Assess GLM coefficient stability by portfolio-row bootstrap
Source:R/model_performance_bootstrap_coefficients.R
bootstrap_coefficients.RdRefit a GLM on repeated bootstrap samples of the estimation portfolio and retain the coefficient estimates from every successful refit. The resulting distribution describes how sensitive individual model coefficients are to sampling variation in the observed portfolio.
Usage
bootstrap_coefficients(
object,
n_resamples = 500,
seed = NULL,
show_progress = interactive()
)Arguments
- object
A fitted
glmobject. Refined GLMs are accepted when their estimation data can be recovered from the model object.- n_resamples
Positive whole number. Number of bootstrap samples. Default is 500.
- seed
Optional single numeric seed for reproducible resampling.
- show_progress
Logical. If
TRUE, display a text progress bar.
Value
An object of class "bootstrap_coefficients". It contains the
original coefficients, a coefficient matrix with one row per requested
resample, indicators for successful model fits, recorded failure messages,
and the resampling settings. Use summary.bootstrap_coefficients() for a
coefficient-level data frame and as_gt() for a formatted table.
Details
Each resample contains the same number of portfolio rows as the original
estimation data and is drawn with replacement. The function recovers these
data from object; a separate data argument is deliberately not required.
Rows omitted during the original model fit are excluded so the resampling
population remains aligned with the fitted GLM.
Original factor levels, the model formula, offsets and model weights are
retained during refitting. A factor level may nevertheless be absent from a
particular bootstrap sample. Its coefficient can then be non-estimable and
is stored as NA for that replicate.
A failed or non-converged GLM refit does not stop the procedure. The failed
replicate is recorded and the function continues. After resampling, an
informative message reports how many requested refits produced usable model
objects. summary.bootstrap_coefficients() reports the number of finite
estimates separately for each coefficient.
Actuarial interpretation
The bootstrap distribution can identify tariff effects that are sensitive to the particular portfolio sample. Wide intervals, material bootstrap bias or a low number of estimable replicates often indicate sparse levels, correlated model terms or limited claim information. These diagnostics should be considered alongside exposure, claim counts, coefficient interpretation and stability across calendar periods.
The row bootstrap represents sampling variation in the observed estimation portfolio. It does not include future trend, parameter uncertainty caused by model selection, structural changes in portfolio composition or dependence between repeated records for the same policy. Where such dependence is material, a cluster-level bootstrap would require a different resampling design.
Examples
model <- glm(
nclaims ~ age_policyholder + zip + offset(log(exposure)),
family = poisson(),
data = MTPL
)
boot <- bootstrap_coefficients(
model,
n_resamples = 25,
seed = 123,
show_progress = FALSE
)
summary(boot, scale = "link")
#> term estimate bootstrap_mean bias bootstrap_se
#> 1 (Intercept) -1.1636200937 -1.220009055 -0.0563889610 0.249137624
#> 2 age_policyholder -0.0170418702 -0.016712389 0.0003294813 0.001285304
#> 3 zip1 -0.0006505428 0.039395119 0.0400456614 0.232329635
#> 4 zip2 -0.1037738083 -0.067240901 0.0365329070 0.243555770
#> 5 zip3 -0.0456536315 -0.007005003 0.0386486282 0.225874270
#> lower upper n_successful n_requested success_rate
#> 1 -1.68483701 -0.82875913 25 25 1
#> 2 -0.01939017 -0.01443457 25 25 1
#> 3 -0.32506741 0.50862020 25 25 1
#> 4 -0.41445244 0.40491816 25 25 1
#> 5 -0.35596929 0.40830170 25 25 1
summary(boot, scale = "exponentiated")
#> term estimate bootstrap_mean bias bootstrap_se lower
#> 1 (Intercept) 0.3123534 0.3039502 -0.008403155 0.073652441 0.1856046
#> 2 age_policyholder 0.9831025 0.9834273 0.000324747 0.001263773 0.9807967
#> 3 zip1 0.9993497 1.0684033 0.069053585 0.263559137 0.7225523
#> 4 zip2 0.9014292 0.9629808 0.061551629 0.249736638 0.6609599
#> 5 zip3 0.9553728 1.0182805 0.062907708 0.241018199 0.7004985
#> upper n_successful n_requested success_rate
#> 1 0.4365920 25 25 1
#> 2 0.9856691 25 25 1
#> 3 1.6686660 25 25 1
#> 4 1.5047469 25 25 1
#> 5 1.5113859 25 25 1
summary(boot, scale = "relativity")
#> term estimate bootstrap_mean bias bootstrap_se lower
#> 1 (Intercept) 0.3123534 0.3039502 -0.008403155 0.073652441 0.1856046
#> 2 age_policyholder 0.9831025 0.9834273 0.000324747 0.001263773 0.9807967
#> 3 zip1 0.9993497 1.0684033 0.069053585 0.263559137 0.7225523
#> 4 zip2 0.9014292 0.9629808 0.061551629 0.249736638 0.6609599
#> 5 zip3 0.9553728 1.0182805 0.062907708 0.241018199 0.7004985
#> upper n_successful n_requested success_rate
#> 1 0.4365920 25 25 1
#> 2 0.9856691 25 25 1
#> 3 1.6686660 25 25 1
#> 4 1.5047469 25 25 1
#> 5 1.5113859 25 25 1
if (requireNamespace("gt", quietly = TRUE)) {
as_gt(boot, scale = "relativity")
}
Original
Mean
Bias
SE
Lower
Upper
Successful
Requested
Success (%)