalent to Bayesian credibility, these factors are arguably credible. This is true even when dealing with factors with small effect sizes, such as the standalone factor for Duration 3.
Plots of effects are much more digestible.
In the plots and tables that follow, we fix all of the other variables at their middle values when extracting final factors.
We generate some supporting tables: a factor grid for attaching to the experience, and a list of interactions present in the model
Code
dat.perm.unk[,..pred.cols] %>%
lapply(levels) %>%
expand.grid() %>%
setDT() ->
dat.perm.unk.grid
dat.perm.unk.grid %>%
model.Matrix(
object=glmnetFormula,
data=.,
sparse=T
) %>%
predict(
cvfit.perm.unk,
newx=.,
s="lambda.min"
) %>%
as.vector() ->
newCoef
dat.perm.unk.grid %>%
add_column(
Factor=exp(newCoef)
) %>%
setDT() ->
dat.perm.unk.grid
write.xlsx(dat.perm.unk.grid,
file="dat.perm.unk.grid.xlsx")
reformatCoefs(cvfit.perm.unk, pred.cols) %>%
filter(Coef != 0 & !is.na(Feature2Name)) %>%
select(Feature1Name,Feature2Name) %>%
distinct() %>%
as.list() %>%
purrr::list_transpose() ->
perm.unk.int.list8.1.6.1.3 Plots of Terms
Below are plots of the 2-way interaction terms, with external factors fixed at their middle values.
- Attained Age x Face Amount Band: A “ridge” between attained ages 35 and 70 is apparent at the lowest face amounts. The ridge vanishes with increasing face amount, then reappears at higher face amounts.
- Duration x Face Amount Band: A similar though smaller “ridge” is observed for durations 6-30.
- Attained Age x Duration: Mortality by attained age steepens with increasing age from 81-100, with declining slope by duration at later durations.
- Face Amount Band x Sex: This interaction may be misleading. There is very little data at such large face amounts, especially for females. This can be observed in the Goodness-of-Fit section.
- Attained Age x Sex: The interaction here appears to be with males aged 46-70, with increased mortality.
8.1.6.1.4 Tables of Terms
Below are tables of the 2-way interaction terms, with external factors fixed at their middle values.
AA_Grp | <10K | 10K - <25K | 25K - <50K | 50K - <100K | 100K - <250K | 250K - <500K | 500K - <1M | 1M - <2.5M | 2.5M - <5M | 5M - <10M | 10M+ |
|---|---|---|---|---|---|---|---|---|---|---|---|
0-17 | 133.4% | 133.4% | 111.8% | 105.6% | 90.2% | 101.5% | 86.4% | 76.0% | 133.4% | 133.4% | 133.4% |
18-25 | 127.9% | 125.1% | 107.2% | 101.2% | 86.5% | 97.4% | 82.9% | 72.9% | 127.9% | 127.9% | 208.9% |
26-30 | 138.9% | 138.9% | 116.4% | 110.0% | 93.9% | 105.8% | 90.0% | 79.2% | 138.9% | 138.9% | 138.9% |
31-35 | 142.8% | 142.8% | 122.7% | 114.8% | 96.5% | 103.4% | 92.6% | 81.4% | 142.8% | 142.8% | 142.8% |
36-40 | 133.4% | 133.4% | 111.8% | 105.6% | 90.2% | 101.5% | 86.4% | 82.0% | 133.4% | 133.4% | 133.4% |
41-45 | 144.4% | 144.4% | 121.0% | 114.3% | 97.6% | 109.9% | 93.6% | 82.3% | 144.4% | 144.4% | 144.4% |
46-50 | 170.5% | 174.4% | 142.9% | 129.5% | 115.2% | 129.8% | 110.5% | 97.2% | 170.5% | 170.5% | 170.5% |
51-55 | 178.2% | 178.2% | 127.5% | 123.5% | 104.0% | 135.7% | 115.5% | 101.6% | 178.2% | 178.2% | 178.2% |
56-60 | 169.6% | 169.1% | 123.8% | 104.0% | 99.7% | 129.1% | 109.9% | 96.7% | 169.6% | 169.6% | 169.6% |
61-65 | 163.4% | 163.4% | 129.4% | 110.8% | 101.0% | 120.5% | 84.2% | 93.1% | 163.4% | 163.4% | 163.4% |
66-70 | 150.3% | 150.3% | 123.8% | 107.6% | 99.1% | 97.5% | 83.7% | 50.5% | 114.1% | 150.3% | 150.3% |
71-75 | 146.4% | 145.4% | 119.9% | 108.1% | 97.6% | 98.4% | 97.2% | 79.4% | 87.5% | 146.4% | 146.4% |
76-80 | 138.2% | 134.6% | 114.6% | 109.4% | 99.9% | 105.2% | 82.6% | 70.6% | 113.6% | 138.2% | 121.6% |
81-85 | 132.1% | 129.3% | 112.2% | 110.9% | 104.9% | 100.6% | 90.0% | 70.4% | 132.1% | 132.1% | 132.1% |
86-90 | 127.4% | 127.5% | 114.0% | 113.9% | 109.3% | 109.7% | 82.6% | 96.9% | 193.6% | 127.4% | 127.4% |
91-95 | 124.5% | 129.8% | 118.7% | 122.6% | 116.9% | 119.9% | 101.5% | 78.9% | 124.5% | 124.5% | 124.5% |
96-100 | 128.5% | 134.4% | 124.8% | 131.2% | 120.7% | 125.6% | 91.1% | 117.0% | 194.3% | 415.3% | 128.5% |
101-105 | 133.6% | 133.6% | 112.0% | 105.8% | 90.3% | 101.7% | 87.1% | 76.2% | 141.5% | 133.6% | 133.6% |
106-110 | 133.4% | 133.4% | 111.8% | 105.6% | 90.2% | 101.5% | 86.4% | 76.0% | 133.4% | 133.4% | 133.4% |
111-115 | 133.4% | 133.4% | 111.8% | 105.6% | 90.2% | 101.5% | 86.4% | 76.0% | 133.4% | 133.4% | 133.4% |
116-120 | 133.4% | 133.4% | 111.8% | 105.6% | 90.2% | 101.5% | 86.4% | 76.0% | 133.4% | 133.4% | 133.4% |
Dur_Grp | <10K | 10K - <25K | 25K - <50K | 50K - <100K | 100K - <250K | 250K - <500K | 500K - <1M | 1M - <2.5M | 2.5M - <5M | 5M - <10M | 10M+ |
|---|---|---|---|---|---|---|---|---|---|---|---|
1-1 | 163.4% | 163.4% | 129.4% | 110.8% | 101.0% | 120.5% | 84.2% | 93.1% | 163.4% | 163.4% | 163.4% |
2-2 | 163.4% | 163.4% | 129.4% | 110.8% | 101.0% | 120.5% | 84.2% | 93.1% | 184.4% | 163.4% | 163.4% |
3-3 | 163.4% | 163.4% | 129.4% | 110.8% | 101.0% | 120.5% | 84.2% | 93.1% | 163.4% | 163.4% | 163.4% |
4-5 | 163.4% | 163.4% | 129.4% | 110.8% | 101.0% | 120.5% | 84.2% | 93.1% | 163.4% | 163.4% | 163.4% |
6-10 | 188.3% | 193.0% | 149.1% | 127.6% | 116.3% | 138.9% | 97.1% | 107.3% | 188.3% | 188.3% | 188.3% |
11-15 | 191.4% | 191.4% | 151.6% | 129.8% | 104.6% | 123.6% | 98.7% | 109.1% | 191.4% | 191.4% | 511.2% |
16-20 | 174.0% | 174.0% | 137.9% | 118.0% | 107.5% | 124.7% | 89.7% | 96.4% | 174.0% | 174.0% | 458.9% |
21-30 | 159.9% | 145.1% | 119.7% | 101.8% | 98.8% | 119.7% | 82.0% | 91.2% | 114.6% | 159.9% | 159.9% |
31-120 | 110.7% | 103.1% | 87.7% | 75.3% | 75.2% | 85.1% | 68.2% | 88.4% | 110.7% | 110.7% | 65.9% |
AA_Grp | 1-1 | 2-2 | 3-3 | 4-5 | 6-10 | 11-15 | 16-20 | 21-30 | 31-120 |
|---|---|---|---|---|---|---|---|---|---|
0-17 | 90.2% | 90.2% | 90.2% | 90.2% | 103.9% | 93.4% | 96.0% | 88.2% | 80.4% |
18-25 | 86.5% | 86.5% | 86.5% | 86.5% | 96.0% | 92.6% | 81.9% | 97.0% | 77.1% |
26-30 | 93.9% | 93.9% | 93.9% | 93.9% | 108.2% | 97.3% | 100.0% | 110.6% | 83.7% |
31-35 | 96.5% | 96.5% | 96.5% | 96.5% | 111.2% | 100.0% | 102.8% | 94.5% | 101.2% |
36-40 | 90.2% | 90.2% | 90.2% | 90.2% | 103.9% | 93.4% | 96.0% | 88.2% | 80.4% |
41-45 | 97.6% | 97.6% | 97.6% | 97.6% | 112.4% | 101.1% | 103.9% | 95.5% | 87.0% |
46-50 | 115.2% | 115.2% | 115.2% | 115.2% | 132.8% | 119.4% | 122.7% | 112.8% | 108.0% |
51-55 | 104.0% | 104.0% | 104.0% | 104.0% | 119.8% | 107.7% | 110.7% | 101.7% | 92.7% |
56-60 | 99.7% | 99.7% | 99.7% | 99.7% | 114.8% | 103.2% | 106.2% | 97.8% | 82.3% |
61-65 | 101.0% | 101.0% | 101.0% | 101.0% | 116.3% | 104.6% | 107.5% | 98.8% | 75.2% |
66-70 | 99.1% | 99.1% | 99.1% | 99.1% | 114.2% | 105.1% | 110.9% | 96.8% | 74.5% |
71-75 | 97.6% | 97.6% | 97.6% | 97.6% | 129.2% | 111.5% | 107.7% | 95.1% | 77.1% |
76-80 | 99.9% | 99.9% | 99.9% | 99.9% | 116.7% | 104.9% | 106.4% | 97.8% | 85.3% |
81-85 | 104.9% | 104.9% | 104.9% | 104.9% | 130.1% | 108.6% | 111.7% | 97.1% | 93.5% |
86-90 | 109.3% | 109.3% | 109.3% | 109.3% | 125.9% | 113.2% | 116.4% | 95.9% | 97.5% |
91-95 | 116.9% | 116.9% | 116.9% | 116.9% | 134.7% | 121.1% | 123.3% | 114.4% | 104.2% |
96-100 | 120.7% | 120.7% | 120.7% | 120.7% | 139.0% | 125.0% | 128.5% | 118.1% | 107.6% |
101-105 | 90.3% | 90.3% | 90.3% | 90.3% | 104.1% | 93.5% | 96.2% | 88.4% | 80.5% |
106-110 | 90.2% | 90.2% | 90.2% | 90.2% | 103.9% | 93.4% | 96.0% | 88.2% | 80.4% |
111-115 | 90.2% | 90.2% | 90.2% | 90.2% | 103.9% | 93.4% | 96.0% | 88.2% | 80.4% |
116-120 | 90.2% | 90.2% | 90.2% | 90.2% | 103.9% | 93.4% | 96.0% | 88.2% | 80.4% |
Face_Amount_Band | F | M |
|---|---|---|
<10K | 163.4% | 175.3% |
10K - <25K | 163.4% | 189.4% |
25K - <50K | 129.4% | 147.4% |
50K - <100K | 110.8% | 124.4% |
100K - <250K | 101.0% | 110.9% |
250K - <500K | 120.5% | 127.6% |
500K - <1M | 84.2% | 90.4% |
1M - <2.5M | 93.1% | 92.9% |
2.5M - <5M | 163.4% | 121.7% |
5M - <10M | 163.4% | 101.1% |
10M+ | 163.4% | 263.6% |
AA_Grp | F | M |
|---|---|---|
0-17 | 90.2% | 93.8% |
18-25 | 86.5% | 89.9% |
26-30 | 93.9% | 97.7% |
31-35 | 96.5% | 104.4% |
36-40 | 90.2% | 93.8% |
41-45 | 97.6% | 101.5% |
46-50 | 115.2% | 119.8% |
51-55 | 104.0% | 120.4% |
56-60 | 99.7% | 115.3% |
61-65 | 101.0% | 110.9% |
66-70 | 99.1% | 112.2% |
71-75 | 97.6% | 104.1% |
76-80 | 99.9% | 103.9% |
81-85 | 104.9% | 108.7% |
86-90 | 109.3% | 109.2% |
91-95 | 116.9% | 117.1% |
96-100 | 120.7% | 125.9% |
101-105 | 90.3% | 101.1% |
106-110 | 90.2% | 93.8% |
111-115 | 90.2% | 93.8% |
116-120 | 90.2% | 93.8% |
Dur_Grp | F | M |
|---|---|---|
1-1 | 101.0% | 110.9% |
2-2 | 101.0% | 110.9% |
3-3 | 101.0% | 110.9% |
4-5 | 101.0% | 110.9% |
6-10 | 116.3% | 127.8% |
11-15 | 104.6% | 114.9% |
16-20 | 107.5% | 119.5% |
21-30 | 98.8% | 111.7% |
31-120 | 75.2% | 82.6% |
8.1.6.2 Goodness-of-Fit
Next comes checking goodness-of-fit, on both a univariate and bivariate basis. Tables are provided which show the ratio of the actual to model predicted deaths and show the associated death counts.
Code
dat.perm.unk.grid%>%
right_join(dat.perm.unk) %>%
mutate(ExpDth_Amt_GLMNet=ExpDth_Amt_VBT2015*Factor) %>%
mutate(Factor=NULL) ->
dat.perm.unk8.1.6.2.1 Univariate Fit Checks
Sex | Death Count | Actual-to-Model |
|---|---|---|
F | 794,865 | 100.0% |
M | 1,603,802 | 100.0% |
Face_Amount_Band | Death Count | Actual-to-Model |
|---|---|---|
<10K | 1,627,430 | 100.4% |
10K - <25K | 539,301 | 100.0% |
25K - <50K | 146,377 | 99.9% |
50K - <100K | 56,491 | 99.9% |
100K - <250K | 23,896 | 99.9% |
250K - <500K | 3,755 | 99.7% |
500K - <1M | 1,027 | 99.4% |
1M - <2.5M | 337 | 99.2% |
2.5M - <5M | 43 | 98.5% |
5M - <10M | 8 | 97.9% |
10M+ | 2 | 108.8% |
AA_Grp | Death Count | Actual-to-Model |
|---|---|---|
0-17 | 1,400 | 80.9% |
18-25 | 3,782 | 98.5% |
26-30 | 3,107 | 102.5% |
31-35 | 4,193 | 102.7% |
36-40 | 5,280 | 101.3% |
41-45 | 7,850 | 102.6% |
46-50 | 14,261 | 102.2% |
51-55 | 26,508 | 101.2% |
56-60 | 47,738 | 100.6% |
61-65 | 80,826 | 100.3% |
66-70 | 129,766 | 100.2% |
71-75 | 199,714 | 100.1% |
76-80 | 312,711 | 100.1% |
81-85 | 482,022 | 100.0% |
86-90 | 571,444 | 100.0% |
91-95 | 396,735 | 99.9% |
96-100 | 103,091 | 99.8% |
101-105 | 7,774 | 103.2% |
106-110 | 410 | 47.6% |
111-115 | 48 | 41.9% |
116-120 | 7 | 32.7% |
Dur_Grp | Death Count | Actual-to-Model |
|---|---|---|
1-1 | 438 | 98.9% |
2-2 | 365 | 103.1% |
3-3 | 374 | 84.0% |
4-5 | 992 | 96.1% |
6-10 | 6,847 | 103.5% |
11-15 | 18,202 | 102.0% |
16-20 | 29,409 | 101.4% |
21-30 | 127,489 | 99.8% |
31-120 | 2,214,551 | 100.0% |
8.1.6.2.2 Bivariate Fit Checks
Face_Amount_Band | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
<10K | 645,414 | 101.0% | 982,016 | 100.0% | ||
10K - <25K | 118,995 | 99.9% | 420,306 | 100.0% | ||
25K - <50K | 20,402 | 99.1% | 125,975 | 100.1% | ||
50K - <100K | 6,596 | 98.6% | 49,895 | 100.1% | ||
100K - <250K | 2,846 | 98.3% | 21,050 | 100.1% | ||
250K - <500K | 459 | 99.5% | 3,296 | 99.8% | ||
500K - <1M | 107 | 95.3% | 920 | 99.9% | ||
1M - <2.5M | 39 | 97.6% | 298 | 99.4% | ||
2.5M - <5M | 6 | 106.9% | 37 | 97.4% | ||
5M - <10M | 1 | 212.5% | 7 | 93.1% | ||
10M+ | 0 | 0.0% | 2 | 120.8% | ||
AA_Grp | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
0-17 | 540 | 83.5% | 860 | 79.4% | ||
18-25 | 954 | 96.9% | 2,828 | 99.0% | ||
26-30 | 888 | 108.5% | 2,219 | 100.3% | ||
31-35 | 1,269 | 100.3% | 2,924 | 103.7% | ||
36-40 | 1,743 | 102.6% | 3,537 | 100.7% | ||
41-45 | 2,470 | 108.8% | 5,380 | 100.2% | ||
46-50 | 4,396 | 103.8% | 9,865 | 101.6% | ||
51-55 | 7,765 | 100.7% | 18,743 | 101.4% | ||
56-60 | 14,099 | 100.4% | 33,639 | 100.7% | ||
61-65 | 24,558 | 100.3% | 56,268 | 100.3% | ||
66-70 | 39,042 | 100.2% | 90,724 | 100.2% | ||
71-75 | 58,725 | 100.1% | 140,989 | 100.1% | ||
76-80 | 95,263 | 100.2% | 217,448 | 100.1% | ||
81-85 | 156,136 | 100.0% | 325,886 | 99.9% | ||
86-90 | 197,182 | 100.0% | 374,262 | 99.9% | ||
91-95 | 142,955 | 100.0% | 253,780 | 99.9% | ||
96-100 | 42,679 | 98.1% | 60,412 | 100.3% | ||
101-105 | 3,967 | 99.2% | 3,807 | 104.7% | ||
106-110 | 208 | 44.9% | 202 | 49.1% | ||
111-115 | 22 | 95.7% | 26 | 22.1% | ||
116-120 | 4 | 53.0% | 3 | 20.7% | ||
Dur_Grp | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
1-1 | 171 | 94.8% | 267 | 101.8% | ||
2-2 | 157 | 131.3% | 208 | 85.4% | ||
3-3 | 128 | 87.7% | 246 | 81.9% | ||
4-5 | 423 | 112.9% | 569 | 87.2% | ||
6-10 | 3,872 | 110.5% | 2,975 | 99.1% | ||
11-15 | 11,771 | 102.3% | 6,431 | 101.7% | ||
16-20 | 19,920 | 100.1% | 9,489 | 102.5% | ||
21-30 | 79,411 | 99.1% | 48,078 | 100.3% | ||
31-120 | 679,012 | 99.9% | 1,535,539 | 100.0% | ||
AA_Grp | Face_Amount_Band: <10K | Face_Amount_Band: 10K - <25K | Face_Amount_Band: 25K - <50K | Face_Amount_Band: 50K - <100K | Face_Amount_Band: 100K - <250K | Face_Amount_Band: 250K - <500K | Face_Amount_Band: 500K - <1M | Face_Amount_Band: 1M - <2 | Face_Amount_Band: 2 | Face_Amount_Band: 5M - <10M | Face_Amount_Band: 10M+ | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | 5M | 5M - <5M | Deaths | Ratio | Deaths | Ratio | ||||||||||||||
Deaths | Ratio | Deaths | Ratio | ||||||||||||||||||||||||||||||
0-17 | 45 | 115.7% | 309 | 60.6% | 673 | 90.6% | 213 | 76.8% | 112 | 70.8% | 36 | 72.5% | 9 | 62.4% | 1 | 17.4% | 1 | 188.8% | 0 | 0.0% | 1 | 317.8% | |||||||||||
18-25 | 291 | 104.9% | 1,246 | 87.9% | 1,425 | 103.5% | 490 | 105.2% | 252 | 93.7% | 56 | 94.8% | 16 | 110.3% | 5 | 79.9% | 0 | 0.0% | 0 | 0.0% | 1 | 157.4% | |||||||||||
26-30 | 500 | 114.5% | 1,220 | 99.9% | 812 | 106.6% | 364 | 109.0% | 172 | 111.7% | 31 | 111.6% | 6 | 89.2% | 2 | 79.3% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
31-35 | 1,225 | 123.3% | 1,688 | 107.1% | 793 | 111.9% | 331 | 114.3% | 137 | 103.6% | 14 | 62.1% | 3 | 55.6% | 2 | 105.4% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
36-40 | 2,378 | 130.1% | 1,912 | 106.7% | 624 | 98.7% | 232 | 92.6% | 115 | 94.9% | 15 | 80.7% | 1 | 25.8% | 3 | 242.4% | 0 | 0.0% | 0 | 0.0% | |||||||||||||
41-45 | 4,381 | 120.7% | 2,464 | 105.9% | 649 | 96.0% | 233 | 93.0% | 108 | 104.9% | 11 | 87.2% | 4 | 142.5% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||||
46-50 | 9,340 | 124.5% | 3,746 | 105.3% | 848 | 95.0% | 235 | 85.1% | 79 | 88.9% | 12 | 129.1% | 1 | 27.9% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||||
51-55 | 17,200 | 119.3% | 7,169 | 102.3% | 1,553 | 94.4% | 454 | 90.9% | 114 | 84.0% | 14 | 78.5% | 2 | 49.5% | 2 | 218.2% | 0 | 0.0% | 0 | 0.0% | |||||||||||||
56-60 | 29,299 | 118.3% | 13,459 | 98.7% | 3,553 | 97.6% | 1,052 | 95.5% | 323 | 93.6% | 41 | 93.7% | 8 | 68.3% | 3 | 127.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||||
61-65 | 45,383 | 112.6% | 25,156 | 99.5% | 7,063 | 98.9% | 2,354 | 98.2% | 755 | 97.4% | 95 | 92.2% | 13 | 72.5% | 7 | 102.2% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
66-70 | 71,147 | 108.7% | 41,761 | 100.3% | 11,323 | 99.3% | 3,901 | 98.9% | 1,418 | 98.7% | 176 | 95.3% | 35 | 88.7% | 5 | 64.5% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
71-75 | 115,269 | 104.8% | 61,200 | 99.7% | 15,373 | 99.5% | 5,334 | 99.2% | 2,117 | 99.1% | 308 | 97.3% | 90 | 104.5% | 22 | 91.5% | 1 | 44.2% | 0 | 0.0% | |||||||||||||
76-80 | 194,394 | 101.6% | 84,970 | 99.8% | 21,616 | 99.6% | 7,794 | 100.2% | 3,259 | 100.6% | 516 | 101.0% | 124 | 96.8% | 33 | 94.5% | 4 | 82.3% | 1 | 121.3% | 0 | 0.0% | |||||||||||
81-85 | 326,729 | 99.3% | 109,588 | 99.8% | 28,762 | 100.3% | 11,066 | 100.4% | 4,838 | 100.4% | 745 | 101.0% | 223 | 101.8% | 62 | 97.0% | 8 | 98.2% | 1 | 103.1% | 0 | 0.0% | |||||||||||
86-90 | 416,187 | 98.4% | 106,577 | 100.2% | 29,501 | 100.3% | 12,307 | 100.3% | 5,617 | 100.4% | 906 | 100.9% | 235 | 100.8% | 99 | 102.4% | 13 | 108.6% | 2 | 106.6% | |||||||||||||
91-95 | 305,604 | 97.8% | 61,551 | 100.3% | 17,364 | 100.5% | 7,882 | 100.6% | 3,497 | 100.7% | 588 | 101.6% | 188 | 102.4% | 51 | 104.0% | 8 | 107.6% | 2 | 85.7% | |||||||||||||
96-100 | 81,098 | 88.9% | 14,416 | 101.3% | 4,221 | 102.1% | 2,135 | 102.3% | 944 | 102.5% | 180 | 105.5% | 56 | 108.2% | 34 | 108.3% | 5 | 129.4% | 2 | 146.0% | |||||||||||||
101-105 | 6,556 | 70.2% | 822 | 89.5% | 217 | 112.8% | 109 | 110.8% | 37 | 126.0% | 11 | 174.1% | 13 | 147.5% | 6 | 125.0% | 3 | 126.7% | |||||||||||||||
106-110 | 350 | 31.1% | 46 | 71.1% | 7 | 54.3% | 5 | 203.2% | 2 | 47.9% | 0 | 0.0% | |||||||||||||||||||||
111-115 | 47 | 59.1% | 1 | 33.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||||||||||||||||
116-120 | 7 | 32.7% | |||||||||||||||||||||||||||||||
Face_Amount_Band | Dur_Grp: 1-1 | Dur_Grp: 2-2 | Dur_Grp: 3-3 | Dur_Grp: 4-5 | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-120 | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||||||
<10K | 91 | 140.7% | 114 | 163.4% | 112 | 130.3% | 470 | 207.1% | 4,800 | 156.0% | 14,815 | 117.3% | 25,467 | 108.4% | 89,995 | 104.3% | 1,491,566 | 99.8% | |||||||||
10K - <25K | 106 | 140.8% | 107 | 121.0% | 114 | 110.2% | 262 | 110.3% | 1,296 | 119.9% | 2,334 | 101.8% | 2,583 | 106.1% | 26,493 | 99.2% | 506,006 | 100.0% | |||||||||
25K - <50K | 163 | 151.3% | 97 | 121.4% | 100 | 131.8% | 165 | 107.7% | 478 | 100.3% | 643 | 95.1% | 851 | 98.2% | 6,952 | 98.8% | 136,928 | 100.0% | |||||||||
50K - <100K | 43 | 96.6% | 24 | 76.2% | 26 | 86.7% | 51 | 91.2% | 150 | 95.9% | 291 | 95.1% | 305 | 92.7% | 2,534 | 98.3% | 53,067 | 100.1% | |||||||||
100K - <250K | 27 | 108.5% | 18 | 84.8% | 15 | 79.0% | 30 | 84.5% | 84 | 86.2% | 93 | 80.2% | 162 | 94.8% | 1,211 | 100.1% | 22,256 | 100.1% | |||||||||
250K - <500K | 6 | 82.6% | 2 | 41.8% | 6 | 89.9% | 10 | 89.1% | 28 | 87.3% | 17 | 62.8% | 30 | 78.5% | 220 | 103.7% | 3,436 | 100.3% | |||||||||
500K - <1M | 1 | 31.7% | 2 | 96.7% | 1 | 43.6% | 3 | 104.6% | 8 | 79.4% | 5 | 65.8% | 9 | 101.4% | 60 | 94.0% | 938 | 100.5% | |||||||||
1M - <2.5M | 1 | 89.4% | 0 | 0.0% | 0 | 0.0% | 1 | 70.9% | 3 | 82.0% | 3 | 106.2% | 1 | 28.2% | 20 | 93.0% | 308 | 100.8% | |||||||||
2.5M - <5M | 0 | 0.0% | 1 | 1320.6% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 3 | 74.6% | 39 | 101.7% | |||||||||
5M - <10M | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 1 | 99.5% | 7 | 103.0% | |||||||||
10M+ | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 1 | 194.0% | 1 | 193.1% | 0 | 0.0% | 0 | 0.0% | |||||||||
AA_Grp | Dur_Grp: 1-1 | Dur_Grp: 2-2 | Dur_Grp: 3-3 | Dur_Grp: 4-5 | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-120 | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||||||
0-17 | 192 | 90.4% | 94 | 99.8% | 82 | 74.7% | 128 | 72.0% | 291 | 65.8% | 348 | 58.2% | 265 | 124.9% | |||||||||||||
18-25 | 39 | 97.4% | 24 | 45.2% | 49 | 67.8% | 105 | 87.2% | 438 | 90.6% | 605 | 108.7% | 1,021 | 93.0% | 1,501 | 104.9% | |||||||||||
26-30 | 7 | 246.7% | 4 | 239.4% | 3 | 110.1% | 12 | 231.0% | 75 | 88.7% | 420 | 103.9% | 451 | 84.5% | 1,961 | 104.5% | 174 | 154.0% | |||||||||
31-35 | 1 | 204.4% | 8 | 430.7% | 5 | 146.0% | 10 | 183.1% | 21 | 110.5% | 121 | 110.9% | 506 | 95.3% | 1,426 | 99.3% | 2,095 | 109.1% | |||||||||
36-40 | 3 | 95.8% | 4 | 46.6% | 5 | 86.2% | 11 | 101.8% | 39 | 213.2% | 56 | 72.6% | 167 | 78.2% | 1,573 | 101.7% | 3,422 | 102.3% | |||||||||
41-45 | 5 | 103.7% | 8 | 108.4% | 13 | 276.0% | 19 | 72.1% | 67 | 149.1% | 115 | 121.8% | 131 | 101.3% | 1,724 | 101.8% | 5,768 | 101.9% | |||||||||
46-50 | 11 | 123.7% | 11 | 90.9% | 17 | 127.8% | 31 | 72.8% | 102 | 90.1% | 181 | 103.5% | 264 | 134.8% | 1,804 | 100.1% | 11,840 | 102.4% | |||||||||
51-55 | 13 | 108.7% | 18 | 142.1% | 24 | 82.3% | 52 | 79.0% | 210 | 101.9% | 402 | 97.8% | 424 | 117.2% | 2,372 | 103.4% | 22,993 | 100.8% | |||||||||
56-60 | 17 | 94.3% | 28 | 205.4% | 28 | 92.0% | 76 | 107.1% | 358 | 121.6% | 613 | 116.5% | 798 | 161.2% | 3,236 | 104.8% | 42,584 | 99.4% | |||||||||
61-65 | 22 | 166.7% | 28 | 132.2% | 26 | 69.3% | 98 | 114.1% | 524 | 142.9% | 945 | 141.8% | 1,130 | 130.1% | 4,761 | 101.8% | 73,292 | 99.7% | |||||||||
66-70 | 19 | 127.0% | 25 | 140.5% | 30 | 121.5% | 112 | 194.8% | 782 | 171.0% | 1,408 | 138.4% | 1,726 | 138.1% | 7,498 | 97.4% | 118,166 | 99.8% | |||||||||
71-75 | 17 | 349.1% | 18 | 172.1% | 18 | 59.0% | 96 | 150.9% | 927 | 164.2% | 2,381 | 126.7% | 2,510 | 125.7% | 11,536 | 98.1% | 182,211 | 99.9% | |||||||||
76-80 | 15 | 303.1% | 17 | 245.1% | 20 | 262.6% | 81 | 126.2% | 1,009 | 170.7% | 3,077 | 121.9% | 4,360 | 113.7% | 18,163 | 98.8% | 285,969 | 99.9% | |||||||||
81-85 | 2 | 429.9% | 4 | 177.3% | 5 | 80.7% | 52 | 143.1% | 1,086 | 165.9% | 3,176 | 99.9% | 5,905 | 93.7% | 24,673 | 98.7% | 447,119 | 100.0% | |||||||||
86-90 | 3 | 1747.4% | 5 | 284.2% | 10 | 609.5% | 38 | 369.0% | 727 | 117.7% | 2,866 | 85.6% | 5,565 | 92.2% | 26,533 | 98.5% | 535,697 | 100.0% | |||||||||
91-95 | 2 | 459.6% | 4 | 146.1% | 2 | 183.8% | 10 | 34.3% | 161 | 60.1% | 1,287 | 75.7% | 3,396 | 76.5% | 15,196 | 99.5% | 376,677 | 100.1% | |||||||||
96-100 | 70 | 107.3% | 65 | 111.8% | 37 | 70.5% | 61 | 295.9% | 8 | 90.8% | 199 | 93.5% | 783 | 67.7% | 3,475 | 91.3% | 98,393 | 100.0% | |||||||||
101-105 | 22 | 126.0% | 1 | 30.9% | 7 | 214.7% | 57 | 132.0% | 7,687 | 101.1% | |||||||||||||||||
106-110 | 1 | 145.9% | 0 | 0.0% | 409 | 50.4% | |||||||||||||||||||||
111-115 | 0 | 0.0% | 48 | 41.9% | |||||||||||||||||||||||
116-120 | 7 | 32.7% | |||||||||||||||||||||||||
8.2 Perm Model, Smoker Distinct
Code
dat.perm.knw <- readRDS("dat.perm.rds")
dat.perm.knw <- dat.perm.knw[Policies_Exposed > 0]
dat.perm.knw <- dat.perm.knw[!(UW == "U/U/U" &
Insurance_Plan == "Perm")]
AA.brks <- c(-1,17,
seq(25,120,5))
AA.lbls <- paste0(
AA.brks[1:(length(AA.brks)-1)]+1,
"-",
AA.brks[2:length(AA.brks)]
)
Dur.brks <- c(0,1,2,3,5,10,15,20,30,120)
Dur.lbls <- paste0(
Dur.brks[1:(length(Dur.brks)-1)]+1,
"-",
Dur.brks[2:length(Dur.brks)]
)
dat.perm.knw[,`:=`(
AA_Grp=cut(Attained_Age,
breaks=AA.brks,
labels=AA.lbls),
Dur_Grp=cut(Duration,
breaks=Dur.brks,
labels=Dur.lbls)
)]
pred.cols <- names(dat.perm.knw)[c(1,5,6,15:17)]
factor.cols <- pred.cols
dat.perm.knw[,
(factor.cols):=lapply(.SD,factor),
.SDcols=factor.cols]
UW.levels<-data.table(UW.levels=dat.perm.knw[,levels(UW)])
UW.levels[,c("NS","Pref_Class","NClasses"):=tstrsplit(UW.levels,"/")]
setkeyv(UW.levels,c("NS","NClasses","Pref_Class"))
set.seed(traintest.seed)
dat.perm.knw %>%
mutate(
IsTraining = (runif(nrow(.)) < training.fraction),
Noise = rnorm(nrow(.)),
.before = 1
) %>%
mutate(Face_Amount_Band=fct_relabel(
Face_Amount_Band,
#function(.) sub(":"," -",.,fixed=T)
function(.) fa.remap[Face_Amount_Band.Old==.,Face_Amount_Band.New]
),
AE_Count=Death_Count/ExpDth_Cnt_VBT2015,
AE_Amount=Death_Claim_Amount/ExpDth_Amt_VBT2015,
UW=factor(UW,levels=UW.levels$UW.levels)
) ->
dat.perm.knw
gbm.pred.cols <- c("Noise",pred.cols)Here is a data preview.
Code
dat.perm.knw %>%
head(10) %>%
flextable()IsTraining | Noise | Sex | Smoker_Status | Attained_Age | Duration | Face_Amount_Band | Insurance_Plan | Number_of_Pfd_Classes | Preferred_Class | Death_Count | Policies_Exposed | ExpDth_Cnt_VBT2015 | Death_Claim_Amount | Amount_Exposed | ExpDth_Amt_VBT2015 | UW | AA_Grp | Dur_Grp | AE_Count | AE_Amount |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
TRUE | 0.72354004 | F | NS | 69 | 6 | 50K - <100K | Perm | 3 | 3 | 0 | 131.846073 | 0.567626054 | 0 | 7,784,406 | 33,476.09 | NS/3/3 | 66-70 | 6-10 | 0.000000 | 0.000000 |
TRUE | 0.16338468 | F | NS | 69 | 6 | 100K - <250K | Perm | 3 | 1 | 0 | 44.808299 | 0.193062743 | 0 | 6,482,107 | 27,954.57 | NS/1/3 | 66-70 | 6-10 | 0.000000 | 0.000000 |
TRUE | -0.18609600 | F | NS | 69 | 6 | 100K - <250K | Perm | U | U | 1 | 104.779827 | 0.463192595 | 118,240 | 15,622,740 | 69,209.88 | NS/U/U | 66-70 | 6-10 | 2.158929 | 1.708427 |
TRUE | -0.32956340 | F | NS | 69 | 6 | 250K - <500K | Perm | U | U | 1 | 23.102442 | 0.102663247 | 312,493 | 7,549,700 | 33,551.89 | NS/U/U | 66-70 | 6-10 | 9.740584 | 9.313723 |
TRUE | 1.35079832 | F | NS | 69 | 6 | 250K - <500K | Perm | 3 | 1 | 1 | 26.586405 | 0.113763949 | 250,000 | 8,384,681 | 35,867.22 | NS/1/3 | 66-70 | 6-10 | 8.790131 | 6.970154 |
TRUE | -0.11456002 | F | NS | 69 | 6 | 250K - <500K | Perm | 3 | 3 | 0 | 36.353317 | 0.155361484 | 0 | 11,840,441 | 50,606.81 | NS/3/3 | 66-70 | 6-10 | 0.000000 | 0.000000 |
FALSE | 0.24543130 | F | NS | 69 | 6 | 500K - <1M | Perm | 3 | 1 | 0 | 13.228370 | 0.056639893 | 0 | 9,111,743 | 38,992.50 | NS/1/3 | 66-70 | 6-10 | 0.000000 | 0.000000 |
TRUE | -0.12631776 | F | NS | 69 | 6 | 500K - <1M | Perm | 3 | 3 | 0 | 20.186301 | 0.086675506 | 0 | 12,134,936 | 52,072.73 | NS/3/3 | 66-70 | 6-10 | 0.000000 | 0.000000 |
TRUE | -0.07584836 | F | NS | 69 | 6 | 1M - <2.5M | Perm | 3 | 2 | 0 | 12.668494 | 0.054094468 | 0 | 16,626,416 | 70,994.79 | NS/2/3 | 66-70 | 6-10 | 0.000000 | 0.000000 |
TRUE | 0.67148672 | F | NS | 69 | 6 | 2.5M - <5M | Perm | 2 | 1 | 0 | 1.906849 | 0.008142245 | 0 | 5,886,563 | 25,135.62 | NS/1/2 | 66-70 | 6-10 | 0.000000 | 0.000000 |
8.2.1 Feature Discovery with Catboost
Code
dat.perm.knw %>%
filter(IsTraining == TRUE) %>%
select(all_of(gbm.pred.cols)) %>%
mutate(Sex = as.numeric(Sex)) %>%
catboost.load_pool(
data=.,
label = dat.perm.knw[IsTraining==TRUE,AE_Amount],
weight = dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]) ->
train_pool_perm_knw
dat.perm.knw %>%
filter(IsTraining == FALSE) %>%
select(all_of(gbm.pred.cols)) %>%
mutate(Sex = as.numeric(Sex)) %>%
catboost.load_pool(
data=.,
label = dat.perm.knw[IsTraining==FALSE,AE_Amount],
weight = dat.perm.knw[IsTraining==FALSE,ExpDth_Amt_VBT2015]) ->
test_pool_perm_knw
if(bUseCache & file.exists(
'dat.term.mod.perm.knw.cbm'
) & !bInvalidateCaches)
{
cb.model.perm.knw <- catboost.load_model(model_path = 'dat.term.mod.perm.knw.cbm')
} else {
cb.model.perm.knw <- catboost.train(learn_pool=train_pool_perm_knw,
test_pool = test_pool_perm_knw,
params=fit_params)
catboost.save_model(cb.model.perm.knw,
model_path = 'dat.term.mod.perm.knw.cbm')
}8.2.2 Feature Importance
Next is to check for the variables with most variability. It is notable that Sex has mean influence not dissimilar to Noise.
Code
shp.perm.knw <- shapviz(
cb.model.perm.knw,
X=as.data.frame(dat.perm.knw[IsTraining==TRUE,..gbm.pred.cols]),
X_pred=train_pool_perm_knw
)
setDT(shp.perm.knw$X)
shp.perm.knw$X[,c("NS","Pref_Class","NClasses"):=tstrsplit(UW,"/")]
sv_importance(shp.perm.knw) + theme_minimal()
8.2.3 Feature Interactions
The top three interactions are face amount band with each of underwriting, duration, and insurance plan. Sex is notably weakly interacting with other variables.
Code
imp.int.perm.knw <- catboost.get_feature_importance(
cb.model.perm.knw,
type="Interaction"
)
mod.ft.map.perm.knw <- data.table(
FeatureNames=names(dat.perm.knw[IsTraining==TRUE,..gbm.pred.cols])
)
mod.ft.map.perm.knw[,ID:=1:nrow(.SD)-1]
imp.int.perm.knw %>%
merge(mod.ft.map.perm.knw,
by.x="feature1_index",
by.y="ID") %>%
merge(mod.ft.map.perm.knw,
by.x="feature2_index",
by.y="ID") %>%
setnames(
old=c("FeatureNames.x","FeatureNames.y"),
new=c("Feature1","Feature2")
) %>%
mutate(feature1_index=NULL,feature2_index=NULL) %>%
as.data.table() %>%
setcolorder(c("Feature1","Feature2","score")) ->
imp.int.perm.knw
imp.int.perm.knw[order(-score)] %>%
filter(Feature1 != "Noise") %>%
flextable() %>%
colformat_double(j="score",digits = 2)Feature1 | Feature2 | score |
|---|---|---|
Face_Amount_Band | UW | 13.56 |
Face_Amount_Band | Dur_Grp | 8.84 |
Face_Amount_Band | Insurance_Plan | 8.57 |
Face_Amount_Band | AA_Grp | 7.82 |
Insurance_Plan | UW | 5.12 |
UW | Dur_Grp | 4.58 |
UW | AA_Grp | 4.29 |
Insurance_Plan | Dur_Grp | 4.07 |
Insurance_Plan | AA_Grp | 3.26 |
AA_Grp | Dur_Grp | 2.69 |
Sex | Face_Amount_Band | 0.74 |
Sex | UW | 0.57 |
Sex | Insurance_Plan | 0.40 |
Sex | AA_Grp | 0.37 |
Sex | Dur_Grp | 0.34 |
8.2.4 Feature Interaction Plots
Each of the interactions are discussed below with plots using SHAP values from both sides of the interaction.
8.2.4.1 UW
8.2.4.1.1 Face Amount Band SHAPs
There does not appear to be a meaningful interaction between underwriting and face amount band embedded in the face amount band SHAP values.
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"Face_Amount_Band"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"Face_Amount_Band"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"Face_Amount_Band"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '3') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, 3 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"Face_Amount_Band"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '4') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for non-smokers, 4 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"Face_Amount_Band"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"Face_Amount_Band"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"Face_Amount_Band"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("for unismokers")) +
theme_minimal()
8.2.4.1.2 UW SHAPs
The notable interaction here is that the distinction between best and second best of three non-smoker classes appears to collapse below 100K.
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"UW"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"UW"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"UW"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '3') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 3 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"UW"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'NS' & NClasses == '4') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for non-smokers, 4 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"UW"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for smokers, unknown preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"UW"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'S' & NClasses == '2') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for smokers, 2 preferred classes")) +
theme_minimal()
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
NS,
Pref_Class,
NClasses)],
shap=shp.perm.knw$S[,"UW"],
response=dat.perm.knw[IsTraining==TRUE,AE_Amount],
offset=dat.perm.knw[IsTraining==TRUE,ExpDth_Amt_VBT2015]
)
) %>%
mutate(NS=factor(NS),Pref_Class=factor(Pref_Class)) %>%
filter(NS == 'U') %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Pref_Class,fill=Pref_Class)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect UW"),
subtitle = paste0("for unismokers")) +
theme_minimal()
8.2.4.2 Insurance Plan
8.2.4.2.1 Face Amount Band SHAPs
Outside of the “Other” plan, it is difficult to identify an interaction within the face amount band SHAP values.
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
Insurance_Plan)],
shap=shp.perm.knw$S[,"Face_Amount_Band"]
)
) %>%
ggplot(aes(y=Insurance_Plan, x=exp(shap),color=Face_Amount_Band,
fill=Face_Amount_Band)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)") +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Face_Amount_Band"),
subtitle = paste0("by insurance plan")) +
theme_minimal()
8.2.4.2.2 Insurance Plan SHAPs
There is some interaction of UL and face amounts under 1M, with UL from 50K - < 1M being markedly higher than the others.
Code
data.table(
cbind(
shp.perm.knw$X[,.(Face_Amount_Band,
Insurance_Plan)],
shap=shp.perm.knw$S[,"Insurance_Plan"]
)
) %>%
ggplot(aes(y=Face_Amount_Band, x=exp(shap),color=Insurance_Plan,fill=Insurance_Plan)) +
stat_density_ridges(alpha=0.9/4,scale=1,quantile_lines = T,quantiles = 0.5) +
scale_x_continuous(labels = scales::percent,
name="Exponentiated SHAP Value (% relative to Offset)",
limits = c(NA,1.5)) +
scale_color_viridis_d() +
scale_fill_viridis_d() +
ggtitle(label=paste0("Ridge plot of SHAP values for Effect Insurance_Plan"),
subtitle = paste0("by face amount band")) +
theme_minimal()
8.2.5 Next Steps in Modeling
The catboost modeling is informative here for exploratory analytics. We next build an elastic net model which includes the main effects plus the top eight interactions from the catboost analysis. This cutoff is chosen arbitrarily. The top three are stronger than the others, while the next five seem to cluster in the middle. These interactions may turn out to be unneeded. Elastic net modeling will reveal which is truly important in a mortality model.
8.2.6 Elastic Net Models
The following formula is used throughout all non-PLT, term models.
Code
glmnetFormula <- as.formula(
paste(c("~ -1",
pred.cols,
imp.int.perm.knw[order(-score)][Feature1 != "Noise",
paste0(Feature1,":",Feature2)]),
collapse=" + ")
)
print(glmnetFormula)~-1 + Sex + Face_Amount_Band + Insurance_Plan + UW + AA_Grp +
Dur_Grp + Face_Amount_Band:UW + Face_Amount_Band:Dur_Grp +
Face_Amount_Band:Insurance_Plan + Face_Amount_Band:AA_Grp +
Insurance_Plan:UW + UW:Dur_Grp + UW:AA_Grp + Insurance_Plan:Dur_Grp +
Insurance_Plan:AA_Grp + AA_Grp:Dur_Grp + Sex:Face_Amount_Band +
Sex:UW + Sex:Insurance_Plan + Sex:AA_Grp + Sex:Dur_GrpThe interactions included in the model are as follows:
Code
data.table(Interaction=imp.int.perm.knw[order(-score)][Feature1 != "Noise",
paste0(Feature1,":",Feature2)]) %>%
flextable()Interaction |
|---|
Face_Amount_Band:UW |
Face_Amount_Band:Dur_Grp |
Face_Amount_Band:Insurance_Plan |
Face_Amount_Band:AA_Grp |
Insurance_Plan:UW |
UW:Dur_Grp |
UW:AA_Grp |
Insurance_Plan:Dur_Grp |
Insurance_Plan:AA_Grp |
AA_Grp:Dur_Grp |
Sex:Face_Amount_Band |
Sex:UW |
Sex:Insurance_Plan |
Sex:AA_Grp |
Sex:Dur_Grp |
8.2.6.1 Model Fit
Code
dat.perm.knw.el <- prepELData(
formula=glmnetFormula,
data=dat.perm.knw,
predictors = pred.cols,
response = "AE_Amount",
weights = "ExpDth_Amt_VBT2015",
#foldid = "FoldID",
useSparse = T
)
set.seed(cvfit.seed)
if(bUseCache & file.exists(
'perm.model.knw.el.rds'
) & !bInvalidateCaches)
{
cvfit.perm.knw <- readRDS('perm.model.knw.el.rds')
} else
{
cvfit.perm.knw <- fitCVGLMNet(
dat.perm.knw.el,
nfolds = 10
)
if(bUseCache)
saveRDS(cvfit.perm.knw, 'perm.model.knw.el.rds')
}8.2.6.1.1 Usual plots for Elastic Net Models
When presenting elastic net models, the cross validation plot for \(\lambda\) and the coefficient shrinkage plots are provided.
At the minimum \(\lambda\) of 0.0002402, the model has 550 parameters.
Code
plot(cvfit.perm.knw)
Code
plot(cvfit.perm.knw$glmnet.fit,xvar="lambda")
8.2.6.1.2 Factor Table
Their exponentiated coefficients are as follows:
Code
reformatCoefs(cvfit.perm.knw, pred.cols) %>%
filter(Coef != 0) %>%
select(Feature1Name,
Feature1Level,
Feature2Name,
Feature2Level,
Coef) %>%
mutate(Coef=exp(Coef)) %>%
flextable() %>%
set_formatter(
Coef=function(x) paste0(sprintf("%.01f", 100*x),"%")
) %>%
theme_vanilla()Feature1Name | Feature1Level | Feature2Name | Feature2Level | Coef |
|---|---|---|---|---|
(Intercept) | (Intercept) | 94.5% | ||
Sex | F | 98.5% | ||
Sex | M | 100.1% | ||
Face_Amount_Band | 10K - <25K | 114.8% | ||
Face_Amount_Band | 25K - <50K | 113.5% | ||
Face_Amount_Band | 50K - <100K | 100.1% | ||
Face_Amount_Band | 100K - <250K | 94.1% | ||
Face_Amount_Band | 250K - <500K | 89.3% | ||
Face_Amount_Band | 500K - <1M | 90.0% | ||
Face_Amount_Band | 1M - <2.5M | 95.8% | ||
Face_Amount_Band | 2.5M - <5M | 99.3% | ||
Face_Amount_Band | 5M - <10M | 92.5% | ||
Face_Amount_Band | 10M+ | 71.3% | ||
Insurance_Plan | UL | 107.0% | ||
Insurance_Plan | VLSG | 96.8% | ||
UW | NS/2/2 | 132.1% | ||
UW | NS/1/3 | 93.5% | ||
UW | NS/2/3 | 97.4% | ||
UW | NS/3/3 | 128.5% | ||
UW | NS/2/4 | 77.7% | ||
UW | NS/4/4 | 117.5% | ||
UW | NS/U/U | 117.6% | ||
UW | S/1/2 | 94.3% | ||
UW | S/2/2 | 123.7% | ||
UW | S/U/U | 118.9% | ||
UW | U/U/U | 106.4% | ||
AA_Grp | 26-30 | 120.0% | ||
AA_Grp | 31-35 | 113.7% | ||
AA_Grp | 36-40 | 100.2% | ||
AA_Grp | 41-45 | 106.2% | ||
AA_Grp | 46-50 | 103.9% | ||
AA_Grp | 56-60 | 95.6% | ||
AA_Grp | 61-65 | 97.9% | ||
AA_Grp | 71-75 | 100.6% | ||
AA_Grp | 76-80 | 102.1% | ||
AA_Grp | 86-90 | 103.8% | ||
AA_Grp | 96-100 | 108.0% | ||
AA_Grp | 101-105 | 82.7% | ||
AA_Grp | 106-110 | 62.2% | ||
AA_Grp | 111-115 | 77.2% | ||
AA_Grp | 116-120 | 96.0% | ||
Dur_Grp | 4-5 | 94.8% | ||
Dur_Grp | 6-10 | 96.3% | ||
Dur_Grp | 11-15 | 98.0% | ||
Dur_Grp | 16-20 | 99.0% | ||
Dur_Grp | 31-120 | 92.4% | ||
Face_Amount_Band | 50K - <100K | UW | NS/2/2 | 99.2% |
Face_Amount_Band | 100K - <250K | UW | NS/2/2 | 98.9% |
Face_Amount_Band | 250K - <500K | UW | NS/2/2 | 100.5% |
Face_Amount_Band | 500K - <1M | UW | NS/2/2 | 103.1% |
Face_Amount_Band | 1M - <2.5M | UW | NS/2/2 | 107.9% |
Face_Amount_Band | 2.5M - <5M | UW | NS/2/2 | 106.2% |
Face_Amount_Band | 5M - <10M | UW | NS/2/2 | 94.5% |
Face_Amount_Band | 10M+ | UW | NS/2/2 | 104.8% |
Face_Amount_Band | 500K - <1M | UW | NS/1/3 | 97.3% |
Face_Amount_Band | 1M - <2.5M | UW | NS/1/3 | 83.3% |
Face_Amount_Band | 10M+ | UW | NS/1/3 | 179.4% |
Face_Amount_Band | 250K - <500K | UW | NS/2/3 | 100.9% |
Face_Amount_Band | 2.5M - <5M | UW | NS/2/3 | 95.5% |
Face_Amount_Band | 5M - <10M | UW | NS/2/3 | 92.2% |
Face_Amount_Band | 10M+ | UW | NS/2/3 | 99.9% |
Face_Amount_Band | 100K - <250K | UW | NS/3/3 | 99.4% |
Face_Amount_Band | 250K - <500K | UW | NS/3/3 | 99.9% |
Face_Amount_Band | 500K - <1M | UW | NS/3/3 | 102.7% |
Face_Amount_Band | 1M - <2.5M | UW | NS/3/3 | 105.7% |
Face_Amount_Band | 2.5M - <5M | UW | NS/3/3 | 107.0% |
Face_Amount_Band | 10M+ | UW | NS/3/3 | 113.9% |
Face_Amount_Band | 10M+ | UW | NS/1/4 | 75.1% |
Face_Amount_Band | 2.5M - <5M | UW | NS/2/4 | 75.6% |
Face_Amount_Band | 5M - <10M | UW | NS/2/4 | 119.6% |
Face_Amount_Band | 2.5M - <5M | UW | NS/4/4 | 132.6% |
Face_Amount_Band | 10M+ | UW | NS/4/4 | 95.9% |
Face_Amount_Band | 10K - <25K | UW | NS/U/U | 107.8% |
Face_Amount_Band | 25K - <50K | UW | NS/U/U | 102.1% |
Face_Amount_Band | 50K - <100K | UW | NS/U/U | 99.2% |
Face_Amount_Band | 100K - <250K | UW | NS/U/U | 97.0% |
Face_Amount_Band | 500K - <1M | UW | NS/U/U | 99.2% |
Face_Amount_Band | 2.5M - <5M | UW | NS/U/U | 98.8% |
Face_Amount_Band | 5M - <10M | UW | NS/U/U | 93.0% |
Face_Amount_Band | 10M+ | UW | NS/U/U | 92.9% |
Face_Amount_Band | 2.5M - <5M | UW | S/1/2 | 112.3% |
Face_Amount_Band | 5M - <10M | UW | S/1/2 | 87.8% |
Face_Amount_Band | 500K - <1M | UW | S/2/2 | 107.3% |
Face_Amount_Band | 1M - <2.5M | UW | S/2/2 | 98.7% |
Face_Amount_Band | 2.5M - <5M | UW | S/2/2 | 94.7% |
Face_Amount_Band | 5M - <10M | UW | S/2/2 | 114.1% |
Face_Amount_Band | 250K - <500K | UW | S/U/U | 100.5% |
Face_Amount_Band | 500K - <1M | UW | S/U/U | 97.7% |
Face_Amount_Band | 1M - <2.5M | UW | S/U/U | 101.0% |
Face_Amount_Band | 2.5M - <5M | UW | S/U/U | 102.7% |
Face_Amount_Band | 5M - <10M | UW | S/U/U | 94.0% |
Face_Amount_Band | 10M+ | UW | S/U/U | 114.4% |
Face_Amount_Band | 50K - <100K | UW | U/U/U | 107.9% |
Face_Amount_Band | 250K - <500K | UW | U/U/U | 92.6% |
Face_Amount_Band | 500K - <1M | UW | U/U/U | 98.5% |
Face_Amount_Band | 1M - <2.5M | UW | U/U/U | 73.6% |
Face_Amount_Band | 10M+ | UW | U/U/U | 229.0% |
Face_Amount_Band | 1M - <2.5M | Dur_Grp | 2-2 | 83.1% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 4-5 | 100.4% |
Face_Amount_Band | 2.5M - <5M | Dur_Grp | 4-5 | 93.0% |
Face_Amount_Band | 5M - <10M | Dur_Grp | 4-5 | 88.5% |
Face_Amount_Band | 10M+ | Dur_Grp | 4-5 | 71.7% |
Face_Amount_Band | 10K - <25K | Dur_Grp | 6-10 | 100.2% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 6-10 | 103.5% |
Face_Amount_Band | 100K - <250K | Dur_Grp | 6-10 | 98.3% |
Face_Amount_Band | 1M - <2.5M | Dur_Grp | 6-10 | 94.5% |
Face_Amount_Band | 2.5M - <5M | Dur_Grp | 6-10 | 96.0% |
Face_Amount_Band | 10M+ | Dur_Grp | 6-10 | 125.6% |
Face_Amount_Band | 100K - <250K | Dur_Grp | 11-15 | 98.2% |
Face_Amount_Band | 1M - <2.5M | Dur_Grp | 11-15 | 99.7% |
Face_Amount_Band | 2.5M - <5M | Dur_Grp | 11-15 | 95.0% |
Face_Amount_Band | 5M - <10M | Dur_Grp | 11-15 | 101.4% |
Face_Amount_Band | 10M+ | Dur_Grp | 11-15 | 95.0% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 16-20 | 98.9% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 16-20 | 98.2% |
Face_Amount_Band | 100K - <250K | Dur_Grp | 16-20 | 94.7% |
Face_Amount_Band | 250K - <500K | Dur_Grp | 16-20 | 99.0% |
Face_Amount_Band | 1M - <2.5M | Dur_Grp | 16-20 | 105.4% |
Face_Amount_Band | 2.5M - <5M | Dur_Grp | 16-20 | 102.2% |
Face_Amount_Band | 10K - <25K | Dur_Grp | 21-30 | 92.5% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 21-30 | 90.4% |
Face_Amount_Band | 50K - <100K | Dur_Grp | 21-30 | 92.2% |
Face_Amount_Band | 100K - <250K | Dur_Grp | 21-30 | 92.9% |
Face_Amount_Band | 250K - <500K | Dur_Grp | 21-30 | 96.3% |
Face_Amount_Band | 1M - <2.5M | Dur_Grp | 21-30 | 102.7% |
Face_Amount_Band | 2.5M - <5M | Dur_Grp | 21-30 | 112.1% |
Face_Amount_Band | 10M+ | Dur_Grp | 21-30 | 101.3% |
Face_Amount_Band | 10K - <25K | Dur_Grp | 31-120 | 96.5% |
Face_Amount_Band | 25K - <50K | Dur_Grp | 31-120 | 95.4% |
Face_Amount_Band | 100K - <250K | Dur_Grp | 31-120 | 100.3% |
Face_Amount_Band | 250K - <500K | Dur_Grp | 31-120 | 102.9% |
Face_Amount_Band | 1M - <2.5M | Dur_Grp | 31-120 | 98.5% |
Face_Amount_Band | 10K - <25K | Insurance_Plan | Perm | 101.0% |
Face_Amount_Band | 100K - <250K | Insurance_Plan | Perm | 98.9% |
Face_Amount_Band | 250K - <500K | Insurance_Plan | Perm | 92.9% |
Face_Amount_Band | 500K - <1M | Insurance_Plan | Perm | 88.8% |
Face_Amount_Band | 1M - <2.5M | Insurance_Plan | Perm | 90.7% |
Face_Amount_Band | 2.5M - <5M | Insurance_Plan | Perm | 85.8% |
Face_Amount_Band | 5M - <10M | Insurance_Plan | Perm | 87.9% |
Face_Amount_Band | 10M+ | Insurance_Plan | Perm | 187.4% |
Face_Amount_Band | 25K - <50K | Insurance_Plan | UL | 100.2% |
Face_Amount_Band | 50K - <100K | Insurance_Plan | UL | 102.8% |
Face_Amount_Band | 100K - <250K | Insurance_Plan | UL | 101.8% |
Face_Amount_Band | 250K - <500K | Insurance_Plan | UL | 102.0% |
Face_Amount_Band | 500K - <1M | Insurance_Plan | UL | 100.9% |
Face_Amount_Band | 1M - <2.5M | Insurance_Plan | UL | 99.6% |
Face_Amount_Band | 2.5M - <5M | Insurance_Plan | UL | 96.3% |
Face_Amount_Band | 5M - <10M | Insurance_Plan | UL | 93.4% |
Face_Amount_Band | 50K - <100K | Insurance_Plan | ULSG | 102.2% |
Face_Amount_Band | 500K - <1M | Insurance_Plan | ULSG | 98.7% |
Face_Amount_Band | 1M - <2.5M | Insurance_Plan | ULSG | 99.9% |
Face_Amount_Band | 2.5M - <5M | Insurance_Plan | ULSG | 98.9% |
Face_Amount_Band | 10M+ | Insurance_Plan | ULSG | 97.7% |
Face_Amount_Band | 50K - <100K | Insurance_Plan | VL | 98.9% |
Face_Amount_Band | 100K - <250K | Insurance_Plan | VL | 97.5% |
Face_Amount_Band | 250K - <500K | Insurance_Plan | VL | 98.0% |
Face_Amount_Band | 2.5M - <5M | Insurance_Plan | VL | 106.5% |
Face_Amount_Band | 10M+ | Insurance_Plan | VL | 99.7% |
Face_Amount_Band | 100K - <250K | Insurance_Plan | VLSG | 97.9% |
Face_Amount_Band | 500K - <1M | Insurance_Plan | VLSG | 97.2% |
Face_Amount_Band | 2.5M - <5M | Insurance_Plan | VLSG | 109.7% |
Face_Amount_Band | 10M+ | Insurance_Plan | VLSG | 122.4% |
Face_Amount_Band | 10M+ | AA_Grp | 18-25 | 220.9% |
Face_Amount_Band | 250K - <500K | AA_Grp | 36-40 | 98.5% |
Face_Amount_Band | 10M+ | AA_Grp | 36-40 | 171.5% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 41-45 | 109.1% |
Face_Amount_Band | 10M+ | AA_Grp | 41-45 | 99.7% |
Face_Amount_Band | 25K - <50K | AA_Grp | 46-50 | 108.9% |
Face_Amount_Band | 100K - <250K | AA_Grp | 46-50 | 97.2% |
Face_Amount_Band | 250K - <500K | AA_Grp | 46-50 | 99.5% |
Face_Amount_Band | 500K - <1M | AA_Grp | 46-50 | 98.3% |
Face_Amount_Band | 10M+ | AA_Grp | 46-50 | 135.8% |
Face_Amount_Band | 10K - <25K | AA_Grp | 51-55 | 116.5% |
Face_Amount_Band | 25K - <50K | AA_Grp | 51-55 | 114.6% |
Face_Amount_Band | 50K - <100K | AA_Grp | 51-55 | 106.7% |
Face_Amount_Band | 500K - <1M | AA_Grp | 51-55 | 99.1% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 51-55 | 92.1% |
Face_Amount_Band | 5M - <10M | AA_Grp | 51-55 | 87.9% |
Face_Amount_Band | 10M+ | AA_Grp | 51-55 | 75.5% |
Face_Amount_Band | 10K - <25K | AA_Grp | 56-60 | 105.0% |
Face_Amount_Band | 25K - <50K | AA_Grp | 56-60 | 105.5% |
Face_Amount_Band | 50K - <100K | AA_Grp | 56-60 | 100.4% |
Face_Amount_Band | 100K - <250K | AA_Grp | 56-60 | 97.4% |
Face_Amount_Band | 250K - <500K | AA_Grp | 56-60 | 96.4% |
Face_Amount_Band | 500K - <1M | AA_Grp | 56-60 | 93.1% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 56-60 | 89.8% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 56-60 | 86.7% |
Face_Amount_Band | 10K - <25K | AA_Grp | 61-65 | 107.6% |
Face_Amount_Band | 25K - <50K | AA_Grp | 61-65 | 105.1% |
Face_Amount_Band | 50K - <100K | AA_Grp | 61-65 | 103.1% |
Face_Amount_Band | 100K - <250K | AA_Grp | 61-65 | 98.5% |
Face_Amount_Band | 250K - <500K | AA_Grp | 61-65 | 93.7% |
Face_Amount_Band | 500K - <1M | AA_Grp | 61-65 | 93.9% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 61-65 | 94.2% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 61-65 | 89.3% |
Face_Amount_Band | 10K - <25K | AA_Grp | 66-70 | 102.1% |
Face_Amount_Band | 25K - <50K | AA_Grp | 66-70 | 100.5% |
Face_Amount_Band | 250K - <500K | AA_Grp | 66-70 | 97.4% |
Face_Amount_Band | 500K - <1M | AA_Grp | 66-70 | 97.2% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 66-70 | 98.9% |
Face_Amount_Band | 5M - <10M | AA_Grp | 66-70 | 102.6% |
Face_Amount_Band | 100K - <250K | AA_Grp | 71-75 | 101.0% |
Face_Amount_Band | 500K - <1M | AA_Grp | 71-75 | 101.9% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 71-75 | 98.2% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 71-75 | 95.8% |
Face_Amount_Band | 5M - <10M | AA_Grp | 71-75 | 87.1% |
Face_Amount_Band | 10M+ | AA_Grp | 71-75 | 74.2% |
Face_Amount_Band | 10K - <25K | AA_Grp | 76-80 | 91.6% |
Face_Amount_Band | 25K - <50K | AA_Grp | 76-80 | 90.3% |
Face_Amount_Band | 50K - <100K | AA_Grp | 76-80 | 94.4% |
Face_Amount_Band | 250K - <500K | AA_Grp | 76-80 | 103.7% |
Face_Amount_Band | 500K - <1M | AA_Grp | 76-80 | 102.8% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 76-80 | 103.3% |
Face_Amount_Band | 10K - <25K | AA_Grp | 81-85 | 88.9% |
Face_Amount_Band | 25K - <50K | AA_Grp | 81-85 | 91.8% |
Face_Amount_Band | 50K - <100K | AA_Grp | 81-85 | 99.2% |
Face_Amount_Band | 100K - <250K | AA_Grp | 81-85 | 106.9% |
Face_Amount_Band | 250K - <500K | AA_Grp | 81-85 | 113.2% |
Face_Amount_Band | 500K - <1M | AA_Grp | 81-85 | 112.0% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 81-85 | 107.0% |
Face_Amount_Band | 5M - <10M | AA_Grp | 81-85 | 96.5% |
Face_Amount_Band | 10M+ | AA_Grp | 81-85 | 86.6% |
Face_Amount_Band | 10K - <25K | AA_Grp | 86-90 | 76.9% |
Face_Amount_Band | 25K - <50K | AA_Grp | 86-90 | 81.7% |
Face_Amount_Band | 50K - <100K | AA_Grp | 86-90 | 88.2% |
Face_Amount_Band | 250K - <500K | AA_Grp | 86-90 | 103.7% |
Face_Amount_Band | 500K - <1M | AA_Grp | 86-90 | 103.7% |
Face_Amount_Band | 5M - <10M | AA_Grp | 86-90 | 101.8% |
Face_Amount_Band | 10M+ | AA_Grp | 86-90 | 119.0% |
Face_Amount_Band | 10K - <25K | AA_Grp | 91-95 | 86.0% |
Face_Amount_Band | 25K - <50K | AA_Grp | 91-95 | 91.1% |
Face_Amount_Band | 50K - <100K | AA_Grp | 91-95 | 99.6% |
Face_Amount_Band | 100K - <250K | AA_Grp | 91-95 | 108.2% |
Face_Amount_Band | 250K - <500K | AA_Grp | 91-95 | 113.1% |
Face_Amount_Band | 500K - <1M | AA_Grp | 91-95 | 112.6% |
Face_Amount_Band | 1M - <2.5M | AA_Grp | 91-95 | 98.6% |
Face_Amount_Band | 2.5M - <5M | AA_Grp | 91-95 | 103.9% |
Face_Amount_Band | 10M+ | AA_Grp | 91-95 | 99.5% |
Face_Amount_Band | 100K - <250K | AA_Grp | 96-100 | 102.3% |
Face_Amount_Band | 500K - <1M | AA_Grp | 96-100 | 106.3% |
Face_Amount_Band | 10M+ | AA_Grp | 96-100 | 76.5% |
Insurance_Plan | Perm | UW | NS/2/2 | 103.0% |
Insurance_Plan | UL | UW | NS/2/2 | 100.7% |
Insurance_Plan | ULSG | UW | NS/2/2 | 100.3% |
Insurance_Plan | VL | UW | NS/2/2 | 99.5% |
Insurance_Plan | UL | UW | NS/1/3 | 87.5% |
Insurance_Plan | ULSG | UW | NS/1/3 | 84.5% |
Insurance_Plan | Perm | UW | NS/2/3 | 108.7% |
Insurance_Plan | UL | UW | NS/2/3 | 96.5% |
Insurance_Plan | VLSG | UW | NS/2/3 | 96.6% |
Insurance_Plan | Perm | UW | NS/3/3 | 116.1% |
Insurance_Plan | VL | UW | NS/3/3 | 110.0% |
Insurance_Plan | VLSG | UW | NS/3/3 | 94.7% |
Insurance_Plan | ULSG | UW | NS/1/4 | 85.8% |
Insurance_Plan | UL | UW | NS/2/4 | 104.0% |
Insurance_Plan | ULSG | UW | NS/2/4 | 89.5% |
Insurance_Plan | ULSG | UW | NS/3/4 | 102.1% |
Insurance_Plan | ULSG | UW | NS/4/4 | 103.0% |
Insurance_Plan | Perm | UW | NS/U/U | 99.6% |
Insurance_Plan | UL | UW | NS/U/U | 98.4% |
Insurance_Plan | ULSG | UW | NS/U/U | 105.7% |
Insurance_Plan | VL | UW | NS/U/U | 103.5% |
Insurance_Plan | VLSG | UW | NS/U/U | 105.3% |
Insurance_Plan | Perm | UW | S/2/2 | 106.9% |
Insurance_Plan | Perm | UW | S/U/U | 102.8% |
Insurance_Plan | ULSG | UW | S/U/U | 119.3% |
Insurance_Plan | VL | UW | S/U/U | 96.6% |
Insurance_Plan | VLSG | UW | S/U/U | 95.8% |
Insurance_Plan | ULSG | UW | U/U/U | 80.0% |
Insurance_Plan | VL | UW | U/U/U | 101.0% |
Insurance_Plan | VLSG | UW | U/U/U | 110.6% |
UW | NS/1/4 | Dur_Grp | 2-2 | 92.5% |
UW | NS/2/2 | Dur_Grp | 3-3 | 100.4% |
UW | NS/3/3 | Dur_Grp | 3-3 | 98.1% |
UW | NS/2/4 | Dur_Grp | 3-3 | 93.2% |
UW | NS/U/U | Dur_Grp | 3-3 | 104.2% |
UW | NS/2/2 | Dur_Grp | 4-5 | 94.8% |
UW | NS/1/3 | Dur_Grp | 4-5 | 111.8% |
UW | NS/2/3 | Dur_Grp | 4-5 | 92.4% |
UW | NS/2/4 | Dur_Grp | 4-5 | 128.7% |
UW | NS/3/4 | Dur_Grp | 4-5 | 127.1% |
UW | NS/4/4 | Dur_Grp | 4-5 | 104.8% |
UW | NS/U/U | Dur_Grp | 4-5 | 104.4% |
UW | S/2/2 | Dur_Grp | 4-5 | 93.3% |
UW | NS/2/2 | Dur_Grp | 6-10 | 99.3% |
UW | NS/1/3 | Dur_Grp | 6-10 | 106.3% |
UW | NS/3/3 | Dur_Grp | 6-10 | 104.5% |
UW | NS/U/U | Dur_Grp | 6-10 | 99.0% |
UW | S/1/2 | Dur_Grp | 6-10 | 89.2% |
UW | S/2/2 | Dur_Grp | 6-10 | 83.8% |
UW | U/U/U | Dur_Grp | 6-10 | 121.0% |
UW | NS/2/2 | Dur_Grp | 11-15 | 103.2% |
UW | NS/1/3 | Dur_Grp | 11-15 | 118.2% |
UW | NS/2/3 | Dur_Grp | 11-15 | 96.6% |
UW | NS/3/3 | Dur_Grp | 11-15 | 103.6% |
UW | NS/3/4 | Dur_Grp | 11-15 | 129.7% |
UW | NS/U/U | Dur_Grp | 11-15 | 97.6% |
UW | S/1/2 | Dur_Grp | 11-15 | 91.7% |
UW | S/2/2 | Dur_Grp | 11-15 | 109.0% |
UW | S/U/U | Dur_Grp | 11-15 | 98.3% |
UW | NS/2/2 | Dur_Grp | 16-20 | 100.6% |
UW | NS/1/3 | Dur_Grp | 16-20 | 94.9% |
UW | NS/2/3 | Dur_Grp | 16-20 | 100.3% |
UW | NS/3/3 | Dur_Grp | 16-20 | 104.1% |
UW | NS/U/U | Dur_Grp | 16-20 | 94.0% |
UW | S/1/2 | Dur_Grp | 16-20 | 108.9% |
UW | S/2/2 | Dur_Grp | 16-20 | 104.9% |
UW | S/U/U | Dur_Grp | 16-20 | 99.1% |
UW | NS/2/2 | Dur_Grp | 21-30 | 100.7% |
UW | NS/2/3 | Dur_Grp | 21-30 | 91.1% |
UW | NS/3/3 | Dur_Grp | 21-30 | 44.6% |
UW | NS/4/4 | Dur_Grp | 21-30 | 69.8% |
UW | S/1/2 | Dur_Grp | 21-30 | 106.9% |
UW | S/2/2 | Dur_Grp | 21-30 | 106.9% |
UW | S/U/U | Dur_Grp | 21-30 | 104.1% |
UW | U/U/U | Dur_Grp | 21-30 | 100.2% |
UW | NS/3/3 | Dur_Grp | 31-120 | 58.8% |
UW | U/U/U | Dur_Grp | 31-120 | 82.3% |
UW | NS/U/U | AA_Grp | 18-25 | 95.5% |
UW | NS/1/3 | AA_Grp | 31-35 | 93.6% |
UW | NS/3/3 | AA_Grp | 36-40 | 108.9% |
UW | NS/1/3 | AA_Grp | 41-45 | 102.0% |
UW | NS/2/3 | AA_Grp | 41-45 | 101.9% |
UW | S/1/2 | AA_Grp | 41-45 | 95.2% |
UW | NS/2/2 | AA_Grp | 46-50 | 106.4% |
UW | NS/1/3 | AA_Grp | 46-50 | 94.1% |
UW | NS/3/3 | AA_Grp | 46-50 | 136.4% |
UW | NS/U/U | AA_Grp | 46-50 | 100.6% |
UW | S/U/U | AA_Grp | 46-50 | 99.0% |
UW | NS/3/3 | AA_Grp | 51-55 | 111.9% |
UW | NS/U/U | AA_Grp | 51-55 | 98.2% |
UW | S/U/U | AA_Grp | 51-55 | 95.6% |
UW | NS/1/3 | AA_Grp | 56-60 | 112.2% |
UW | NS/U/U | AA_Grp | 56-60 | 99.1% |
UW | S/2/2 | AA_Grp | 56-60 | 108.5% |
UW | U/U/U | AA_Grp | 56-60 | 110.6% |
UW | NS/2/2 | AA_Grp | 61-65 | 106.2% |
UW | NS/1/3 | AA_Grp | 61-65 | 115.2% |
UW | NS/3/3 | AA_Grp | 61-65 | 117.8% |
UW | NS/1/4 | AA_Grp | 61-65 | 94.8% |
UW | NS/2/4 | AA_Grp | 61-65 | 94.9% |
UW | NS/4/4 | AA_Grp | 61-65 | 107.9% |
UW | S/U/U | AA_Grp | 61-65 | 94.9% |
UW | U/U/U | AA_Grp | 61-65 | 110.5% |
UW | NS/2/2 | AA_Grp | 66-70 | 110.1% |
UW | NS/1/3 | AA_Grp | 66-70 | 78.5% |
UW | NS/2/3 | AA_Grp | 66-70 | 97.5% |
UW | NS/3/3 | AA_Grp | 66-70 | 106.6% |
UW | NS/1/4 | AA_Grp | 66-70 | 95.9% |
UW | NS/2/4 | AA_Grp | 66-70 | 99.9% |
UW | NS/U/U | AA_Grp | 66-70 | 113.4% |
UW | S/U/U | AA_Grp | 66-70 | 101.9% |
UW | U/U/U | AA_Grp | 66-70 | 133.0% |
UW | NS/1/3 | AA_Grp | 71-75 | 113.1% |
UW | NS/3/3 | AA_Grp | 71-75 | 104.6% |
UW | NS/4/4 | AA_Grp | 71-75 | 114.9% |
UW | NS/U/U | AA_Grp | 71-75 | 100.6% |
UW | S/1/2 | AA_Grp | 71-75 | 104.4% |
UW | S/2/2 | AA_Grp | 71-75 | 99.9% |
UW | U/U/U | AA_Grp | 71-75 | 108.0% |
UW | NS/1/3 | AA_Grp | 76-80 | 94.3% |
UW | NS/2/3 | AA_Grp | 76-80 | 86.1% |
UW | NS/3/3 | AA_Grp | 76-80 | 94.5% |
UW | NS/2/4 | AA_Grp | 76-80 | 94.9% |
UW | NS/3/4 | AA_Grp | 76-80 | 113.0% |
UW | S/1/2 | AA_Grp | 76-80 | 120.7% |
UW | S/U/U | AA_Grp | 76-80 | 107.4% |
UW | U/U/U | AA_Grp | 76-80 | 103.8% |
UW | NS/2/2 | AA_Grp | 81-85 | 96.4% |
UW | NS/1/3 | AA_Grp | 81-85 | 101.1% |
UW | NS/2/3 | AA_Grp | 81-85 | 97.6% |
UW | NS/3/3 | AA_Grp | 81-85 | 94.1% |
UW | NS/3/4 | AA_Grp | 81-85 | 101.3% |
UW | S/2/2 | AA_Grp | 81-85 | 102.9% |
UW | S/U/U | AA_Grp | 81-85 | 111.0% |
UW | NS/2/2 | AA_Grp | 86-90 | 100.0% |
UW | NS/1/3 | AA_Grp | 86-90 | 84.6% |
UW | NS/2/3 | AA_Grp | 86-90 | 89.3% |
UW | NS/3/3 | AA_Grp | 86-90 | 82.1% |
UW | NS/2/4 | AA_Grp | 86-90 | 124.8% |
UW | NS/3/4 | AA_Grp | 86-90 | 74.8% |
UW | NS/4/4 | AA_Grp | 86-90 | 89.6% |
UW | NS/U/U | AA_Grp | 86-90 | 104.6% |
UW | S/U/U | AA_Grp | 86-90 | 103.3% |
UW | NS/2/2 | AA_Grp | 91-95 | 89.4% |
UW | NS/1/3 | AA_Grp | 91-95 | 90.6% |
UW | NS/2/3 | AA_Grp | 91-95 | 106.0% |
UW | NS/3/3 | AA_Grp | 91-95 | 77.9% |
UW | NS/4/4 | AA_Grp | 91-95 | 87.1% |
UW | NS/U/U | AA_Grp | 91-95 | 102.2% |
UW | S/U/U | AA_Grp | 91-95 | 85.7% |
UW | NS/2/2 | AA_Grp | 96-100 | 98.3% |
UW | NS/2/3 | AA_Grp | 96-100 | 103.4% |
UW | NS/3/3 | AA_Grp | 96-100 | 81.5% |
UW | U/U/U | AA_Grp | 96-100 | 98.7% |
UW | U/U/U | AA_Grp | 101-105 | 94.1% |
Insurance_Plan | Perm | Dur_Grp | 2-2 | 119.8% |
Insurance_Plan | ULSG | Dur_Grp | 2-2 | 90.1% |
Insurance_Plan | ULSG | Dur_Grp | 4-5 | 98.1% |
Insurance_Plan | VLSG | Dur_Grp | 4-5 | 97.4% |
Insurance_Plan | UL | Dur_Grp | 6-10 | 93.3% |
Insurance_Plan | ULSG | Dur_Grp | 6-10 | 101.0% |
Insurance_Plan | VLSG | Dur_Grp | 6-10 | 98.3% |
Insurance_Plan | UL | Dur_Grp | 11-15 | 90.6% |
Insurance_Plan | ULSG | Dur_Grp | 11-15 | 98.8% |
Insurance_Plan | VLSG | Dur_Grp | 11-15 | 110.5% |
Insurance_Plan | Perm | Dur_Grp | 16-20 | 98.3% |
Insurance_Plan | UL | Dur_Grp | 16-20 | 96.3% |
Insurance_Plan | ULSG | Dur_Grp | 16-20 | 104.0% |
Insurance_Plan | Perm | Dur_Grp | 21-30 | 94.7% |
Insurance_Plan | UL | Dur_Grp | 21-30 | 103.0% |
Insurance_Plan | ULSG | Dur_Grp | 31-120 | 62.7% |
Insurance_Plan | VL | AA_Grp | 18-25 | 100.7% |
Insurance_Plan | ULSG | AA_Grp | 41-45 | 104.5% |
Insurance_Plan | UL | AA_Grp | 46-50 | 107.5% |
Insurance_Plan | VL | AA_Grp | 46-50 | 91.6% |
Insurance_Plan | Perm | AA_Grp | 51-55 | 99.4% |
Insurance_Plan | UL | AA_Grp | 51-55 | 103.4% |
Insurance_Plan | ULSG | AA_Grp | 51-55 | 113.2% |
Insurance_Plan | VLSG | AA_Grp | 51-55 | 98.9% |
Insurance_Plan | UL | AA_Grp | 56-60 | 103.4% |
Insurance_Plan | VL | AA_Grp | 56-60 | 98.8% |
Insurance_Plan | Perm | AA_Grp | 61-65 | 93.3% |
Insurance_Plan | ULSG | AA_Grp | 61-65 | 91.9% |
Insurance_Plan | VL | AA_Grp | 61-65 | 103.5% |
Insurance_Plan | Perm | AA_Grp | 66-70 | 87.2% |
Insurance_Plan | UL | AA_Grp | 66-70 | 92.9% |
Insurance_Plan | ULSG | AA_Grp | 66-70 | 98.0% |
Insurance_Plan | Perm | AA_Grp | 71-75 | 93.3% |
Insurance_Plan | UL | AA_Grp | 71-75 | 103.2% |
Insurance_Plan | ULSG | AA_Grp | 71-75 | 92.3% |
Insurance_Plan | VL | AA_Grp | 71-75 | 104.3% |
Insurance_Plan | VLSG | AA_Grp | 71-75 | 103.2% |
Insurance_Plan | UL | AA_Grp | 76-80 | 104.2% |
Insurance_Plan | VL | AA_Grp | 76-80 | 96.6% |
Insurance_Plan | VLSG | AA_Grp | 76-80 | 99.9% |
Insurance_Plan | Perm | AA_Grp | 81-85 | 100.6% |
Insurance_Plan | UL | AA_Grp | 81-85 | 102.0% |
Insurance_Plan | ULSG | AA_Grp | 81-85 | 99.4% |
Insurance_Plan | Perm | AA_Grp | 86-90 | 102.6% |
Insurance_Plan | UL | AA_Grp | 86-90 | 97.0% |
Insurance_Plan | ULSG | AA_Grp | 86-90 | 100.9% |
Insurance_Plan | VL | AA_Grp | 86-90 | 102.1% |
Insurance_Plan | Perm | AA_Grp | 91-95 | 101.8% |
Insurance_Plan | UL | AA_Grp | 91-95 | 92.4% |
Insurance_Plan | ULSG | AA_Grp | 91-95 | 101.6% |
Insurance_Plan | VL | AA_Grp | 91-95 | 97.0% |
Insurance_Plan | Perm | AA_Grp | 96-100 | 104.0% |
Insurance_Plan | ULSG | AA_Grp | 96-100 | 85.1% |
Insurance_Plan | VL | AA_Grp | 96-100 | 108.8% |
Insurance_Plan | UL | AA_Grp | 101-105 | 82.4% |
AA_Grp | 41-45 | Dur_Grp | 2-2 | 100.4% |
AA_Grp | 46-50 | Dur_Grp | 2-2 | 91.8% |
AA_Grp | 51-55 | Dur_Grp | 2-2 | 78.0% |
AA_Grp | 61-65 | Dur_Grp | 2-2 | 107.1% |
AA_Grp | 66-70 | Dur_Grp | 2-2 | 81.9% |
AA_Grp | 41-45 | Dur_Grp | 3-3 | 107.8% |
AA_Grp | 56-60 | Dur_Grp | 3-3 | 96.5% |
AA_Grp | 61-65 | Dur_Grp | 3-3 | 97.8% |
AA_Grp | 71-75 | Dur_Grp | 3-3 | 98.8% |
AA_Grp | 46-50 | Dur_Grp | 4-5 | 98.6% |
AA_Grp | 56-60 | Dur_Grp | 4-5 | 89.4% |
AA_Grp | 61-65 | Dur_Grp | 4-5 | 97.2% |
AA_Grp | 71-75 | Dur_Grp | 4-5 | 105.9% |
AA_Grp | 81-85 | Dur_Grp | 4-5 | 99.1% |
AA_Grp | 86-90 | Dur_Grp | 4-5 | 105.8% |
AA_Grp | 91-95 | Dur_Grp | 4-5 | 87.9% |
AA_Grp | 18-25 | Dur_Grp | 6-10 | 112.9% |
AA_Grp | 46-50 | Dur_Grp | 6-10 | 111.6% |
AA_Grp | 51-55 | Dur_Grp | 6-10 | 99.6% |
AA_Grp | 56-60 | Dur_Grp | 6-10 | 112.0% |
AA_Grp | 66-70 | Dur_Grp | 6-10 | 96.5% |
AA_Grp | 71-75 | Dur_Grp | 6-10 | 102.4% |
AA_Grp | 76-80 | Dur_Grp | 6-10 | 91.8% |
AA_Grp | 81-85 | Dur_Grp | 6-10 | 94.1% |
AA_Grp | 86-90 | Dur_Grp | 6-10 | 99.1% |
AA_Grp | 91-95 | Dur_Grp | 6-10 | 77.7% |
AA_Grp | 96-100 | Dur_Grp | 6-10 | 119.9% |
AA_Grp | 46-50 | Dur_Grp | 11-15 | 104.0% |
AA_Grp | 61-65 | Dur_Grp | 11-15 | 99.7% |
AA_Grp | 66-70 | Dur_Grp | 11-15 | 98.2% |
AA_Grp | 71-75 | Dur_Grp | 11-15 | 99.0% |
AA_Grp | 76-80 | Dur_Grp | 11-15 | 107.7% |
AA_Grp | 86-90 | Dur_Grp | 11-15 | 91.4% |
AA_Grp | 91-95 | Dur_Grp | 11-15 | 98.8% |
AA_Grp | 96-100 | Dur_Grp | 11-15 | 104.1% |
AA_Grp | 56-60 | Dur_Grp | 16-20 | 99.6% |
AA_Grp | 66-70 | Dur_Grp | 16-20 | 103.1% |
AA_Grp | 76-80 | Dur_Grp | 16-20 | 98.8% |
AA_Grp | 81-85 | Dur_Grp | 16-20 | 99.9% |
AA_Grp | 86-90 | Dur_Grp | 16-20 | 102.8% |
AA_Grp | 91-95 | Dur_Grp | 16-20 | 108.4% |
AA_Grp | 101-105 | Dur_Grp | 16-20 | 110.4% |
AA_Grp | 41-45 | Dur_Grp | 21-30 | 96.6% |
AA_Grp | 46-50 | Dur_Grp | 21-30 | 99.8% |
AA_Grp | 56-60 | Dur_Grp | 21-30 | 99.7% |
AA_Grp | 61-65 | Dur_Grp | 21-30 | 102.4% |
AA_Grp | 66-70 | Dur_Grp | 21-30 | 103.3% |
AA_Grp | 71-75 | Dur_Grp | 21-30 | 101.1% |
AA_Grp | 81-85 | Dur_Grp | 21-30 | 103.8% |
AA_Grp | 86-90 | Dur_Grp | 21-30 | 103.3% |
AA_Grp | 91-95 | Dur_Grp | 21-30 | 104.9% |
AA_Grp | 61-65 | Dur_Grp | 31-120 | 100.3% |
AA_Grp | 71-75 | Dur_Grp | 31-120 | 103.0% |
AA_Grp | 76-80 | Dur_Grp | 31-120 | 103.6% |
AA_Grp | 81-85 | Dur_Grp | 31-120 | 104.8% |
AA_Grp | 96-100 | Dur_Grp | 31-120 | 93.3% |
AA_Grp | 101-105 | Dur_Grp | 31-120 | 75.9% |
AA_Grp | 106-110 | Dur_Grp | 31-120 | 87.8% |
AA_Grp | 111-115 | Dur_Grp | 31-120 | 90.4% |
AA_Grp | 116-120 | Dur_Grp | 31-120 | 98.9% |
Sex | M | Face_Amount_Band | 10K - <25K | 111.3% |
Sex | M | Face_Amount_Band | 25K - <50K | 108.3% |
Sex | M | Face_Amount_Band | 50K - <100K | 107.7% |
Sex | M | Face_Amount_Band | 100K - <250K | 104.5% |
Sex | M | Face_Amount_Band | 250K - <500K | 99.5% |
Sex | M | Face_Amount_Band | 500K - <1M | 97.4% |
Sex | M | Face_Amount_Band | 1M - <2.5M | 91.9% |
Sex | M | Face_Amount_Band | 2.5M - <5M | 93.5% |
Sex | M | Face_Amount_Band | 5M - <10M | 96.6% |
Sex | M | Face_Amount_Band | 10M+ | 89.6% |
Sex | M | UW | NS/2/2 | 99.9% |
Sex | M | UW | NS/1/3 | 93.8% |
Sex | M | UW | NS/2/3 | 106.0% |
Sex | M | UW | NS/1/4 | 84.3% |
Sex | M | UW | NS/2/4 | 137.4% |
Sex | M | UW | S/1/2 | 105.8% |
Sex | M | UW | S/2/2 | 94.6% |
Sex | M | UW | U/U/U | 110.1% |
Sex | M | Insurance_Plan | Perm | 97.8% |
Sex | M | Insurance_Plan | UL | 104.3% |
Sex | M | Insurance_Plan | VL | 100.9% |
Sex | M | Insurance_Plan | VLSG | 100.5% |
Sex | M | AA_Grp | 18-25 | 103.0% |
Sex | M | AA_Grp | 31-35 | 105.4% |
Sex | M | AA_Grp | 36-40 | 121.1% |
Sex | M | AA_Grp | 51-55 | 101.3% |
Sex | M | AA_Grp | 56-60 | 111.4% |
Sex | M | AA_Grp | 61-65 | 106.1% |
Sex | M | AA_Grp | 71-75 | 98.7% |
Sex | M | AA_Grp | 81-85 | 93.9% |
Sex | M | AA_Grp | 86-90 | 100.5% |
Sex | M | AA_Grp | 96-100 | 85.2% |
Sex | M | Dur_Grp | 2-2 | 118.4% |
Sex | M | Dur_Grp | 3-3 | 100.9% |
Sex | M | Dur_Grp | 6-10 | 100.7% |
Sex | M | Dur_Grp | 11-15 | 96.3% |
Sex | M | Dur_Grp | 16-20 | 99.4% |
Sex | M | Dur_Grp | 21-30 | 98.3% |
Sex | M | Dur_Grp | 31-120 | 99.5% |
Note that interaction terms must be considered together. For example, UW interacts with Face Amount Band, so these should be considered in combination. The slate of UW without a second feature apply to the base level of Face Amount Band (and any other factor with which UW interacts).
Since penalization is roughly equivalent to Bayesian credibility using a combination of Gaussian and Laplace priors, these factors are arguably credible. This is true even when dealing with factors with small effect sizes, such as the standalone factor for Duration 3.
Plots and tables of effects are much more digestible. As it happens, all but Sex are involved in feature interactions. Those factors can be read from the table above.
In the plots and tables that follow, we fix all of the other variables at their middle values when extracting final factors.
We generate some supporting tables: a factor grid for attaching to the experience, and a list of interactions present in the model
Code
dat.perm.knw[,..pred.cols] %>%
mutate(Face_Amount_Band=fct_drop(Face_Amount_Band)) %>%
lapply(levels) %>%
expand.grid() ->
dat.perm.knw.grid
dat.perm.knw.grid %>%
model.Matrix(
object=glmnetFormula,
data=.,
sparse=T
) %>%
predict(
cvfit.perm.knw,
newx=.,
s="lambda.min"
) %>%
as.vector() ->
newCoef
dat.perm.knw.grid %>%
add_column(
Factor=exp(newCoef)
) %>%
setDT() ->
dat.perm.knw.grid
dat.perm.knw.grid %>%
filter(!(Insurance_Plan == "Perm" & UW == "U/U/U")) %>%
write.xlsx(
file="dat.perm.knw.grid.xlsx")
reformatCoefs(cvfit.perm.knw, pred.cols) %>%
filter(Coef != 0 & !is.na(Feature2Name)) %>%
select(Feature1Name,Feature2Name) %>%
distinct() %>%
as.list() %>%
purrr::list_transpose() ->
perm.knw.int.list8.2.6.1.3 Plots of Terms
Below are plots of the 2-way interaction terms, with external factors fixed at their middle values.
Effects tend to be subtle, and the following call out the ones that stand out in the plots. Inspecting the coefficient table will reveal where others are located.
- Face Amount Band x Sex: The gradient in mortality with increasing face amount band is steeper than for females.
- Sex x UW: preferred differentials seem to vary by Sex.
8.2.6.1.4 Tables of Terms
Below are tables of the 2-way interaction terms, with external factors fixed at their middle values.
Face_Amount_Band | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
<10K | 89.8% | 120.3% | 94.5% | 78.1% | 135.9% | 85.2% | 88.6% | 114.1% | 119.5% | 108.5% | 84.7% | 103.7% | 101.4% | 105.6% |
10K - <25K | 110.9% | 148.5% | 116.8% | 96.4% | 167.9% | 105.2% | 109.5% | 141.0% | 147.6% | 144.5% | 104.6% | 128.1% | 125.2% | 130.5% |
25K - <50K | 107.4% | 143.8% | 113.1% | 93.4% | 162.6% | 101.9% | 106.0% | 136.5% | 142.9% | 132.4% | 101.3% | 124.0% | 121.3% | 126.3% |
50K - <100K | 95.7% | 127.1% | 100.7% | 83.2% | 144.8% | 90.8% | 94.4% | 121.6% | 127.3% | 114.6% | 90.2% | 110.5% | 108.0% | 121.4% |
100K - <250K | 84.8% | 112.3% | 89.2% | 73.7% | 127.5% | 80.4% | 83.6% | 107.7% | 112.7% | 99.2% | 79.9% | 97.8% | 95.7% | 99.7% |
250K - <500K | 76.6% | 103.1% | 80.7% | 67.2% | 115.8% | 72.7% | 75.6% | 97.4% | 101.9% | 92.5% | 72.3% | 88.5% | 86.9% | 83.4% |
500K - <1M | 76.5% | 105.6% | 78.4% | 66.5% | 118.9% | 72.6% | 75.5% | 97.2% | 101.8% | 91.7% | 72.2% | 94.8% | 84.4% | 88.7% |
1M - <2.5M | 80.7% | 116.6% | 70.8% | 70.1% | 129.1% | 76.5% | 79.6% | 102.5% | 107.3% | 97.4% | 76.1% | 92.0% | 92.0% | 69.8% |
2.5M - <5M | 71.2% | 101.3% | 75.0% | 59.1% | 115.4% | 67.6% | 53.2% | 90.5% | 125.6% | 85.0% | 75.4% | 77.9% | 82.6% | 83.8% |
5M - <10M | 68.7% | 86.9% | 72.3% | 55.1% | 104.0% | 65.2% | 81.1% | 87.3% | 91.4% | 77.1% | 56.9% | 90.5% | 72.9% | 80.8% |
10M+ | 45.9% | 64.5% | 86.7% | 39.9% | 79.2% | 32.7% | 45.3% | 58.4% | 58.6% | 51.5% | 43.3% | 53.0% | 59.3% | 123.7% |
Dur_Grp | <10K | 10K - <25K | 25K - <50K | 50K - <100K | 100K - <250K | 250K - <500K | 500K - <1M | 1M - <2.5M | 2.5M - <5M | 5M - <10M | 10M+ |
|---|---|---|---|---|---|---|---|---|---|---|---|
1-1 | 74.8% | 92.4% | 89.4% | 79.4% | 70.6% | 63.8% | 63.7% | 67.2% | 48.2% | 77.4% | 53.3% |
2-2 | 80.1% | 98.9% | 95.8% | 85.0% | 75.6% | 68.3% | 68.2% | 59.8% | 51.7% | 82.8% | 57.1% |
3-3 | 68.1% | 84.1% | 81.5% | 72.3% | 64.3% | 58.1% | 58.0% | 61.2% | 43.9% | 70.5% | 48.6% |
4-5 | 88.6% | 109.5% | 106.0% | 94.4% | 83.6% | 75.6% | 75.5% | 79.6% | 53.2% | 81.1% | 45.3% |
6-10 | 67.2% | 83.2% | 83.2% | 71.3% | 62.4% | 57.3% | 57.3% | 57.1% | 41.6% | 69.5% | 60.2% |
11-15 | 66.2% | 81.8% | 79.2% | 70.3% | 61.4% | 56.5% | 56.4% | 59.3% | 40.6% | 69.5% | 44.8% |
16-20 | 71.3% | 88.1% | 84.3% | 74.3% | 63.7% | 60.2% | 60.7% | 67.5% | 47.0% | 73.7% | 50.8% |
21-30 | 78.8% | 90.1% | 85.2% | 77.1% | 69.1% | 64.8% | 67.2% | 72.7% | 57.0% | 81.5% | 57.0% |
31-120 | 69.3% | 82.6% | 79.0% | 73.5% | 65.5% | 60.8% | 59.0% | 61.3% | 44.7% | 71.6% | 49.4% |
Face_Amount_Band | Other | Perm | UL | ULSG | VL | VLSG |
|---|---|---|---|---|---|---|
<10K | 79.7% | 74.3% | 88.6% | 64.3% | 82.5% | 75.1% |
10K - <25K | 98.4% | 92.6% | 109.5% | 79.4% | 101.8% | 92.8% |
25K - <50K | 95.1% | 88.7% | 106.0% | 76.8% | 98.4% | 89.6% |
50K - <100K | 82.5% | 77.0% | 94.4% | 68.1% | 84.4% | 77.8% |
100K - <250K | 73.8% | 68.1% | 83.6% | 59.6% | 74.5% | 68.2% |
250K - <500K | 66.7% | 57.8% | 75.6% | 53.8% | 67.6% | 62.8% |
500K - <1M | 67.3% | 55.8% | 75.5% | 53.6% | 69.7% | 61.7% |
1M - <2.5M | 71.9% | 60.8% | 79.6% | 58.0% | 74.4% | 67.7% |
2.5M - <5M | 49.6% | 39.7% | 53.2% | 39.6% | 54.7% | 51.3% |
5M - <10M | 78.0% | 64.0% | 81.1% | 63.0% | 80.7% | 73.5% |
10M+ | 40.7% | 71.2% | 45.3% | 32.1% | 42.1% | 47.0% |
AA_Grp | <10K | 10K - <25K | 25K - <50K | 50K - <100K | 100K - <250K | 250K - <500K | 500K - <1M | 1M - <2.5M | 2.5M - <5M | 5M - <10M | 10M+ |
|---|---|---|---|---|---|---|---|---|---|---|---|
0-17 | 98.1% | 112.6% | 111.6% | 101.4% | 94.0% | 89.4% | 89.0% | 93.6% | 65.9% | 89.8% | 50.2% |
18-25 | 98.1% | 112.6% | 111.6% | 101.4% | 94.0% | 89.4% | 89.0% | 93.6% | 65.9% | 89.8% | 110.9% |
26-30 | 117.7% | 135.1% | 133.9% | 121.6% | 112.8% | 107.2% | 106.8% | 112.3% | 79.1% | 107.7% | 60.2% |
31-35 | 111.6% | 128.1% | 126.9% | 115.3% | 106.9% | 101.6% | 101.2% | 106.4% | 75.0% | 102.1% | 57.1% |
36-40 | 98.3% | 112.8% | 111.8% | 101.6% | 94.2% | 88.2% | 89.2% | 93.8% | 66.0% | 90.0% | 86.2% |
41-45 | 104.2% | 119.6% | 118.5% | 107.7% | 99.8% | 94.9% | 94.5% | 99.4% | 76.4% | 95.3% | 53.1% |
46-50 | 108.1% | 124.1% | 134.0% | 111.7% | 100.7% | 98.0% | 96.4% | 103.1% | 72.6% | 98.9% | 75.1% |
51-55 | 101.4% | 135.6% | 132.2% | 111.8% | 97.2% | 92.4% | 91.2% | 96.8% | 62.8% | 81.6% | 39.2% |
56-60 | 86.7% | 104.5% | 104.1% | 90.0% | 81.0% | 76.1% | 73.3% | 74.3% | 50.5% | 79.4% | 44.4% |
61-65 | 88.6% | 109.5% | 106.0% | 94.4% | 83.6% | 75.6% | 75.5% | 79.6% | 53.2% | 81.1% | 45.3% |
66-70 | 91.1% | 106.8% | 104.1% | 94.1% | 87.3% | 80.8% | 80.3% | 85.9% | 61.2% | 85.5% | 46.6% |
71-75 | 107.9% | 123.9% | 122.8% | 111.5% | 104.4% | 98.3% | 99.8% | 101.0% | 69.5% | 86.0% | 41.0% |
76-80 | 99.1% | 104.1% | 101.8% | 96.7% | 94.9% | 93.6% | 92.4% | 97.6% | 66.5% | 90.6% | 50.7% |
81-85 | 99.3% | 101.3% | 103.6% | 101.7% | 101.7% | 102.4% | 100.9% | 101.3% | 66.7% | 87.7% | 44.0% |
86-90 | 130.4% | 115.0% | 121.1% | 118.8% | 125.0% | 123.2% | 122.7% | 124.4% | 87.6% | 121.5% | 79.4% |
91-95 | 79.7% | 78.6% | 82.6% | 81.9% | 82.5% | 82.1% | 81.4% | 74.9% | 55.6% | 72.9% | 40.5% |
96-100 | 106.0% | 121.6% | 120.6% | 109.5% | 103.9% | 96.5% | 102.2% | 101.1% | 71.2% | 97.0% | 41.5% |
101-105 | 66.9% | 76.7% | 76.0% | 69.1% | 64.0% | 60.9% | 60.6% | 63.8% | 44.9% | 61.2% | 34.2% |
106-110 | 61.0% | 70.1% | 69.4% | 63.1% | 58.5% | 55.6% | 55.4% | 58.2% | 41.0% | 55.9% | 31.2% |
111-115 | 75.7% | 86.9% | 86.2% | 78.3% | 72.6% | 69.0% | 68.7% | 72.2% | 50.9% | 69.3% | 38.7% |
116-120 | 94.2% | 108.1% | 107.1% | 97.3% | 90.2% | 85.8% | 85.5% | 89.8% | 63.3% | 86.2% | 48.2% |
Insurance_Plan | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Other | 77.8% | 102.3% | 93.6% | 70.0% | 117.1% | 73.8% | 73.8% | 98.8% | 103.4% | 92.6% | 73.3% | 89.8% | 87.8% | 91.5% |
Perm | 71.7% | 97.2% | 86.3% | 70.2% | 125.4% | 68.0% | 68.1% | 91.1% | 95.4% | 85.0% | 67.6% | 88.5% | 83.2% | 84.3% |
UL | 84.8% | 112.3% | 89.2% | 73.7% | 127.5% | 80.4% | 83.6% | 107.7% | 112.7% | 99.2% | 79.9% | 97.8% | 95.7% | 99.7% |
ULSG | 70.2% | 92.6% | 71.3% | 63.2% | 105.6% | 57.1% | 59.6% | 91.0% | 96.1% | 88.3% | 66.2% | 81.0% | 94.5% | 66.0% |
VL | 78.5% | 102.8% | 94.4% | 70.7% | 129.9% | 74.4% | 74.5% | 99.7% | 104.4% | 96.7% | 74.0% | 90.6% | 85.6% | 93.2% |
VLSG | 71.8% | 94.5% | 86.4% | 62.5% | 102.4% | 68.1% | 68.2% | 91.2% | 95.5% | 90.0% | 67.7% | 82.9% | 77.7% | 93.4% |
Dur_Grp | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1-1 | 92.0% | 128.6% | 86.6% | 86.5% | 138.4% | 87.2% | 70.6% | 92.0% | 116.7% | 103.2% | 86.7% | 113.8% | 103.8% | 108.2% |
2-2 | 98.5% | 137.7% | 92.8% | 92.7% | 148.3% | 86.4% | 75.6% | 98.5% | 125.0% | 110.5% | 92.9% | 121.9% | 111.2% | 115.9% |
3-3 | 89.9% | 126.3% | 84.7% | 84.6% | 132.7% | 85.3% | 64.3% | 89.9% | 114.1% | 105.1% | 84.8% | 111.3% | 101.5% | 105.8% |
4-5 | 84.8% | 112.3% | 89.2% | 73.7% | 127.5% | 80.4% | 83.6% | 107.7% | 112.7% | 99.2% | 79.9% | 97.8% | 95.7% | 99.7% |
6-10 | 81.3% | 112.8% | 81.4% | 76.5% | 127.8% | 77.1% | 62.4% | 81.3% | 103.1% | 90.3% | 68.4% | 84.3% | 91.8% | 115.6% |
11-15 | 80.0% | 115.3% | 89.0% | 72.7% | 124.7% | 75.9% | 61.4% | 103.7% | 101.5% | 87.6% | 69.2% | 107.9% | 88.8% | 94.1% |
16-20 | 83.1% | 116.8% | 74.2% | 78.4% | 130.1% | 78.8% | 63.7% | 83.1% | 105.4% | 87.6% | 85.3% | 107.8% | 92.9% | 97.7% |
21-30 | 90.1% | 126.8% | 84.8% | 77.1% | 60.5% | 85.4% | 69.1% | 90.1% | 79.7% | 101.0% | 90.8% | 119.1% | 105.8% | 106.1% |
31-120 | 85.5% | 119.5% | 80.5% | 80.4% | 75.7% | 81.1% | 65.5% | 85.5% | 108.4% | 95.9% | 80.6% | 105.7% | 96.5% | 82.7% |
AA_Grp | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0-17 | 90.4% | 112.7% | 82.6% | 78.6% | 115.5% | 90.4% | 94.0% | 114.9% | 111.4% | 105.9% | 85.2% | 104.4% | 107.5% | 96.2% |
18-25 | 90.4% | 112.7% | 82.6% | 78.6% | 115.5% | 90.4% | 94.0% | 114.9% | 111.4% | 101.1% | 85.2% | 104.4% | 107.5% | 96.2% |
26-30 | 108.5% | 135.2% | 99.1% | 94.3% | 138.5% | 108.5% | 112.8% | 137.8% | 133.7% | 127.0% | 102.3% | 125.2% | 129.0% | 115.4% |
31-35 | 102.8% | 128.2% | 87.9% | 89.4% | 131.3% | 102.8% | 106.9% | 130.6% | 126.7% | 120.4% | 96.9% | 118.7% | 122.3% | 109.4% |
36-40 | 90.6% | 112.9% | 82.8% | 78.7% | 126.0% | 90.6% | 94.2% | 115.1% | 111.6% | 106.1% | 85.4% | 104.6% | 107.7% | 96.4% |
41-45 | 96.0% | 119.7% | 89.5% | 85.1% | 122.7% | 96.0% | 99.8% | 122.0% | 118.3% | 112.4% | 86.2% | 110.8% | 114.2% | 102.1% |
46-50 | 96.8% | 128.5% | 83.2% | 84.1% | 168.6% | 96.8% | 100.7% | 123.0% | 119.3% | 114.1% | 91.3% | 111.8% | 114.0% | 103.0% |
51-55 | 93.5% | 116.5% | 85.4% | 81.2% | 133.6% | 93.5% | 97.2% | 118.7% | 115.2% | 107.5% | 88.1% | 107.9% | 106.3% | 99.4% |
56-60 | 77.9% | 97.1% | 79.8% | 67.7% | 99.5% | 77.9% | 81.0% | 98.9% | 96.0% | 90.3% | 73.4% | 97.5% | 92.6% | 91.6% |
61-65 | 84.8% | 112.3% | 89.2% | 73.7% | 127.5% | 80.4% | 83.6% | 107.7% | 112.7% | 99.2% | 79.9% | 97.8% | 95.7% | 99.7% |
66-70 | 84.0% | 115.3% | 60.3% | 71.2% | 114.4% | 80.6% | 87.3% | 106.8% | 103.6% | 111.6% | 79.2% | 97.0% | 101.8% | 118.8% |
71-75 | 100.4% | 125.2% | 103.8% | 87.3% | 134.1% | 100.4% | 104.4% | 127.6% | 142.1% | 118.3% | 98.8% | 115.8% | 119.4% | 115.4% |
76-80 | 96.2% | 120.0% | 82.9% | 72.0% | 116.1% | 96.2% | 94.9% | 138.2% | 118.6% | 112.7% | 109.5% | 111.1% | 122.9% | 106.2% |
81-85 | 97.8% | 117.5% | 90.4% | 82.9% | 117.5% | 97.8% | 101.7% | 125.9% | 120.5% | 114.5% | 92.2% | 116.1% | 129.0% | 104.0% |
86-90 | 96.3% | 120.1% | 74.4% | 74.7% | 101.0% | 96.3% | 125.0% | 91.5% | 106.4% | 118.0% | 90.8% | 111.2% | 118.3% | 102.5% |
91-95 | 79.4% | 88.5% | 65.7% | 73.1% | 79.0% | 79.4% | 82.5% | 100.9% | 85.2% | 95.0% | 74.8% | 91.6% | 80.9% | 84.4% |
96-100 | 99.9% | 122.4% | 91.3% | 89.8% | 104.0% | 99.9% | 103.9% | 126.9% | 123.1% | 117.0% | 94.2% | 115.3% | 118.8% | 104.9% |
101-105 | 61.6% | 76.8% | 56.3% | 53.5% | 78.7% | 61.6% | 64.0% | 78.3% | 75.9% | 72.1% | 58.1% | 71.1% | 73.3% | 61.6% |
106-110 | 56.2% | 70.1% | 51.4% | 48.9% | 71.8% | 56.2% | 58.5% | 71.5% | 69.3% | 65.9% | 53.0% | 64.9% | 66.9% | 59.8% |
111-115 | 69.8% | 87.0% | 63.8% | 60.7% | 89.1% | 69.8% | 72.6% | 88.7% | 86.0% | 81.7% | 65.8% | 80.6% | 83.0% | 74.2% |
116-120 | 86.8% | 108.2% | 79.3% | 75.4% | 110.9% | 86.8% | 90.2% | 110.3% | 107.0% | 101.6% | 81.8% | 100.2% | 103.2% | 92.3% |
Dur_Grp | Other | Perm | UL | ULSG | VL | VLSG |
|---|---|---|---|---|---|---|
1-1 | 62.3% | 57.4% | 70.6% | 51.2% | 62.8% | 59.0% |
2-2 | 66.7% | 73.7% | 75.6% | 49.4% | 67.3% | 63.2% |
3-3 | 56.7% | 52.3% | 64.3% | 46.7% | 57.2% | 53.8% |
4-5 | 73.8% | 68.1% | 83.6% | 59.6% | 74.5% | 68.2% |
6-10 | 59.0% | 54.4% | 62.4% | 49.0% | 59.5% | 54.9% |
11-15 | 59.8% | 55.1% | 61.4% | 48.6% | 60.3% | 62.6% |
16-20 | 58.4% | 52.9% | 63.7% | 49.9% | 58.9% | 55.3% |
21-30 | 59.2% | 51.7% | 69.1% | 48.7% | 59.8% | 56.1% |
31-120 | 57.9% | 53.3% | 65.5% | 29.8% | 58.4% | 54.8% |
AA_Grp | Other | Perm | UL | ULSG | VL | VLSG |
|---|---|---|---|---|---|---|
0-17 | 83.0% | 82.0% | 94.0% | 72.9% | 80.9% | 76.6% |
18-25 | 83.0% | 82.0% | 94.0% | 72.9% | 81.5% | 76.6% |
26-30 | 99.5% | 98.4% | 112.8% | 87.4% | 97.1% | 91.9% |
31-35 | 94.4% | 93.3% | 106.9% | 82.9% | 92.0% | 87.1% |
36-40 | 83.1% | 82.2% | 94.2% | 73.0% | 81.1% | 76.8% |
41-45 | 88.1% | 87.1% | 99.8% | 80.8% | 85.9% | 81.4% |
46-50 | 82.6% | 81.7% | 100.7% | 72.5% | 73.8% | 76.3% |
51-55 | 83.0% | 81.6% | 97.2% | 82.5% | 80.9% | 75.8% |
56-60 | 69.1% | 68.3% | 81.0% | 60.7% | 66.5% | 63.8% |
61-65 | 73.8% | 68.1% | 83.6% | 59.6% | 74.5% | 68.2% |
66-70 | 82.9% | 71.4% | 87.3% | 71.3% | 80.8% | 76.5% |
71-75 | 89.3% | 82.4% | 104.4% | 72.4% | 90.9% | 85.1% |
76-80 | 80.4% | 79.5% | 94.9% | 70.6% | 75.7% | 74.1% |
81-85 | 88.0% | 87.5% | 101.7% | 76.8% | 85.8% | 81.2% |
86-90 | 113.7% | 115.3% | 125.0% | 100.8% | 113.2% | 105.0% |
91-95 | 78.9% | 79.4% | 82.5% | 70.3% | 74.6% | 72.8% |
96-100 | 91.7% | 94.3% | 103.9% | 68.5% | 97.3% | 84.6% |
101-105 | 68.6% | 67.8% | 64.0% | 60.2% | 66.9% | 63.3% |
106-110 | 51.6% | 51.0% | 58.5% | 45.3% | 50.3% | 47.7% |
111-115 | 64.0% | 63.3% | 72.6% | 56.2% | 62.5% | 59.1% |
116-120 | 79.6% | 78.7% | 90.2% | 69.9% | 77.7% | 73.5% |
AA_Grp | 1-1 | 2-2 | 3-3 | 4-5 | 6-10 | 11-15 | 16-20 | 21-30 | 31-120 |
|---|---|---|---|---|---|---|---|---|---|
0-17 | 77.1% | 77.1% | 71.8% | 94.0% | 68.1% | 67.2% | 69.6% | 73.7% | 71.4% |
18-25 | 77.1% | 77.1% | 71.8% | 94.0% | 76.9% | 67.2% | 69.6% | 73.7% | 71.4% |
26-30 | 92.5% | 92.5% | 86.2% | 112.8% | 81.7% | 80.7% | 83.5% | 88.4% | 85.7% |
31-35 | 87.7% | 87.7% | 81.7% | 106.9% | 77.5% | 76.5% | 79.2% | 83.9% | 81.2% |
36-40 | 77.2% | 77.2% | 72.0% | 94.2% | 68.3% | 67.4% | 69.7% | 73.9% | 71.6% |
41-45 | 81.9% | 82.2% | 82.2% | 99.8% | 72.4% | 71.4% | 73.9% | 75.6% | 75.9% |
46-50 | 83.7% | 76.9% | 78.0% | 100.7% | 82.5% | 75.9% | 75.6% | 79.9% | 77.6% |
51-55 | 79.7% | 62.2% | 74.2% | 97.2% | 70.1% | 69.5% | 72.0% | 76.2% | 73.8% |
56-60 | 74.2% | 74.2% | 66.8% | 81.0% | 73.5% | 64.7% | 66.8% | 70.8% | 68.8% |
61-65 | 70.6% | 75.6% | 64.3% | 83.6% | 62.4% | 61.4% | 63.7% | 69.1% | 65.5% |
66-70 | 71.6% | 58.6% | 66.7% | 87.3% | 61.0% | 61.3% | 66.6% | 70.7% | 66.3% |
71-75 | 80.8% | 80.8% | 74.4% | 104.4% | 73.1% | 69.8% | 73.0% | 78.2% | 77.1% |
76-80 | 77.8% | 77.8% | 72.5% | 94.9% | 63.1% | 73.1% | 69.4% | 74.4% | 74.7% |
81-85 | 84.1% | 84.1% | 78.3% | 101.7% | 69.9% | 73.3% | 75.8% | 83.5% | 81.7% |
86-90 | 96.8% | 96.8% | 90.2% | 125.0% | 84.8% | 77.2% | 89.9% | 95.7% | 89.7% |
91-95 | 77.0% | 77.0% | 71.8% | 82.5% | 52.9% | 66.4% | 75.4% | 77.3% | 71.4% |
96-100 | 85.2% | 85.2% | 79.4% | 103.9% | 90.2% | 77.4% | 76.9% | 81.5% | 73.7% |
101-105 | 52.5% | 52.5% | 48.9% | 64.0% | 46.4% | 45.8% | 52.4% | 50.2% | 37.0% |
106-110 | 48.0% | 48.0% | 44.7% | 58.5% | 42.4% | 41.8% | 43.3% | 45.9% | 39.0% |
111-115 | 59.5% | 59.5% | 55.4% | 72.6% | 52.6% | 51.9% | 53.7% | 56.9% | 49.9% |
116-120 | 74.0% | 74.0% | 68.9% | 90.2% | 65.4% | 64.5% | 66.8% | 70.8% | 67.8% |
Face_Amount_Band | F | M |
|---|---|---|
<10K | 88.6% | 137.0% |
10K - <25K | 109.5% | 188.4% |
25K - <50K | 106.0% | 177.5% |
50K - <100K | 94.4% | 157.3% |
100K - <250K | 83.6% | 135.1% |
250K - <500K | 75.6% | 116.3% |
500K - <1M | 75.5% | 113.8% |
1M - <2.5M | 79.6% | 113.1% |
2.5M - <5M | 53.2% | 76.9% |
5M - <10M | 81.1% | 121.1% |
10M+ | 45.3% | 62.8% |
Sex | NS/1/2 | NS/2/2 | NS/1/3 | NS/2/3 | NS/3/3 | NS/1/4 | NS/2/4 | NS/3/4 | NS/4/4 | NS/U/U | S/1/2 | S/2/2 | S/U/U | U/U/U |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
F | 84.8% | 112.3% | 89.2% | 73.7% | 127.5% | 80.4% | 83.6% | 107.7% | 112.7% | 99.2% | 79.9% | 97.8% | 95.7% | 99.7% |
M | 99.6% | 131.8% | 98.3% | 91.8% | 149.9% | 79.6% | 135.1% | 126.6% | 132.5% | 116.7% | 99.4% | 108.8% | 112.5% | 129.0% |
Insurance_Plan | F | M |
|---|---|---|
Other | 73.8% | 114.3% |
Perm | 68.1% | 103.1% |
UL | 83.6% | 135.1% |
ULSG | 59.6% | 92.3% |
VL | 74.5% | 116.4% |
VLSG | 68.2% | 106.0% |
AA_Grp | F | M |
|---|---|---|
0-17 | 94.0% | 143.1% |
18-25 | 94.0% | 147.3% |
26-30 | 112.8% | 171.6% |
31-35 | 106.9% | 171.5% |
36-40 | 94.2% | 173.6% |
41-45 | 99.8% | 151.9% |
46-50 | 100.7% | 153.2% |
51-55 | 97.2% | 149.8% |
56-60 | 81.0% | 137.3% |
61-65 | 83.6% | 135.1% |
66-70 | 87.3% | 132.8% |
71-75 | 104.4% | 156.9% |
76-80 | 94.9% | 144.4% |
81-85 | 101.7% | 145.3% |
86-90 | 125.0% | 191.1% |
91-95 | 82.5% | 125.6% |
96-100 | 103.9% | 134.6% |
101-105 | 64.0% | 97.5% |
106-110 | 58.5% | 89.0% |
111-115 | 72.6% | 110.4% |
116-120 | 90.2% | 137.3% |
Dur_Grp | F | M |
|---|---|---|
1-1 | 70.6% | 114.0% |
2-2 | 75.6% | 144.5% |
3-3 | 64.3% | 104.7% |
4-5 | 83.6% | 135.1% |
6-10 | 62.4% | 101.4% |
11-15 | 61.4% | 95.4% |
16-20 | 63.7% | 102.3% |
21-30 | 69.1% | 109.7% |
31-120 | 65.5% | 105.3% |
8.2.6.2 Goodness-of-Fit
Next comes checking goodness-of-fit, on both a univariate and bivariate basis. Tables are provided which show the ratio of the actual to model predicted deaths and show the associated death counts.
Code
dat.perm.knw.grid %>%
right_join(dat.perm.knw) %>%
mutate(ExpDth_Amt_GLMNet=ExpDth_Amt_VBT2015*Factor) %>%
mutate(Factor=NULL) ->
dat.perm.knw8.2.6.2.1 Univariate Fit Checks
Sex | Death Count | Actual-to-Model |
|---|---|---|
F | 509,660 | 100.0% |
M | 693,462 | 100.0% |
Face_Amount_Band | Death Count | Actual-to-Model |
|---|---|---|
<10K | 144,194 | 113.4% |
10K - <25K | 284,132 | 100.5% |
25K - <50K | 244,005 | 100.2% |
50K - <100K | 246,768 | 100.1% |
100K - <250K | 194,495 | 99.9% |
250K - <500K | 46,489 | 99.8% |
500K - <1M | 22,485 | 99.8% |
1M - <2.5M | 14,772 | 99.9% |
2.5M - <5M | 2,919 | 99.8% |
5M - <10M | 2,025 | 99.8% |
10M+ | 838 | 99.8% |
Insurance_Plan | Death Count | Actual-to-Model |
|---|---|---|
Other | 2,986 | 98.5% |
Perm | 628,166 | 100.0% |
UL | 406,569 | 100.0% |
ULSG | 72,864 | 100.0% |
VL | 72,371 | 100.1% |
VLSG | 20,166 | 99.6% |
UW | Death Count | Actual-to-Model |
|---|---|---|
NS/1/2 | 45,097 | 99.6% |
NS/2/2 | 84,588 | 100.1% |
NS/1/3 | 7,038 | 99.5% |
NS/2/3 | 13,974 | 99.8% |
NS/3/3 | 35,709 | 100.1% |
NS/1/4 | 2,397 | 98.4% |
NS/2/4 | 2,766 | 98.3% |
NS/3/4 | 2,035 | 101.8% |
NS/4/4 | 4,180 | 101.2% |
NS/U/U | 710,163 | 100.0% |
S/1/2 | 8,012 | 98.7% |
S/2/2 | 14,701 | 101.1% |
S/U/U | 241,685 | 100.2% |
U/U/U | 30,777 | 101.0% |
AA_Grp | Death Count | Actual-to-Model |
|---|---|---|
0-17 | 1,588 | 73.2% |
18-25 | 6,083 | 101.8% |
26-30 | 5,395 | 105.7% |
31-35 | 6,362 | 103.8% |
36-40 | 8,206 | 101.8% |
41-45 | 13,458 | 101.1% |
46-50 | 24,192 | 100.6% |
51-55 | 43,169 | 99.8% |
56-60 | 66,765 | 99.8% |
61-65 | 95,105 | 99.8% |
66-70 | 122,641 | 99.9% |
71-75 | 146,304 | 100.1% |
76-80 | 173,224 | 100.1% |
81-85 | 203,208 | 100.0% |
86-90 | 183,307 | 100.1% |
91-95 | 87,840 | 99.9% |
96-100 | 15,512 | 100.7% |
101-105 | 664 | 87.7% |
106-110 | 55 | 22.0% |
111-115 | 31 | 7.4% |
116-120 | 13 | 4.5% |
Dur_Grp | Death Count | Actual-to-Model |
|---|---|---|
1-1 | 5,348 | 108.8% |
2-2 | 6,945 | 99.9% |
3-3 | 8,476 | 100.9% |
4-5 | 19,807 | 99.6% |
6-10 | 66,221 | 99.9% |
11-15 | 101,761 | 99.9% |
16-20 | 170,607 | 99.9% |
21-30 | 670,560 | 100.0% |
31-120 | 153,397 | 99.8% |
Unidimensional goodness-of-fit is generally good, with some spots with poor fit. Examples of poor fit include the very lowest face amounts, the extremes of attained age (juveniles and the oldest ages), and duration 1.
8.2.6.2.2 Bivariate Fit Checks
Face_Amount_Band | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
<10K | 95,801 | 107.5% | 48,393 | 126.6% | ||
10K - <25K | 152,406 | 100.0% | 131,726 | 100.9% | ||
25K - <50K | 94,543 | 100.0% | 149,462 | 100.4% | ||
50K - <100K | 79,467 | 99.9% | 167,301 | 100.2% | ||
100K - <250K | 56,221 | 99.5% | 138,274 | 100.1% | ||
250K - <500K | 14,847 | 99.9% | 31,642 | 99.8% | ||
500K - <1M | 7,842 | 99.8% | 14,643 | 99.8% | ||
1M - <2.5M | 5,976 | 100.0% | 8,796 | 99.8% | ||
2.5M - <5M | 1,314 | 100.0% | 1,605 | 99.7% | ||
5M - <10M | 865 | 100.0% | 1,160 | 99.7% | ||
10M+ | 378 | 99.9% | 460 | 99.7% | ||
Insurance_Plan | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
Other | 949 | 105.1% | 2,037 | 95.4% | ||
Perm | 295,165 | 100.2% | 333,001 | 99.9% | ||
UL | 150,335 | 100.0% | 256,234 | 100.1% | ||
ULSG | 30,909 | 100.0% | 41,955 | 100.0% | ||
VL | 24,150 | 99.7% | 48,221 | 100.2% | ||
VLSG | 8,152 | 97.5% | 12,014 | 100.6% | ||
UW | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
NS/1/2 | 15,578 | 98.9% | 29,519 | 100.0% | ||
NS/2/2 | 34,658 | 100.5% | 49,930 | 99.8% | ||
NS/1/3 | 2,955 | 99.9% | 4,083 | 99.3% | ||
NS/2/3 | 5,515 | 99.1% | 8,459 | 100.3% | ||
NS/3/3 | 14,796 | 100.1% | 20,913 | 100.1% | ||
NS/1/4 | 1,074 | 100.9% | 1,323 | 96.4% | ||
NS/2/4 | 1,064 | 90.6% | 1,702 | 102.8% | ||
NS/3/4 | 718 | 103.0% | 1,317 | 101.2% | ||
NS/4/4 | 1,752 | 103.5% | 2,428 | 99.8% | ||
NS/U/U | 306,182 | 100.2% | 403,981 | 100.0% | ||
S/1/2 | 2,526 | 93.0% | 5,486 | 101.9% | ||
S/2/2 | 5,574 | 105.3% | 9,127 | 98.4% | ||
S/U/U | 107,653 | 100.5% | 134,032 | 100.0% | ||
U/U/U | 9,615 | 99.8% | 21,162 | 101.4% | ||
AA_Grp | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
0-17 | 577 | 70.3% | 1,011 | 74.7% | ||
18-25 | 1,592 | 89.5% | 4,491 | 105.6% | ||
26-30 | 1,515 | 106.1% | 3,880 | 105.5% | ||
31-35 | 2,090 | 100.8% | 4,272 | 105.2% | ||
36-40 | 2,926 | 98.9% | 5,280 | 103.1% | ||
41-45 | 5,089 | 101.7% | 8,369 | 100.8% | ||
46-50 | 8,920 | 101.2% | 15,272 | 100.4% | ||
51-55 | 15,811 | 98.1% | 27,358 | 100.5% | ||
56-60 | 23,303 | 98.2% | 43,462 | 100.3% | ||
61-65 | 33,547 | 98.7% | 61,558 | 100.2% | ||
66-70 | 43,958 | 100.0% | 78,683 | 99.9% | ||
71-75 | 55,088 | 101.0% | 91,216 | 99.8% | ||
76-80 | 69,560 | 100.4% | 103,664 | 100.0% | ||
81-85 | 91,310 | 100.2% | 111,898 | 99.9% | ||
86-90 | 92,578 | 100.0% | 90,729 | 100.1% | ||
91-95 | 51,021 | 99.8% | 36,819 | 100.1% | ||
96-100 | 10,253 | 102.1% | 5,259 | 97.4% | ||
101-105 | 475 | 94.9% | 189 | 81.6% | ||
106-110 | 31 | 30.2% | 24 | 17.2% | ||
111-115 | 13 | 11.3% | 18 | 6.0% | ||
116-120 | 3 | 3.4% | 10 | 4.9% | ||
Dur_Grp | Sex: F | Sex: M | ||||
|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | |||
1-1 | 2,066 | 115.9% | 3,282 | 105.6% | ||
2-2 | 2,797 | 94.6% | 4,148 | 102.4% | ||
3-3 | 3,602 | 99.6% | 4,874 | 101.7% | ||
4-5 | 8,694 | 98.7% | 11,113 | 100.2% | ||
6-10 | 29,892 | 99.7% | 36,329 | 100.1% | ||
11-15 | 47,079 | 100.0% | 54,682 | 99.9% | ||
16-20 | 80,747 | 100.0% | 89,860 | 99.8% | ||
21-30 | 281,086 | 100.2% | 389,474 | 99.9% | ||
31-120 | 53,697 | 99.9% | 99,700 | 99.8% | ||
Face_Amount_Band | Insurance_Plan: Other | Insurance_Plan: Perm | Insurance_Plan: UL | Insurance_Plan: ULSG | Insurance_Plan: VL | Insurance_Plan: VLSG | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | |||||||
<10K | 809 | 120.7% | 131,213 | 113.1% | 9,445 | 114.5% | 159 | 104.3% | 942 | 131.9% | 1,626 | 122.1% | ||||||
10K - <25K | 873 | 113.5% | 220,099 | 100.5% | 57,377 | 99.1% | 1,861 | 107.4% | 1,968 | 120.5% | 1,954 | 101.2% | ||||||
25K - <50K | 438 | 100.7% | 116,434 | 99.8% | 106,894 | 100.5% | 7,988 | 103.6% | 8,502 | 102.1% | 3,749 | 97.5% | ||||||
50K - <100K | 291 | 103.9% | 77,321 | 100.0% | 119,421 | 100.2% | 15,049 | 102.1% | 31,874 | 99.1% | 2,812 | 97.3% | ||||||
100K - <250K | 377 | 115.0% | 58,883 | 99.8% | 85,089 | 100.1% | 24,815 | 100.3% | 19,722 | 99.3% | 5,609 | 97.7% | ||||||
250K - <500K | 118 | 126.5% | 14,052 | 99.6% | 15,258 | 100.4% | 9,322 | 100.1% | 5,236 | 99.0% | 2,503 | 98.3% | ||||||
500K - <1M | 35 | 90.3% | 6,276 | 99.5% | 6,655 | 100.4% | 5,914 | 99.5% | 2,473 | 100.9% | 1,132 | 97.5% | ||||||
1M - <2.5M | 31 | 137.5% | 3,271 | 99.6% | 4,256 | 99.7% | 5,217 | 99.8% | 1,355 | 100.9% | 642 | 100.7% | ||||||
2.5M - <5M | 7 | 107.6% | 433 | 98.6% | 963 | 99.4% | 1,224 | 99.6% | 198 | 102.8% | 94 | 106.3% | ||||||
5M - <10M | 5 | 95.4% | 129 | 97.7% | 834 | 99.6% | 957 | 100.3% | 69 | 103.5% | 31 | 95.3% | ||||||
10M+ | 2 | 41.9% | 55 | 103.2% | 377 | 99.8% | 358 | 99.7% | 32 | 96.4% | 14 | 110.1% | ||||||
UW | Face_Amount_Band: <10K | Face_Amount_Band: 10K - <25K | Face_Amount_Band: 25K - <50K | Face_Amount_Band: 50K - <100K | Face_Amount_Band: 100K - <250K | Face_Amount_Band: 250K - <500K | Face_Amount_Band: 500K - <1M | Face_Amount_Band: 1M - <2 | Face_Amount_Band: 2 | Face_Amount_Band: 5M - <10M | Face_Amount_Band: 10M+ | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | 5M | 5M - <5M | Deaths | Ratio | Deaths | Ratio | ||||||||||||||
Deaths | Ratio | Deaths | Ratio | ||||||||||||||||||||||||||||||
NS/1/2 | 104 | 185.3% | 805 | 119.5% | 3,338 | 107.7% | 7,353 | 109.0% | 20,096 | 99.5% | 6,769 | 99.5% | 3,522 | 100.2% | 2,403 | 98.6% | 383 | 96.0% | 248 | 103.2% | 76 | 96.3% | |||||||||||
NS/2/2 | 4,345 | 106.2% | 13,900 | 97.8% | 15,618 | 97.1% | 17,769 | 98.5% | 19,846 | 99.4% | 6,421 | 100.8% | 3,453 | 100.8% | 2,387 | 100.6% | 466 | 101.2% | 294 | 99.0% | 89 | 101.6% | |||||||||||
NS/1/3 | 3 | 32.8% | 16 | 151.0% | 128 | 109.1% | 701 | 101.1% | 2,807 | 100.1% | 1,542 | 97.7% | 906 | 96.7% | 614 | 97.6% | 151 | 102.7% | 92 | 97.9% | 78 | 102.7% | |||||||||||
NS/2/3 | 7 | 225.0% | 238 | 151.9% | 647 | 112.6% | 1,647 | 108.5% | 5,064 | 101.6% | 2,507 | 102.2% | 1,573 | 99.5% | 1,443 | 100.1% | 365 | 98.5% | 336 | 99.1% | 147 | 99.1% | |||||||||||
NS/3/3 | 337 | 132.6% | 1,919 | 100.5% | 3,707 | 104.3% | 5,760 | 96.7% | 12,232 | 99.0% | 4,730 | 98.9% | 2,919 | 101.0% | 2,447 | 100.6% | 698 | 100.8% | 666 | 99.7% | 294 | 100.6% | |||||||||||
NS/1/4 | 0 | 0.0% | 2 | 122.9% | 136 | 95.4% | 229 | 104.6% | 993 | 99.1% | 503 | 105.2% | 301 | 106.1% | 176 | 99.5% | 31 | 86.6% | 21 | 104.7% | 5 | 78.1% | |||||||||||
NS/2/4 | 3 | 920.9% | 6 | 277.5% | 271 | 106.5% | 363 | 100.8% | 1,130 | 102.4% | 428 | 96.4% | 271 | 99.1% | 213 | 97.1% | 30 | 82.2% | 37 | 109.6% | 14 | 94.9% | |||||||||||
NS/3/4 | 0 | 0.0% | 0 | 0.0% | 134 | 96.6% | 189 | 95.3% | 973 | 101.6% | 334 | 101.0% | 173 | 94.4% | 162 | 103.8% | 38 | 113.1% | 22 | 93.5% | 10 | 105.2% | |||||||||||
NS/4/4 | 6 | 245.9% | 126 | 98.6% | 580 | 91.9% | 900 | 97.2% | 1,409 | 103.2% | 482 | 95.9% | 298 | 102.9% | 244 | 102.2% | 78 | 109.2% | 43 | 102.9% | 14 | 90.7% | |||||||||||
NS/U/U | 93,900 | 118.0% | 180,839 | 100.7% | 154,030 | 100.4% | 153,961 | 99.8% | 98,451 | 99.9% | 17,596 | 99.8% | 6,922 | 99.6% | 3,642 | 100.3% | 525 | 99.0% | 216 | 98.6% | 81 | 98.4% | |||||||||||
S/1/2 | 43 | 145.5% | 510 | 117.9% | 954 | 99.7% | 1,705 | 103.2% | 3,606 | 101.6% | 703 | 95.5% | 268 | 91.3% | 175 | 105.0% | 35 | 118.8% | 7 | 69.3% | 6 | 80.6% | |||||||||||
S/2/2 | 472 | 108.1% | 2,681 | 102.9% | 3,245 | 102.3% | 3,573 | 101.6% | 3,353 | 102.9% | 727 | 102.8% | 386 | 108.3% | 205 | 93.7% | 28 | 83.5% | 21 | 117.7% | 10 | 94.3% | |||||||||||
S/U/U | 42,091 | 103.9% | 76,218 | 100.4% | 52,987 | 99.0% | 44,425 | 99.6% | 20,796 | 99.9% | 3,164 | 101.7% | 1,300 | 97.9% | 594 | 102.2% | 81 | 107.0% | 19 | 86.4% | 10 | 115.6% | |||||||||||
U/U/U | 2,883 | 121.0% | 6,872 | 95.5% | 8,230 | 106.5% | 8,193 | 103.9% | 3,739 | 101.0% | 583 | 90.8% | 193 | 87.6% | 67 | 78.7% | 10 | 102.2% | 3 | 154.2% | 4 | 228.9% | |||||||||||
AA_Grp | Face_Amount_Band: <10K | Face_Amount_Band: 10K - <25K | Face_Amount_Band: 25K - <50K | Face_Amount_Band: 50K - <100K | Face_Amount_Band: 100K - <250K | Face_Amount_Band: 250K - <500K | Face_Amount_Band: 500K - <1M | Face_Amount_Band: 1M - <2 | Face_Amount_Band: 2 | Face_Amount_Band: 5M - <10M | Face_Amount_Band: 10M+ | ||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | 5M | 5M - <5M | Deaths | Ratio | Deaths | Ratio | ||||||||||||||
Deaths | Ratio | Deaths | Ratio | ||||||||||||||||||||||||||||||
0-17 | 25 | 192.9% | 218 | 75.5% | 550 | 80.9% | 504 | 74.2% | 241 | 79.8% | 36 | 61.8% | 10 | 59.1% | 3 | 58.7% | 1 | 296.2% | 0 | 0.0% | 0 | 0.0% | |||||||||||
18-25 | 139 | 138.9% | 1,312 | 95.5% | 1,816 | 93.5% | 1,787 | 95.0% | 832 | 96.1% | 130 | 80.4% | 41 | 76.8% | 19 | 119.4% | 2 | 152.9% | 1 | 100.0% | 4 | 237.2% | |||||||||||
26-30 | 206 | 148.4% | 1,221 | 100.2% | 1,545 | 107.0% | 1,420 | 112.0% | 758 | 106.6% | 156 | 94.9% | 60 | 108.8% | 24 | 125.3% | 5 | 270.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||
31-35 | 230 | 172.6% | 1,296 | 104.3% | 1,749 | 112.3% | 1,587 | 114.6% | 1,040 | 111.3% | 296 | 107.1% | 110 | 95.0% | 49 | 105.4% | 5 | 138.3% | 0 | 0.0% | 0 | 0.0% | |||||||||||
36-40 | 285 | 176.5% | 1,465 | 105.8% | 2,079 | 105.6% | 1,974 | 101.2% | 1,562 | 94.6% | 478 | 88.7% | 217 | 88.5% | 122 | 112.1% | 13 | 127.0% | 5 | 113.0% | 6 | 160.4% | |||||||||||
41-45 | 547 | 211.5% | 2,206 | 129.3% | 3,022 | 118.4% | 3,125 | 100.9% | 2,964 | 96.2% | 915 | 99.3% | 427 | 99.2% | 211 | 98.7% | 29 | 123.9% | 9 | 130.9% | 3 | 65.3% | |||||||||||
46-50 | 1,025 | 244.9% | 3,536 | 143.2% | 5,023 | 113.3% | 6,157 | 103.0% | 5,848 | 97.8% | 1,525 | 96.4% | 654 | 95.7% | 359 | 99.1% | 38 | 95.6% | 17 | 110.7% | 10 | 117.1% | |||||||||||
51-55 | 1,460 | 229.5% | 5,886 | 129.4% | 8,491 | 107.6% | 12,148 | 102.5% | 11,082 | 100.1% | 2,464 | 99.5% | 1,018 | 97.2% | 541 | 101.0% | 54 | 90.3% | 18 | 84.1% | 7 | 81.3% | |||||||||||
56-60 | 2,006 | 171.5% | 8,820 | 115.7% | 13,371 | 104.3% | 19,303 | 101.5% | 17,347 | 99.2% | 3,614 | 98.4% | 1,451 | 97.9% | 716 | 98.0% | 79 | 93.1% | 42 | 103.2% | 16 | 104.4% | |||||||||||
61-65 | 3,262 | 153.5% | 14,805 | 109.0% | 19,969 | 102.8% | 27,605 | 101.1% | 22,195 | 99.4% | 4,325 | 98.7% | 1,845 | 98.4% | 922 | 98.5% | 104 | 94.9% | 52 | 103.0% | 21 | 101.6% | |||||||||||
66-70 | 5,970 | 138.2% | 24,155 | 105.1% | 27,700 | 102.0% | 32,505 | 100.6% | 24,177 | 99.7% | 4,718 | 98.8% | 2,046 | 98.6% | 1,118 | 98.8% | 151 | 97.4% | 73 | 104.3% | 28 | 98.3% | |||||||||||
71-75 | 11,618 | 135.6% | 35,392 | 103.2% | 33,679 | 100.0% | 33,402 | 100.6% | 23,492 | 100.5% | 4,855 | 100.7% | 2,271 | 101.3% | 1,281 | 99.0% | 199 | 97.3% | 82 | 96.3% | 33 | 94.9% | |||||||||||
76-80 | 21,901 | 118.2% | 46,689 | 97.4% | 37,370 | 98.4% | 32,761 | 99.1% | 24,068 | 100.1% | 5,479 | 101.0% | 2,601 | 101.1% | 1,731 | 100.8% | 334 | 101.6% | 198 | 98.8% | 92 | 99.5% | |||||||||||
81-85 | 35,530 | 111.9% | 57,081 | 97.8% | 39,491 | 98.5% | 32,457 | 99.2% | 24,964 | 100.5% | 6,545 | 100.9% | 3,399 | 100.9% | 2,535 | 100.5% | 571 | 99.9% | 437 | 99.3% | 198 | 99.2% | |||||||||||
86-90 | 37,686 | 98.3% | 51,750 | 97.2% | 31,811 | 98.0% | 25,835 | 98.9% | 21,428 | 100.1% | 6,396 | 100.8% | 3,658 | 100.8% | 2,957 | 100.4% | 795 | 99.6% | 686 | 100.4% | 305 | 100.5% | |||||||||||
91-95 | 18,828 | 109.3% | 24,228 | 94.8% | 13,911 | 96.2% | 11,988 | 97.9% | 10,368 | 101.2% | 3,709 | 101.5% | 2,182 | 101.4% | 1,731 | 99.3% | 445 | 101.2% | 350 | 100.0% | 100 | 98.7% | |||||||||||
96-100 | 3,370 | 103.9% | 3,891 | 83.5% | 2,305 | 88.1% | 2,078 | 96.9% | 2,001 | 106.0% | 805 | 105.9% | 477 | 106.1% | 429 | 101.3% | 89 | 102.8% | 54 | 100.2% | 13 | 88.5% | |||||||||||
101-105 | 104 | 124.4% | 155 | 77.5% | 104 | 73.4% | 103 | 71.7% | 113 | 76.0% | 39 | 86.2% | 16 | 56.3% | 22 | 84.7% | 5 | 106.5% | 1 | 36.4% | 2 | 186.1% | |||||||||||
106-110 | 2 | 45.0% | 13 | 21.3% | 9 | 19.1% | 15 | 27.8% | 9 | 16.3% | 3 | 14.5% | 2 | 26.8% | 2 | 31.8% | 0 | 0.0% | 0 | 0.0% | |||||||||||||
111-115 | 0 | 0.0% | 9 | 16.7% | 7 | 16.5% | 10 | 27.8% | 5 | 11.9% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | 0 | 0.0% | |||||||||||||||
116-120 | 0 | 0.0% | 4 | 19.7% | 3 | 15.4% | 4 | 12.7% | 1 | 1.8% | 1 | 5.9% | 0 | 0.0% | 0 | 0.0% | |||||||||||||||||
Face_Amount_Band | Dur_Grp: 1-1 | Dur_Grp: 2-2 | Dur_Grp: 3-3 | Dur_Grp: 4-5 | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-120 | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||||||
<10K | 189 | 330.5% | 273 | 230.5% | 352 | 220.6% | 951 | 187.5% | 2,516 | 141.2% | 7,446 | 132.2% | 24,926 | 120.5% | 89,688 | 109.3% | 17,853 | 113.1% | |||||||||
10K - <25K | 1,056 | 253.3% | 1,229 | 155.5% | 1,387 | 150.9% | 2,959 | 131.3% | 8,277 | 116.6% | 16,386 | 106.1% | 38,473 | 98.8% | 176,131 | 99.3% | 38,234 | 97.0% | |||||||||
25K - <50K | 1,152 | 154.5% | 1,402 | 122.4% | 1,682 | 124.7% | 3,579 | 112.4% | 10,224 | 106.0% | 15,681 | 103.5% | 30,499 | 98.2% | 142,628 | 99.6% | 37,158 | 98.5% | |||||||||
50K - <100K | 1,000 | 135.6% | 1,348 | 114.2% | 1,607 | 112.0% | 3,822 | 108.0% | 11,946 | 100.7% | 18,207 | 100.2% | 31,509 | 99.1% | 142,244 | 99.8% | 35,085 | 99.5% | |||||||||
100K - <250K | 1,147 | 111.3% | 1,646 | 103.8% | 2,007 | 101.2% | 4,925 | 101.1% | 17,426 | 99.3% | 24,729 | 99.5% | 29,849 | 99.6% | 92,538 | 99.9% | 20,228 | 100.6% | |||||||||
250K - <500K | 419 | 110.6% | 553 | 97.0% | 705 | 100.8% | 1,693 | 99.6% | 6,378 | 99.5% | 8,612 | 100.0% | 8,182 | 99.3% | 16,700 | 99.7% | 3,247 | 101.7% | |||||||||
500K - <1M | 215 | 108.9% | 283 | 94.5% | 387 | 103.0% | 917 | 98.1% | 3,792 | 99.4% | 4,946 | 99.7% | 4,079 | 100.0% | 6,768 | 99.8% | 1,098 | 101.3% | |||||||||
1M - <2.5M | 129 | 98.7% | 151 | 90.3% | 264 | 103.7% | 678 | 100.6% | 3,261 | 99.6% | 3,978 | 99.7% | 2,568 | 100.5% | 3,332 | 100.4% | 411 | 97.1% | |||||||||
2.5M - <5M | 23 | 112.8% | 35 | 96.5% | 44 | 92.6% | 150 | 96.4% | 1,006 | 99.5% | 854 | 99.4% | 348 | 101.6% | 397 | 101.5% | 62 | 103.6% | |||||||||
5M - <10M | 12 | 96.0% | 18 | 108.0% | 29 | 94.1% | 98 | 96.9% | 940 | 99.8% | 677 | 100.4% | 131 | 98.4% | 103 | 102.0% | 17 | 95.4% | |||||||||
10M+ | 6 | 92.5% | 7 | 98.1% | 12 | 90.8% | 35 | 95.0% | 455 | 100.4% | 245 | 99.4% | 43 | 101.8% | 31 | 103.6% | 4 | 80.1% | |||||||||
UW | Insurance_Plan: Other | Insurance_Plan: Perm | Insurance_Plan: UL | Insurance_Plan: ULSG | Insurance_Plan: VL | Insurance_Plan: VLSG | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | |||||||
NS/1/2 | 28 | 167.8% | 9,854 | 98.2% | 19,946 | 99.9% | 6,492 | 99.3% | 6,729 | 99.4% | 2,048 | 103.1% | ||||||
NS/2/2 | 109 | 80.5% | 29,357 | 100.5% | 35,033 | 100.3% | 7,951 | 100.4% | 9,150 | 99.3% | 2,988 | 98.4% | ||||||
NS/1/3 | 54 | 262.5% | 940 | 99.4% | 2,030 | 98.5% | 3,278 | 99.0% | 376 | 105.8% | 360 | 94.0% | ||||||
NS/2/3 | 54 | 104.3% | 1,214 | 104.4% | 3,880 | 99.4% | 7,607 | 100.1% | 630 | 96.9% | 589 | 94.2% | ||||||
NS/3/3 | 103 | 102.1% | 4,770 | 102.4% | 10,193 | 100.0% | 18,371 | 100.0% | 1,305 | 103.4% | 967 | 96.1% | ||||||
NS/1/4 | 3 | 22.7% | 40 | 90.5% | 167 | 104.3% | 1,893 | 97.3% | 78 | 83.1% | 216 | 116.6% | ||||||
NS/2/4 | 2 | 70.0% | 58 | 95.4% | 281 | 110.4% | 2,202 | 98.0% | 52 | 108.4% | 171 | 77.3% | ||||||
NS/3/4 | 2 | 1.5% | 34 | 110.0% | 207 | 103.8% | 1,503 | 102.8% | 84 | 109.8% | 205 | 92.5% | ||||||
NS/4/4 | 4 | 17.8% | 213 | 100.8% | 889 | 102.3% | 2,747 | 101.8% | 143 | 113.7% | 184 | 103.7% | ||||||
NS/U/U | 630 | 107.8% | 413,063 | 99.9% | 240,127 | 99.9% | 13,494 | 100.7% | 34,748 | 100.5% | 8,101 | 102.4% | ||||||
S/1/2 | 16 | 88.9% | 2,256 | 98.7% | 2,472 | 101.8% | 1,954 | 98.5% | 916 | 91.8% | 398 | 101.0% | ||||||
S/2/2 | 23 | 30.5% | 3,891 | 105.4% | 6,007 | 100.3% | 2,503 | 98.9% | 1,694 | 102.6% | 583 | 104.3% | ||||||
S/U/U | 101 | 132.5% | 162,476 | 100.3% | 59,630 | 100.4% | 2,590 | 107.2% | 13,843 | 98.6% | 3,045 | 91.3% | ||||||
U/U/U | 1,857 | 103.0% | 25,707 | 100.1% | 279 | 57.9% | 2,623 | 109.5% | 311 | 133.0% | ||||||||
AA_Grp | Insurance_Plan: Other | Insurance_Plan: Perm | Insurance_Plan: UL | Insurance_Plan: ULSG | Insurance_Plan: VL | Insurance_Plan: VLSG | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | |||||||
0-17 | 1 | 18.4% | 521 | 72.7% | 699 | 75.4% | 164 | 72.9% | 143 | 77.3% | 60 | 61.2% | ||||||
18-25 | 9 | 80.8% | 2,420 | 91.1% | 2,608 | 97.8% | 326 | 82.3% | 551 | 126.4% | 169 | 142.9% | ||||||
26-30 | 6 | 76.2% | 2,468 | 112.6% | 2,089 | 100.3% | 245 | 103.5% | 474 | 107.1% | 113 | 94.7% | ||||||
31-35 | 8 | 28.2% | 2,943 | 101.8% | 2,412 | 103.2% | 326 | 118.0% | 503 | 103.1% | 170 | 99.5% | ||||||
36-40 | 17 | 45.0% | 3,610 | 102.2% | 3,128 | 103.6% | 442 | 108.0% | 732 | 104.9% | 277 | 85.7% | ||||||
41-45 | 28 | 146.3% | 6,093 | 98.0% | 4,732 | 103.7% | 783 | 108.1% | 1,296 | 96.4% | 526 | 101.0% | ||||||
46-50 | 51 | 58.2% | 11,203 | 100.7% | 8,215 | 102.1% | 1,359 | 103.1% | 2,529 | 96.4% | 835 | 102.6% | ||||||
51-55 | 92 | 118.5% | 19,304 | 98.9% | 15,387 | 101.2% | 2,377 | 102.9% | 4,698 | 98.0% | 1,311 | 95.4% | ||||||
56-60 | 149 | 77.6% | 28,744 | 100.0% | 24,995 | 100.7% | 4,176 | 99.4% | 6,870 | 98.5% | 1,831 | 99.2% | ||||||
61-65 | 186 | 73.1% | 40,716 | 99.4% | 36,575 | 100.0% | 6,393 | 98.9% | 8,972 | 101.3% | 2,263 | 102.5% | ||||||
66-70 | 239 | 150.0% | 55,704 | 99.5% | 45,924 | 99.6% | 8,704 | 99.2% | 9,542 | 101.1% | 2,528 | 103.2% | ||||||
71-75 | 285 | 102.8% | 71,766 | 99.5% | 52,740 | 100.4% | 9,722 | 99.3% | 9,205 | 101.4% | 2,586 | 104.5% | ||||||
76-80 | 408 | 151.3% | 93,678 | 100.3% | 57,803 | 100.3% | 10,492 | 100.3% | 8,388 | 98.5% | 2,455 | 94.9% | ||||||
81-85 | 494 | 96.1% | 117,775 | 100.3% | 62,957 | 100.2% | 11,325 | 99.7% | 8,197 | 99.4% | 2,460 | 98.0% | ||||||
86-90 | 560 | 68.2% | 109,701 | 100.3% | 54,624 | 99.8% | 10,035 | 100.2% | 6,568 | 101.5% | 1,819 | 97.4% | ||||||
91-95 | 342 | 95.2% | 51,937 | 100.6% | 26,775 | 99.7% | 4,941 | 100.4% | 3,140 | 96.4% | 705 | 94.3% | ||||||
96-100 | 104 | 162.2% | 9,255 | 103.0% | 4,626 | 100.6% | 932 | 97.4% | 538 | 115.9% | 57 | 71.4% | ||||||
101-105 | 7 | 68.9% | 320 | 95.7% | 236 | 63.5% | 75 | 100.6% | 25 | 140.1% | 1 | 132.4% | ||||||
106-110 | 0 | 0.0% | 8 | 204.5% | 24 | 16.4% | 23 | 20.8% | 0 | 0.0% | ||||||||
111-115 | 0 | 0.0% | 16 | 7.0% | 15 | 7.9% | ||||||||||||
116-120 | 4 | 1.6% | 9 | 8.9% | ||||||||||||||
Dur_Grp | Insurance_Plan: Other | Insurance_Plan: Perm | Insurance_Plan: UL | Insurance_Plan: ULSG | Insurance_Plan: VL | Insurance_Plan: VLSG | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | |||||||
1-1 | 28 | 62.0% | 2,537 | 127.8% | 1,269 | 121.3% | 1,386 | 103.2% | 54 | 87.7% | 74 | 58.9% | ||||||
2-2 | 17 | 82.3% | 2,754 | 107.4% | 1,749 | 105.8% | 2,245 | 96.6% | 65 | 65.1% | 115 | 95.5% | ||||||
3-3 | 24 | 56.2% | 3,097 | 97.9% | 2,198 | 101.1% | 2,861 | 101.6% | 139 | 93.7% | 157 | 114.3% | ||||||
4-5 | 86 | 117.9% | 6,749 | 101.3% | 5,071 | 100.6% | 6,975 | 99.3% | 415 | 97.4% | 511 | 92.3% | ||||||
6-10 | 272 | 102.0% | 17,121 | 99.9% | 19,345 | 99.8% | 24,167 | 100.1% | 2,936 | 99.8% | 2,380 | 98.1% | ||||||
11-15 | 117 | 79.2% | 32,893 | 99.4% | 31,282 | 99.8% | 20,581 | 99.8% | 11,005 | 100.5% | 5,883 | 101.2% | ||||||
16-20 | 67 | 321.3% | 81,452 | 99.7% | 58,148 | 99.8% | 7,129 | 100.8% | 17,580 | 99.9% | 6,231 | 98.7% | ||||||
21-30 | 627 | 71.5% | 384,784 | 99.9% | 240,103 | 100.1% | 6,697 | 100.6% | 34,226 | 100.3% | 4,123 | 106.6% | ||||||
31-120 | 1,748 | 112.1% | 96,779 | 99.9% | 47,404 | 99.9% | 823 | 71.8% | 5,951 | 101.7% | 692 | 115.5% | ||||||
AA_Grp | UW: NS/U/U | UW: S/U/U | UW: U/U/U | UW: NS/1/2 | UW: NS/2/2 | UW: NS/1/3 | UW: NS/2/3 | UW: NS/3/3 | UW: NS/1/4 | UW: NS/2/4 | UW: NS/3/4 | UW: NS/4/4 | UW: S/1/2 | UW: S/2/2 | ||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | |||||||||||||||
0-17 | 642 | 66.1% | 405 | 86.9% | 541 | 75.4% | ||||||||||||||||||||||||||||||||||||
18-25 | 2,909 | 88.8% | 1,189 | 126.6% | 1,492 | 109.2% | 73 | 91.1% | 36 | 97.7% | 63 | 98.0% | 30 | 95.5% | 114 | 67.3% | 35 | 74.4% | 10 | 102.4% | 4 | 33.8% | 19 | 54.7% | 34 | 62.0% | 75 | 473.8% | ||||||||||||||
26-30 | 2,628 | 99.5% | 943 | 136.0% | 1,020 | 102.9% | 121 | 96.6% | 64 | 64.7% | 110 | 115.0% | 48 | 104.1% | 203 | 148.4% | 26 | 69.6% | 10 | 80.6% | 13 | 53.6% | 35 | 79.5% | 74 | 107.3% | 100 | 118.8% | ||||||||||||||
31-35 | 2,993 | 104.2% | 1,077 | 125.2% | 925 | 100.6% | 197 | 81.4% | 244 | 106.0% | 149 | 67.2% | 104 | 122.8% | 248 | 119.4% | 77 | 119.2% | 13 | 64.6% | 29 | 127.1% | 36 | 215.6% | 113 | 110.0% | 157 | 112.8% | ||||||||||||||
36-40 | 3,702 | 93.1% | 1,413 | 92.5% | 920 | 101.1% | 441 | 102.1% | 469 | 101.8% | 222 | 93.3% | 156 | 114.7% | 317 | 121.4% | 76 | 84.9% | 34 | 113.3% | 21 | 153.1% | 49 | 125.2% | 149 | 109.0% | 237 | 114.8% | ||||||||||||||
41-45 | 6,116 | 97.0% | 2,617 | 91.2% | 776 | 113.2% | 952 | 93.6% | 862 | 94.9% | 361 | 110.4% | 300 | 115.1% | 534 | 111.1% | 133 | 107.3% | 82 | 132.0% | 64 | 123.0% | 88 | 106.2% | 216 | 67.4% | 357 | 116.9% | ||||||||||||||
46-50 | 11,979 | 101.8% | 5,253 | 94.1% | 507 | 120.3% | 1,633 | 91.9% | 1,656 | 107.2% | 447 | 91.6% | 428 | 105.7% | 821 | 107.4% | 178 | 120.6% | 85 | 88.8% | 83 | 101.2% | 131 | 128.7% | 439 | 96.2% | 552 | 98.4% | ||||||||||||||
51-55 | 22,124 | 99.1% | 9,749 | 96.9% | 541 | 147.2% | 2,718 | 95.6% | 2,977 | 102.9% | 558 | 103.0% | 662 | 100.3% | 1,357 | 105.1% | 207 | 97.6% | 150 | 102.6% | 156 | 106.2% | 220 | 114.9% | 762 | 95.8% | 988 | 98.3% | ||||||||||||||
56-60 | 34,103 | 99.4% | 16,152 | 99.0% | 1,024 | 134.2% | 3,725 | 100.5% | 4,352 | 99.5% | 734 | 105.1% | 906 | 97.1% | 2,149 | 100.5% | 278 | 111.1% | 220 | 87.5% | 198 | 84.9% | 292 | 83.8% | 1,131 | 92.8% | 1,501 | 109.0% | ||||||||||||||
61-65 | 48,484 | 100.0% | 23,995 | 98.7% | 1,522 | 120.6% | 4,508 | 98.2% | 6,441 | 101.9% | 844 | 104.8% | 1,276 | 100.3% | 3,319 | 102.3% | 288 | 84.9% | 298 | 84.1% | 265 | 82.6% | 482 | 115.3% | 1,261 | 93.5% | 2,122 | 94.8% | ||||||||||||||
66-70 | 62,985 | 100.4% | 32,526 | 101.0% | 2,065 | 116.7% | 4,695 | 97.0% | 8,215 | 101.6% | 759 | 92.7% | 1,653 | 97.1% | 4,485 | 101.8% | 297 | 84.8% | 375 | 87.4% | 282 | 101.9% | 562 | 110.0% | 1,317 | 98.0% | 2,425 | 96.9% | ||||||||||||||
71-75 | 79,010 | 100.3% | 37,347 | 100.9% | 2,472 | 113.6% | 5,098 | 90.2% | 10,044 | 100.9% | 813 | 104.7% | 1,781 | 98.0% | 4,852 | 101.4% | 291 | 113.1% | 382 | 112.2% | 271 | 102.5% | 632 | 110.3% | 1,005 | 111.0% | 2,306 | 93.1% | ||||||||||||||
76-80 | 103,004 | 100.1% | 37,578 | 101.2% | 2,962 | 110.7% | 5,702 | 102.5% | 12,535 | 99.2% | 657 | 96.3% | 1,826 | 98.1% | 4,936 | 99.2% | 212 | 90.7% | 397 | 88.6% | 262 | 114.5% | 563 | 98.9% | 769 | 113.4% | 1,821 | 98.6% | ||||||||||||||
81-85 | 131,733 | 100.1% | 35,105 | 101.3% | 4,020 | 101.3% | 6,564 | 98.5% | 15,019 | 99.3% | 658 | 102.4% | 2,108 | 99.1% | 5,100 | 99.5% | 160 | 107.0% | 351 | 96.3% | 211 | 112.0% | 469 | 101.6% | 448 | 103.6% | 1,262 | 109.5% | ||||||||||||||
86-90 | 125,799 | 100.2% | 24,798 | 101.7% | 5,230 | 97.1% | 5,658 | 102.9% | 13,382 | 100.4% | 498 | 96.7% | 1,764 | 99.2% | 4,554 | 99.6% | 106 | 68.3% | 241 | 109.5% | 124 | 78.6% | 367 | 93.0% | 228 | 85.5% | 558 | 97.1% | ||||||||||||||
91-95 | 61,162 | 100.4% | 9,766 | 95.3% | 3,742 | 94.2% | 2,563 | 102.6% | 6,842 | 99.2% | 149 | 89.9% | 792 | 101.5% | 2,217 | 99.1% | 30 | 114.0% | 106 | 103.5% | 46 | 131.0% | 173 | 84.4% | 59 | 118.3% | 193 | 114.9% | ||||||||||||||
96-100 | 10,451 | 100.8% | 1,639 | 103.3% | 933 | 75.8% | 436 | 122.2% | 1,398 | 97.2% | 11 | 66.0% | 133 | 111.0% | 401 | 94.7% | 3 | 103.1% | 12 | 153.1% | 4 | 23.4% | 51 | 99.5% | 6 | 168.1% | 34 | 44.0% | ||||||||||||||
101-105 | 331 | 108.4% | 130 | 102.4% | 68 | 13.4% | 13 | 136.3% | 51 | 109.4% | 5 | 197.8% | 7 | 108.8% | 43 | 28.6% | 0 | 0.0% | 2 | 110.3% | 7 | 27.6% | 1 | 595.5% | 6 | 52.9% | ||||||||||||||||
106-110 | 8 | 179.5% | 3 | 143.7% | 8 | 5.1% | 1 | 108.9% | 32 | 31.9% | 2 | 5.2% | 1 | 1.8% | ||||||||||||||||||||||||||||
111-115 | 0 | 0.0% | 5 | 2.0% | 0 | 0.0% | 20 | 34.6% | 2 | 4.8% | 4 | 42.8% | ||||||||||||||||||||||||||||||
116-120 | 4 | 2.5% | 7 | 25.9% | 0 | 0.0% | 2 | 63.3% | ||||||||||||||||||||||||||||||||||
UW | Dur_Grp: 1-1 | Dur_Grp: 2-2 | Dur_Grp: 3-3 | Dur_Grp: 4-5 | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-120 | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||||||
NS/1/2 | 85 | 78.6% | 146 | 177.8% | 214 | 171.4% | 488 | 62.0% | 3,129 | 100.1% | 8,689 | 98.4% | 13,534 | 98.7% | 17,588 | 100.5% | 1,224 | 118.2% | |||||||||
NS/2/2 | 133 | 125.6% | 140 | 96.5% | 244 | 137.9% | 849 | 89.8% | 6,018 | 99.4% | 17,296 | 100.3% | 22,596 | 100.4% | 33,941 | 100.5% | 3,371 | 94.9% | |||||||||
NS/1/3 | 215 | 79.0% | 332 | 91.1% | 392 | 97.3% | 927 | 104.2% | 2,568 | 101.0% | 1,920 | 101.4% | 642 | 92.0% | 40 | 51.5% | 2 | 28.8% | |||||||||
NS/2/3 | 223 | 99.1% | 364 | 101.1% | 451 | 105.0% | 1,209 | 96.7% | 5,262 | 100.3% | 4,819 | 99.5% | 1,467 | 103.6% | 179 | 63.6% | 0 | 0.0% | |||||||||
NS/3/3 | 1,152 | 114.3% | 1,611 | 99.3% | 1,970 | 96.1% | 4,485 | 101.0% | 14,771 | 100.2% | 9,774 | 100.3% | 1,252 | 103.8% | 572 | 78.4% | 122 | 40.7% | |||||||||
NS/1/4 | 104 | 104.3% | 172 | 75.9% | 243 | 109.0% | 472 | 99.6% | 898 | 97.6% | 465 | 105.7% | 43 | 65.9% | 0 | 0.0% | 0 | 0.0% | |||||||||
NS/2/4 | 99 | 76.3% | 142 | 78.3% | 181 | 80.6% | 482 | 107.3% | 1,095 | 97.9% | 629 | 108.8% | 136 | 97.4% | 2 | 74.9% | 0 | 0.0% | |||||||||
NS/3/4 | 65 | 71.8% | 127 | 98.7% | 144 | 91.0% | 334 | 112.1% | 778 | 97.1% | 554 | 110.1% | 33 | 101.6% | 0 | 0.0% | |||||||||||
NS/4/4 | 231 | 137.9% | 306 | 112.8% | 383 | 99.5% | 848 | 105.5% | 1,604 | 99.6% | 639 | 103.5% | 85 | 65.4% | 66 | 19.3% | 18 | 21.3% | |||||||||
NS/U/U | 1,909 | 126.7% | 2,351 | 101.9% | 2,761 | 110.0% | 6,404 | 103.9% | 19,610 | 99.2% | 38,118 | 99.5% | 92,885 | 99.7% | 444,936 | 100.0% | 101,189 | 100.2% | |||||||||
S/1/2 | 122 | 142.1% | 176 | 76.2% | 215 | 72.1% | 487 | 88.7% | 1,682 | 95.1% | 1,916 | 94.7% | 1,651 | 106.8% | 1,643 | 108.4% | 120 | 167.6% | |||||||||
S/2/2 | 437 | 112.6% | 474 | 130.8% | 540 | 78.4% | 1,079 | 86.6% | 2,846 | 95.7% | 3,016 | 103.8% | 2,847 | 106.0% | 3,115 | 107.4% | 347 | 86.5% | |||||||||
S/U/U | 466 | 225.9% | 525 | 81.3% | 643 | 90.1% | 1,545 | 104.3% | 5,164 | 104.6% | 12,728 | 97.9% | 31,327 | 99.0% | 151,687 | 100.3% | 37,600 | 100.4% | |||||||||
U/U/U | 107 | 94.9% | 79 | 52.1% | 95 | 70.0% | 198 | 75.7% | 796 | 129.4% | 1,198 | 100.8% | 2,109 | 106.4% | 16,791 | 101.8% | 9,404 | 96.0% | |||||||||
AA_Grp | Dur_Grp: 1-1 | Dur_Grp: 2-2 | Dur_Grp: 3-3 | Dur_Grp: 4-5 | Dur_Grp: 6-10 | Dur_Grp: 11-15 | Dur_Grp: 16-20 | Dur_Grp: 21-30 | Dur_Grp: 31-120 | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | Deaths | Ratio | ||||||||||
0-17 | 173 | 68.1% | 105 | 49.6% | 104 | 92.0% | 140 | 73.3% | 358 | 72.1% | 390 | 86.1% | 318 | 68.2% | |||||||||||||
18-25 | 270 | 84.7% | 222 | 142.7% | 194 | 85.5% | 388 | 90.6% | 858 | 124.1% | 751 | 92.3% | 1,338 | 89.3% | 2,062 | 98.0% | |||||||||||
26-30 | 144 | 111.2% | 154 | 82.3% | 173 | 139.5% | 310 | 134.0% | 668 | 99.8% | 674 | 104.2% | 617 | 97.4% | 2,513 | 102.2% | 142 | 102.6% | |||||||||
31-35 | 167 | 127.1% | 179 | 94.3% | 170 | 93.5% | 367 | 122.4% | 905 | 99.4% | 990 | 111.8% | 841 | 96.7% | 2,006 | 95.6% | 737 | 106.6% | |||||||||
36-40 | 179 | 188.7% | 197 | 79.6% | 182 | 119.0% | 407 | 89.9% | 1,045 | 105.0% | 1,401 | 95.8% | 1,515 | 98.3% | 2,712 | 97.1% | 568 | 92.2% | |||||||||
41-45 | 241 | 89.4% | 295 | 123.8% | 324 | 122.4% | 603 | 103.0% | 1,537 | 100.7% | 2,110 | 103.1% | 2,708 | 95.5% | 4,940 | 93.2% | 700 | 96.2% | |||||||||
46-50 | 368 | 110.1% | 368 | 79.0% | 425 | 111.5% | 810 | 91.9% | 2,164 | 103.1% | 3,160 | 102.9% | 4,617 | 102.3% | 11,001 | 97.6% | 1,279 | 103.6% | |||||||||
51-55 | 475 | 96.9% | 538 | 80.7% | 659 | 103.1% | 1,253 | 103.1% | 3,316 | 97.7% | 4,811 | 101.8% | 7,390 | 100.4% | 21,380 | 99.7% | 3,347 | 101.8% | |||||||||
56-60 | 655 | 135.9% | 812 | 107.7% | 927 | 91.1% | 1,786 | 94.9% | 4,650 | 101.7% | 6,376 | 99.4% | 10,273 | 98.6% | 34,227 | 99.4% | 7,059 | 98.6% | |||||||||
61-65 | 856 | 101.0% | 1,020 | 109.6% | 1,238 | 92.0% | 2,522 | 96.5% | 6,282 | 99.1% | 8,325 | 98.7% | 13,454 | 99.6% | 49,923 | 100.4% | 11,485 | 102.3% | |||||||||
66-70 | 735 | 108.8% | 1,135 | 86.4% | 1,419 | 99.5% | 3,162 | 98.6% | 7,861 | 98.9% | 10,137 | 98.9% | 16,691 | 101.0% | 65,377 | 100.4% | 16,124 | 101.3% | |||||||||
71-75 | 483 | 80.5% | 842 | 106.8% | 1,086 | 91.1% | 2,945 | 103.1% | 9,258 | 100.9% | 12,280 | 99.1% | 19,613 | 99.1% | 80,264 | 100.3% | 19,533 | 101.4% | |||||||||
76-80 | 295 | 95.9% | 549 | 98.8% | 747 | 100.3% | 2,208 | 102.4% | 9,054 | 99.4% | 14,574 | 100.7% | 25,716 | 99.2% | 97,363 | 100.1% | 22,718 | 101.2% | |||||||||
81-85 | 146 | 98.8% | 321 | 102.7% | 532 | 114.9% | 1,761 | 97.0% | 8,778 | 99.7% | 15,015 | 100.1% | 29,833 | 99.4% | 120,517 | 100.2% | 26,305 | 101.1% | |||||||||
86-90 | 59 | 217.0% | 111 | 153.6% | 211 | 98.9% | 897 | 105.2% | 6,832 | 99.8% | 12,830 | 99.7% | 23,281 | 100.5% | 113,684 | 100.2% | 25,402 | 99.1% | |||||||||
91-95 | 50 | 127.3% | 44 | 278.0% | 50 | 95.8% | 188 | 68.8% | 2,406 | 99.1% | 6,698 | 99.6% | 10,510 | 101.0% | 53,214 | 100.5% | 14,680 | 101.0% | |||||||||
96-100 | 52 | 143.3% | 53 | 96.0% | 30 | 164.7% | 48 | 172.0% | 243 | 108.1% | 1,196 | 102.1% | 1,805 | 99.9% | 8,967 | 98.8% | 3,118 | 90.4% | |||||||||
101-105 | 5 | 129.1% | 12 | 334.1% | 6 | 128.2% | 43 | 90.6% | 82 | 149.0% | 356 | 68.6% | 160 | 34.7% | |||||||||||||
106-110 | 5 | 70.0% | 32 | 42.9% | 18 | 9.2% | |||||||||||||||||||||
111-115 | 0 | 0.0% | 0 | 0.0% | 20 | 31.4% | 11 | 3.2% | |||||||||||||||||||
116-120 | 2 | 24.8% | 11 | 3.7% | |||||||||||||||||||||||
As with other models, tor the bivariate fit checks, the fit can be great in some cases and poor in others. This could be due to a need for higher level interactions.
9 Impact on Trend of Adjusting for Other Variables
Even though the goal of this work is to support other analysis, it is worth examining the impact on trend of controlling for other variables. In the table below, it can be seen that there is a narrower spread of ratios between 2011 and 2017, 103.5% to 98.1% for the ratios against the model, and 98.3% to 89.4% for the ratios against the 2015 VBT. This is a meaningful reduction in residual trend.
Code
ilec_arrow_src <- '/workspace/Projects/ILEC/VBT/Data/ilecdata'
dat.arrow <- arrow::open_dataset(ilec_arrow_src)
AA.brks <- c(-1,17,
seq(25,115,5))
AA.lbls <- paste0(
AA.brks[1:(length(AA.brks)-1)]+1,
"-",
AA.brks[2:length(AA.brks)]
)
Dur.brks <- c(0,1,2,3,5,10,15,20,30,100)
Dur.lbls <- paste0(
Dur.brks[1:(length(Dur.brks)-1)]+1,
"-",
Dur.brks[2:length(Dur.brks)]
)
dat.arrow %>%
filter(Observation_Year >= 2011
& Observation_Year <= 2017
& Insurance_Plan == 'Term'
& SOA_Post_Lvl_Ind != 'PLT') %>%
#select(!Observation_Year) %>%
group_by(
Sex,
Smoker_Status,
Attained_Age,
Duration,
Face_Amount_Band,
SOA_Post_Lvl_Ind,
Number_of_Pfd_Classes,
Preferred_Class,
Observation_Year
) %>%
summarize(
Death_Count=sum(Death_Count),
Policies_Exposed=sum(Policies_Exposed),
ExpDth_Cnt_VBT2015=sum(ExpDth_Cnt_VBT2015),
Death_Claim_Amount=sum(Death_Claim_Amount),
Amount_Exposed=sum(Amount_Exposed),
ExpDth_Amt_VBT2015=sum(ExpDth_Amt_VBT2015)
) %>%
collect() %>%
as.data.table() %>%
mutate(
Smoker_Status=as.character(Smoker_Status),
Preferred_Class=as.character(Preferred_Class),
Number_of_Pfd_Classes=as.character(Number_of_Pfd_Classes)
) %>%
mutate(Smoker_Status=ifelse(is.na(Smoker_Status),"U",Smoker_Status),
Number_of_Pfd_Classes=ifelse(is.na(Number_of_Pfd_Classes),"U",
Number_of_Pfd_Classes),
Preferred_Class=ifelse(is.na(Preferred_Class),"U",Preferred_Class),
UW=paste0(Smoker_Status,"/",Preferred_Class,"/",Number_of_Pfd_Classes),
AA_Grp=cut(Attained_Age,breaks=AA.brks,labels = AA.lbls),
Dur_Grp=cut(Duration,breaks=Dur.brks,labels=Dur.lbls),
Subset="TermNoPLT",
Face_Amount_Band=fct_relabel(
Face_Amount_Band,
#function(.) sub(":"," -",.,fixed=T)
function(.) fa.remap[Face_Amount_Band.Old==.,Face_Amount_Band.New]
)
) %>%
left_join(
y=rbind(dat.term.noplt.lt100k.grid,dat.term.noplt.100kp.grid)
) %>%
group_by(
Subset,
Observation_Year
) %>%
summarize(
Death_Count=sum(Death_Count),
Death_Amount=sum(Death_Claim_Amount),
TabularClaimsAmount=sum(ExpDth_Amt_VBT2015),
ModelClaimsAmount=sum(ExpDth_Amt_VBT2015*Factor)
) %>%
data.table() ->
dat.term.noplt.2
dat.arrow %>%
filter(Observation_Year >= 2011
& Observation_Year <= 2017
& Insurance_Plan == 'Term'
& SOA_Post_Lvl_Ind == 'PLT') %>%
#select(!Observation_Year) %>%
group_by(
Sex,
Smoker_Status,
Attained_Age,
Duration,
Face_Amount_Band,
SOA_Antp_Lvl_TP,
Number_of_Pfd_Classes,
Preferred_Class,
Observation_Year
) %>%
summarize(
Death_Count=sum(Death_Count),
Policies_Exposed=sum(Policies_Exposed),
ExpDth_Cnt_VBT2015=sum(ExpDth_Cnt_VBT2015),
Death_Claim_Amount=sum(Death_Claim_Amount),
Amount_Exposed=sum(Amount_Exposed),
ExpDth_Amt_VBT2015=sum(ExpDth_Amt_VBT2015)
) %>%
collect() %>%
as.data.table() %>%
mutate(
Smoker_Status=as.character(Smoker_Status),
Preferred_Class=as.character(Preferred_Class),
Number_of_Pfd_Classes=as.character(Number_of_Pfd_Classes)
) %>%
mutate(Smoker_Status=ifelse(is.na(Smoker_Status),"U",Smoker_Status),
Number_of_Pfd_Classes=ifelse(is.na(Number_of_Pfd_Classes),"U",
Number_of_Pfd_Classes),
Preferred_Class=ifelse(is.na(Preferred_Class),"U",Preferred_Class),
UW=paste0(Smoker_Status,"/",Preferred_Class,"/",Number_of_Pfd_Classes),
AA_Grp=cut(Attained_Age,breaks=AA.brks,labels = AA.lbls),
Dur_Grp=cut(Duration,breaks=Dur.brks,labels=Dur.lbls),
Subset="TermPLT",
Face_Amount_Band=fct_relabel(
Face_Amount_Band,
#function(.) sub(":"," -",.,fixed=T)
function(.) fa.remap[Face_Amount_Band.Old==.,Face_Amount_Band.New]
)
)%>%
left_join(
y=dat.term.plt.grid
) %>%
group_by(
Subset,
Observation_Year
) %>%
summarize(
Death_Count=sum(Death_Count),
Death_Amount=sum(Death_Claim_Amount),
TabularClaimsAmount=sum(ExpDth_Amt_VBT2015),
ModelClaimsAmount=sum(ExpDth_Amt_VBT2015*Factor)
) ->
dat.term.plt.2
AA.brks <- c(-1,17,
seq(25,120,5))
AA.lbls <- paste0(
AA.brks[1:(length(AA.brks)-1)]+1,
"-",
AA.brks[2:length(AA.brks)]
)
Dur.brks <- c(0,1,2,3,5,10,15,20,30,120)
Dur.lbls <- paste0(
Dur.brks[1:(length(Dur.brks)-1)]+1,
"-",
Dur.brks[2:length(Dur.brks)]
)
dat.arrow %>%
filter(Observation_Year >= 2011
& Observation_Year <= 2017
& Insurance_Plan != 'Term') %>%
#select(!Observation_Year) %>%
group_by(
Sex,
Smoker_Status,
Attained_Age,
Duration,
Face_Amount_Band,
SOA_Post_Lvl_Ind,
Number_of_Pfd_Classes,
Preferred_Class,
Observation_Year,
Insurance_Plan
) %>%
summarize(
Death_Count=sum(Death_Count),
Policies_Exposed=sum(Policies_Exposed),
ExpDth_Cnt_VBT2015=sum(ExpDth_Cnt_VBT2015),
Death_Claim_Amount=sum(Death_Claim_Amount),
Amount_Exposed=sum(Amount_Exposed),
ExpDth_Amt_VBT2015=sum(ExpDth_Amt_VBT2015)
) %>%
collect() %>%
as.data.table() %>%
mutate(
Smoker_Status=as.character(Smoker_Status),
Preferred_Class=as.character(Preferred_Class),
Number_of_Pfd_Classes=as.character(Number_of_Pfd_Classes)
) %>%
mutate(Smoker_Status=ifelse(is.na(Smoker_Status),"U",Smoker_Status),
Number_of_Pfd_Classes=ifelse(is.na(Number_of_Pfd_Classes),"U",
Number_of_Pfd_Classes),
Preferred_Class=ifelse(is.na(Preferred_Class),"U",Preferred_Class),
UW=paste0(Smoker_Status,"/",Preferred_Class,"/",Number_of_Pfd_Classes),
AA_Grp=cut(Attained_Age,breaks=AA.brks,labels = AA.lbls),
Dur_Grp=cut(Duration,breaks=Dur.brks,labels=Dur.lbls),
Subset=ifelse(Insurance_Plan=="Perm" & UW=="U/U/U", "Perm_Unk","Perm_Knw"),
Face_Amount_Band=fct_relabel(
Face_Amount_Band,
#function(.) sub(":"," -",.,fixed=T)
function(.) fa.remap[Face_Amount_Band.Old==.,Face_Amount_Band.New]
)
) %>%
left_join(
y=dat.perm.knw.grid[!(Insurance_Plan=="Perm" & UW == "U/U/U")]
) %>%
rename(
Factor_KNW = Factor
) %>%
left_join(
y=dat.perm.unk.grid
) %>%
mutate(
Factor = ifelse(is.na(Factor_KNW),Factor,Factor_KNW)
) %>%
group_by(
Subset,
Observation_Year
) %>%
summarize(
Death_Count=sum(Death_Count),
Death_Amount=sum(Death_Claim_Amount),
TabularClaimsAmount=sum(ExpDth_Amt_VBT2015),
ModelClaimsAmount=sum(ExpDth_Amt_VBT2015*Factor)
) ->
dat.perm.2
dat.illustration <- rbind(
dat.term.noplt.2,
dat.term.plt.2,
dat.perm.2
)
rm(dat.term.noplt.2, dat.term.plt.2, dat.perm.2)
dat.illustration %>%
group_by(Observation_Year) %>%
summarize(
Death_Count=sum(Death_Count),
Death_Amount=sum(Death_Amount),
TabularClaimsAmount=sum(TabularClaimsAmount),
ModelClaimsAmount=sum(ModelClaimsAmount),
A_E_Tbl=Death_Amount/TabularClaimsAmount,
A_E_Mod=Death_Amount/ModelClaimsAmount
) %>%
flextable() %>%
set_formatter(
A_E_Tbl = function(x) {
if(is.numeric(x))
sprintf( "%.1f%%", x*100 )
else
x
},
A_E_Mod = function(x) {
if(is.numeric(x))
sprintf( "%.1f%%", x*100 )
else
x
}
) %>%
colformat_num(j=c("Death_Count","Death_Amount",
"TabularClaimsAmount","ModelClaimsAmount") ) %>%
colformat_int(j="Observation_Year",big.mark="") %>%
set_header_labels(
Observation_Year = "Observation Year",
Death_Count = "Death Count",
Death_Amount = "Death Amount",
TabularClaimsAmount="15VBT Tabular Claims",
ModelClaimsAmount = "Model Predicted Claims",
A_E_Tbl = "Actual-to-15VBT",
A_E_Mod = "Actual-to-Model"
)Observation Year | Death Count | Death Amount | 15VBT Tabular Claims | Model Predicted Claims | Actual-to-15VBT | Actual-to-Model |
|---|---|---|---|---|---|---|
2011 | 563,694 | 26,101,825,065 | 26,560,415,265 | 25,224,268,217 | 98.3% | 103.5% |
2012 | 537,286 | 27,828,587,056 | 28,843,616,822 | 27,075,644,852 | 96.5% | 102.8% |
2013 | 554,199 | 30,043,247,445 | 32,019,431,009 | 30,071,134,913 | 93.8% | 99.9% |
2014 | 560,393 | 32,777,977,745 | 35,396,309,259 | 33,012,977,593 | 92.6% | 99.3% |
2015 | 565,853 | 35,479,567,171 | 38,423,917,677 | 35,522,249,984 | 92.3% | 99.9% |
2016 | 552,127 | 37,188,498,560 | 41,266,090,988 | 37,745,327,915 | 90.1% | 98.5% |
2017 | 558,579 | 38,975,688,945 | 43,595,587,331 | 39,743,791,962 | 89.4% | 98.1% |
The ratios with fitted trend lines from a GLM bear this out visually. The fitted GLMs show an average 1.5% decline per annum in ratios against the 2015 VBT versus an average 0.8% decline per annum of the ratios against the model.
Code
mod.glm.tbl <- glm(
Death_Amount ~ Observation_Year,
data=dat.illustration,
family=quasipoisson,
offset=log(TabularClaimsAmount)
)
mod.glm.mdl <- glm(
Death_Amount ~ Observation_Year,
data=dat.illustration,
family=quasipoisson,
offset=log(ModelClaimsAmount)
)
dat.illustration %>%
group_by(Observation_Year) %>%
summarize(
Death_Count=sum(Death_Count),
Death_Amount=sum(Death_Amount),
TabularClaimsAmount=sum(TabularClaimsAmount),
ModelClaimsAmount=sum(ModelClaimsAmount),
A_E_Tbl=Death_Amount/TabularClaimsAmount,
A_E_Mod=Death_Amount/ModelClaimsAmount
) %>%
ggplot(aes(x=Observation_Year)) +
geom_line(aes(y=A_E_Tbl)) +
geom_line(aes(y=A_E_Mod),color="green") +
geom_smooth(aes(y=A_E_Tbl,weight=TabularClaimsAmount),
method.args=list(family="quasipoisson"),
method="glm",linetype=2) +
geom_smooth(aes(y=A_E_Mod,weight=ModelClaimsAmount),
method.args=list(family="quasipoisson"),
method="glm",color="green",linetype=2) +
annotate(geom="text",
label=paste0("Residual Trend vs. 15VBT: ", sprintf( "%.1f%%", (exp(mod.glm.tbl$coefficients[2])-1)*100 ), " p.a."),
x=2013,y=.92) +
annotate(geom="text",
label=paste0("Residual Trend vs. Model: ", sprintf( "%.1f%%", (exp(mod.glm.mdl$coefficients[2])-1)*100 ), " p.a."),
x=2015,y=1.02) +
scale_y_continuous(name="Actual vs. Model or Table",labels = scales::percent) +
scale_x_continuous(name="Observation Year") +
ggtitle(label="Actual Experience versus Models",subtitle="with GLM trends") +
theme_minimal()
In the chart below, we can see a substantial year-over-year growth in face amounts exposed for Term, Perm, and UL/VL. The reader is invited to explore the data themselves to understand prevalence shifts, which is beyond the scope of this work.
Code
dat.arrow %>%
filter(Observation_Year >= 2011
& Observation_Year <= 2017) %>%
group_by(
Insurance_Plan,
Face_Amount_Band,
Observation_Year
) %>%
summarise(
Amount_Exposed=sum(Amount_Exposed)
) %>%
collect() %>%
ungroup(Face_Amount_Band) %>%
mutate(Amount_Exposed=Amount_Exposed/sum(Amount_Exposed),
Face_Amount_Band=fct_relabel(
Face_Amount_Band,
function(.) substr(.,1,2)
)
) %>%
data.table() %>%
ggplot(aes(x=Observation_Year)) +
geom_bar(aes(y=Amount_Exposed),stat="identity") +
facet_grid(rows=vars(Insurance_Plan),cols=vars(Face_Amount_Band)) +
theme_minimal() +
ggtitle("Exposure Trends 2011-17",
subtitle = "by Face Amount Band and Insurance Plan") +
scale_y_continuous(name="Amount Exposed (% of Total Exposure)",
labels = scales::percent) +
scale_x_continuous(name="Observation Year") +
theme(axis.text.x = element_text(angle=90))
10 Running the Workbook
To run this workbook, you will need the supporting R functions and a compatible dataset. The supporting R functions are embedded here if for some reason they are not provided with this document. The dataset is an Arrow dataset based on the standard download from the Society of Actuaries. The CSV was converted to Parquet files split by gender and observation year.
Code
# catboost.shapviz.R
shapviz.catboost.Model <- function(object, X_pred, X = X_pred, collapse = NULL, ...) {
if (!requireNamespace("catboost", quietly = TRUE)) {
stop("Package 'catboost' not installed")
}
stopifnot(
"X must be a matrix or data.frame. It can't be an object of class catboost.Pool" =
is.matrix(X) || is.data.frame(X),
"X_pred must be a matrix, a data.frame, or a catboost.Pool" =
is.matrix(X_pred) || is.data.frame(X_pred) || inherits(X_pred, "catboost.Pool"),
"X_pred must have column names" = !is.null(colnames(X_pred))
)
if (!inherits(X_pred, "catboost.Pool")) {
X_pred <- catboost.load_pool(X_pred)
}
S <- catboost.get_feature_importance(object, X_pred, type = "ShapValues", ...)
# Call matrix method
pp <- ncol(X_pred) + 1
baseline <- S[1, pp]
S <- S[, -pp, drop = FALSE]
colnames(S) <- colnames(X_pred)
shapviz(S, X = X, baseline = baseline, collapse = collapse)
}
#glmnet_support.R
prepELData <- function( formula, data, predictors, response, offset=NULL, weights=NULL,
foldid=NULL, useSparse=FALSE, dropunused=FALSE ) {
if(is.null(formula))
stop("formula must be provided")
if(is.null(data))
stop("data must be provided")
if(is.null(response))
stop("response must be provided")
# if(useSparse) {
# outMat <- sparse.model.matrix(
# formula,
# data[,..predictors]
# )
# } else {
# outMat <- model.matrix(
# formula,
# data[,..predictors]
# )
# }
outMat <- model.Matrix(
formula,
data[,..predictors],
sparse=useSparse,
drop.unused.levels = dropunused
)
outResp <- as.matrix(data[[response]])
if(is.null(offset))
outOffset <- NULL
else
outOffset <- as.matrix(data[[offset]])
if(is.null(weights))
outWeights <- NULL
else
outWeights <- as.matrix(data[[weights]])
if(is.null(foldid))
outFoldID <- NULL
else
outFoldID <- as.matrix(data[[foldid]])
list(input.matrix=outMat,
response=outResp,
offset = outOffset,
weights = outWeights,
foldid = outFoldID)
}
fitCVGLMNet <- function(datalist,alpha=0.5,
nfolds=ifelse(is.null(datalist$foldid),5,max(datalist$foldid))) {
cl <- makeCluster(nfolds)
registerDoParallel(cl)
#glmnet.control(itrace = 1)
cvfit <- try(
{
cv.glmnet(
x=datalist$input.matrix,
y=datalist$response,
offset=datalist$offset,
weights=datalist$weights,
family="poisson",
alpha=alpha,
nfolds=nfolds,
foldid = datalist$foldid,
parallel=T,
standardize=F)
}
)
stopCluster(cl)
cvfit
}
# https://stackoverflow.com/questions/6457290/how-to-check-the-amount-of-ram
available_memory <- function()
{
# Get operating system
OS <- tolower(Sys.info()["sysname"])
# Branch based on OS
if(OS == "windows"){ # Windows
# System information
system_info <- system("systeminfo", intern = TRUE)
# Get available memory
value <- system_info[
grep("Available Physical Memory", system_info)
]
# Remove extraneous information
value <- gsub("Available Physical Memory: ", "", value)
value <- gsub("\\,", "", value)
# Convert to bytes
value_split <- unlist(strsplit(value, split = " "))
# Check for second value
bytes <- as.numeric(value_split[1]) * switch(
value_split[2],
"KB" = 1e03,
"MB" = 1e06,
"GB" = 1e09
)
}else if(OS == "linux"){ # Linux
# Split system information
info_split <- strsplit(system("free -b", intern = TRUE), split = " ")
# Remove "Mem:" and "Swap:"
info_split <- lapply(info_split, function(x){gsub("Mem:", "", x)})
info_split <- lapply(info_split, function(x){gsub("Swap:", "", x)})
# Get actual values
info_split <- lapply(info_split, function(x){x[x != ""]})
# Bind values
info_split <- do.call(rbind, info_split[1:2])
# Get free values
bytes <- as.numeric(info_split[2, info_split[1,] == "free"])
}else{ # Mac
# System information
system_info <- system("top -l 1 -s 0 | grep PhysMem", intern = TRUE)
# Get everything after comma
unused <- gsub(" .*,", "", system_info)
# Get values only
value <- gsub("PhysMem: ", "", unused)
value <- gsub(" unused.", "", value)
# Check for bytes
if(grepl("M", value)){
bytes <- as.numeric(gsub("M", "", value)) * 1e06
}else if(grepl("G", value)){
bytes <- as.numeric(gsub("G", "", value)) * 1e09
}else if(grepl("K", value)){
bytes <- as.numeric(gsub("K", "", value)) * 1e03
}
}
# Return bytes
return(bytes)
}
reformatCoefs <- function(cvfit,pred.cols,s="lambda.min") {
coef(cvfit,s=s) %>%
as.matrix() %>%
as.data.table(keep.rownames=T) %>%
setnames(c("rn","s1"),c("CoefName","Coef")) ->
coefs
coefs[,c("Feature1","Feature2") := tstrsplit(CoefName,":")]
walk(pred.cols,\(x)
coefs[startsWith(Feature1,x),
`:=`(Feature1Name=x
)]
)
coefs[,
Feature1Level:=mapply(
function(f,fname) {
str_sub(
f,
end=-1,
start=nchar(fname)-nchar(f)
)
},
Feature1,
Feature1Name,
SIMPLIFY = "vector"
)]
walk(pred.cols,\(x)
coefs[startsWith(Feature2,x),
`:=`(Feature2Name=x
)]
)
coefs[,
Feature2Level:=mapply(
function(f,fname) {
str_sub(
f,
end=-1,
start=nchar(fname)-nchar(f)
)
},
Feature2,
Feature2Name,
SIMPLIFY = "vector"
)]
coefs[Feature1=="(Intercept)",
`:=`(Feature1Name="(Intercept)",
Feature1Level="(Intercept)")]
coefs[,`:=`(Feature1=NULL, Feature2=NULL)]
coefs
}
plotCVNetCoefs <- function(
model.grid,
vars,
factorcol,
pred.cols,
whichlevel = "mid"
) {
v1 <- sym(vars[1])
v2 <- sym(vars[2])
vf <- sym(factorcol)
model.grid[,..pred.cols] %>%
lapply(levels) %>%
imap(.f=\(x,idx) {
if(idx %in% vars[1:2]) {
retval <- x
} else {
if(whichlevel == "first")
retval <- x[1]
else if(whichlevel == "last")
retval <- x[length(x)]
else if(whichlevel == "mid")
retval <- x[length(x)/2]
}
retval
}) %>%
expand.grid() %>%
setDT() ->
filter.frame
filter.frame %>%
select(!c(!!v1,!!v2)) %>%
distinct() %>%
imap( .f = \(x,idx) paste0(idx,": ",x)) %>%
paste(collapse=", ") %>%
paste0("Other fixed variables - ",.) ->
st
model.grid %>%
inner_join(filter.frame) %>%
ggplot(aes(x=!!v1,y=!!vf)) +
geom_point() +
facet_wrap(vars(!!v2)) +
scale_y_continuous(labels = scales::percent) +
geom_hline(yintercept=1,linetype=2) +
ggtitle(label=paste0("Coefficients for ",vars[1], " by ", vars[2]),
subtitle = st) +
theme_minimal() +
theme(
axis.text.x = element_text(angle=90)
)
}
tableCVNetCoefs <- function(
model.grid,
vars,
factorcol,
pred.cols,
whichlevel = "mid"
) {
v1 <- sym(vars[1])
v2 <- sym(vars[2])
vf <- sym(factorcol)
model.grid[,..pred.cols] %>%
lapply(levels) %>%
imap(.f=\(x,idx) {
if(idx %in% vars[1:2]) {
retval <- x
} else {
if(whichlevel == "first")
retval <- x[1]
else if(whichlevel == "last")
retval <- x[length(x)]
else if(whichlevel == "mid")
retval <- x[length(x)/2]
}
retval
}) %>%
expand.grid() %>%
setDT() ->
filter.frame
filter.frame %>%
select(!c(!!v1,!!v2)) %>%
distinct() %>%
imap( .f = \(x,idx) paste0(idx,": ",x)) %>%
paste(collapse=", ") %>%
paste0("Other fixed variables - ",.) ->
st
model.grid %>%
inner_join(filter.frame) %>%
select(!!v1,!!v2,Factor) %>%
pivot_wider(names_from=!!v2,
values_from=Factor)
}
# support_fns.R
generate_tabset <- function(tabs,
tabtitle,
tablevel = 1) {
# markdown <- paste0(
# paste(rep("#",tablevel),collapse=""),
# " ",
# tabtitle,
# " ",
# "{.tabset}\n\n")
# markdown <- "::: panel-tabset"
markdown <- ""
for (i in seq_along(tabs)) {
title <- names(tabs)[i]
content <- tabs[[i]]
markdown <- paste0(markdown,
paste(rep("#",tablevel + 1),collapse=""),
" ",
title,
"\n\n",
content,
"\n\n")
}
# markdown <- paste0(markdown,"\n",":::")
return(markdown)
}The dataset is extracted from the ILEC data. Provided variable names and their content are identical and that the data objects are stored in RDS files of the appropriate names, then the workbook should run as is.
Computation is not onerous. A GPU was used for gradient boosting in anticipation of needing substantial computing power. Early attempts greatly benefited from it. However, as modeling progressed, the gradient boosting models became simple enough that it could run reasonably well on CPU. For elastic net, the use of sparse matrices ensures that memory should not be an issue except in the most basic environment. CPU usage is a different matter. By default, we use 10 cores for cross-validation. If 10 cores are available, the elastic net models typically require only a few minutes to run. If you do not have 10 cores, adjust your expectations accordingly.
The workbook, when executed, will carry out the following:
Load the data and apply transformations.
If not already made, fit Catboost models, and exhibit results.
If not already made, fit elastic net models, and exhibit results.
Generate factor tables for attaching to experience data.
11 About the Society of Actuaries Research Institute
Serving as the research arm of the Society of Actuaries (SOA), the SOA Research Institute provides objective, data-driven research bringing together tried and true practices and future-focused approaches to address societal challenges and your business needs. The Institute provides trusted knowledge, extensive experience and new technologies to help effectively identify, predict and manage risks.
Representing the thousands of actuaries who help conduct critical research, the SOA Research Institute provides clarity and solutions on risks and societal challenges. The Institute connects actuaries, academics, employers, the insurance industry, regulators, research partners, foundations and research institutions, sponsors and non-governmental organizations, building an effective network which provides support, knowledge and expertise regarding the management of risk to benefit the industry and the public.
Managed by experienced actuaries and research experts from a broad range of industries, the SOA Research Institute creates, funds, develops and distributes research to elevate actuaries as leaders in measuring and managing risk. These efforts include studies, essay collections, webcasts, research papers, survey reports, and original research on topics impacting society.
Harnessing its peer-reviewed research, leading-edge technologies, new data tools and innovative practices, the Institute seeks to understand the underlying causes of risk and the possible outcomes. The Institute develops objective research spanning a variety of topics with its strategic research programs: aging and retirement; actuarial innovation and technology; mortality and longevity; diversity, equity and inclusion; health care cost trends; and catastrophe and climate risk. The Institute has a large volume of topical research available, including an expanding collection of international and market-specific research, experience studies, models and timely research.
Society of Actuaries Research Institute
8770 W Bryn Mawr Ave, Suite 1000
Chicago, IL 60631
www.SOA.org
12 Session Information
Information on the environment and package versions used for this analysis.
Code
sessionInfo()R version 4.3.3 (2024-02-29)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 22.04.4 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so; LAPACK version 3.10.0
locale:
[1] C
time zone: Etc/UTC
tzcode source: system (glibc)
attached base packages:
[1] parallel stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] arrow_15.0.1 ggridges_0.5.6 MatrixModels_0.5-3 ftExtra_0.6.2
[5] flextable_0.9.5 openxlsx_4.2.5.2 glmnet_4.1-8 Matrix_1.6-3
[9] doParallel_1.0.17 iterators_1.0.14 foreach_1.5.2 patchwork_1.2.0
[13] shapviz_0.9.3 dtplyr_1.3.1 lubridate_1.9.3 forcats_1.0.0
[17] stringr_1.5.1 dplyr_1.1.4 purrr_1.0.2 readr_2.1.5
[21] tidyr_1.3.1 tibble_3.2.1 ggplot2_3.5.0 tidyverse_2.0.0
[25] data.table_1.15.2 catboost_1.2.2
loaded via a namespace (and not attached):
[1] tidyselect_1.2.1 viridisLite_0.4.2 farver_2.1.1
[4] fastmap_1.1.1 fontquiver_0.2.1 promises_1.2.1
[7] digest_0.6.35 timechange_0.3.0 mime_0.12
[10] lifecycle_1.0.4 gfonts_0.2.0 ellipsis_0.3.2
[13] survival_3.5-7 magrittr_2.0.3 compiler_4.3.3
[16] rlang_1.1.3 tools_4.3.3 utf8_1.2.4
[19] yaml_2.3.8 knitr_1.45 labeling_0.4.3
[22] askpass_1.2.0 htmlwidgets_1.6.4 bit_4.0.5
[25] xgboost_1.7.7.1 curl_5.2.1 xml2_1.3.6
[28] httpcode_0.3.0 withr_3.0.0 grid_4.3.3
[31] fansi_1.0.6 gdtools_0.3.7 xtable_1.8-4
[34] colorspace_2.1-0 scales_1.3.0 crul_1.4.0
[37] cli_3.6.2 rmarkdown_2.26 crayon_1.5.2
[40] ragg_1.3.0 generics_0.1.3 rstudioapi_0.15.0
[43] tzdb_0.4.0 splines_4.3.3 assertthat_0.2.1
[46] vctrs_0.6.5 jsonlite_1.8.8 fontBitstreamVera_0.1.1
[49] hms_1.1.3 bit64_4.0.5 systemfonts_1.0.6
[52] glue_1.7.0 codetools_0.2-19 stringi_1.8.3
[55] shape_1.4.6.1 gtable_0.3.4 later_1.3.2
[58] munsell_0.5.0 pillar_1.9.0 htmltools_0.5.7
[61] openssl_2.1.1 R6_2.5.1 textshaping_0.3.7
[64] evaluate_0.23 shiny_1.8.0 lattice_0.22-5
[67] fontLiberation_0.1.0 httpuv_1.6.14 uuid_1.2-0
[70] Rcpp_1.0.12 zip_2.3.1 nlme_3.1-163
[73] mgcv_1.9-1 officer_0.6.5 xfun_0.42
[76] pkgconfig_2.0.3