Actuarial›Exam PA›Generalized Linear Models
Exam PA topic · 30–40% of exam

Generalized Linear Models

Building, evaluating, and interpreting GLMs in R for common actuarial applications.

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Per-objective worked-example outlines

For each learning objective on Generalized Linear Models, here is the approach an exam item would test — the setup, the ordering of your reasoning, and the formula or identity you need to bring to the page. Approaches, not full solutions, by design. Verify against the current soa.org syllabus before your sitting.

Fit GLMs with appropriate distributions and link functions

Setup

You have a response variable and several predictors and must fit one or more GLMs in R using glm().

Approach

Choose the response family (Poisson for counts, binomial for binary, Gamma for positive skewed amounts) and the link function (log for log-linear effects, logit for log-odds, identity for additive). Fit with glm(y ~ x1 + x2, family = ...). Iterate by adding interactions and basis splines suggested by EDA. Watch convergence warnings — they often signal separation or numerical issues.

Key identity

glm(formula, family = family(link = link), data = df).

Evaluate model fit using deviance, AIC, and residual diagnostics

Setup

You have several candidate GLMs and must select the best.

Approach

Compare nested models with the deviance (likelihood ratio) test: 2(ll_full - ll_reduced) ~ chi-square(df_diff). For non-nested models, compare AIC; lower is better. Plot Pearson and deviance residuals against fitted values and against predictors. Check for influential points using Cook's distance.

Key identity

AIC = 2k - 2 ln L; deviance LRT: 2 Δll ~ χ²(Δdf).

Interpret coefficients and generate predictions on new data

Setup

A fitted GLM has coefficients on the link scale and you must interpret them and predict on a holdout set.

Approach

On the link scale, β_j is the change in g(E[Y]) per unit change in x_j. For log link, exp(β_j) is the multiplicative effect on E[Y]. For logit, exp(β_j) is the odds ratio. Use predict(model, newdata, type = "response") to get predictions on the original scale. For categorical predictors, interpret each level vs the reference level.

Key identity

predict(model, newdata, type = "response") for original-scale predictions.

Common exam traps on Generalized Linear Models

Recurring patterns where candidates lose points on Generalized Linear Models-style items. Each entry pairs the trap with the fix.

Trap

Interpreting log-link coefficients as additive effects on the response.

Fix

A log-link coefficient is additive on the log scale, multiplicative on the response scale (exp(β)).

Trap

Using type = "link" when the question asks for predicted probabilities.

Fix

Use type = "response" to get the prediction on the original scale.

Trap

Comparing AIC across models fit on different data sets.

Fix

AIC requires identical observations; refit on the same data when comparing.

Trap

Ignoring offset terms in count regression.

Fix

When exposure varies (e.g., policy years), include log(exposure) as an offset in Poisson regression.

Where to find Generalized Linear Models in popular manuals

Pointers to where each major vendor covers this topic, so you can grab the right chapter without combing the full manual. We do not reproduce vendor content — just the location. Chapter and lesson numbers shift between editions; use these as a guide, not as a citation.

ACTEX

GLM chapter in the PA manual with R code examples

Coaching Actuaries

Learn modules on GLMs in R; Adapt category "GLMs / PA"

The Infinite Actuary

PA GLM video block including model selection

7-day Generalized Linear Models micro plan

A focused 7-day sub-schedule for Generalized Linear Models specifically, at roughly 1.5–2.5 hours per day. Drop it inside your full Exam PA plan as a single coverage module.

Day 1

Read the GLM chapter; practice fitting Poisson, binomial, and Gamma GLMs on a sample dataset in R.

Day 2

Drill coefficient interpretation under each link function on 10 example outputs.

Day 3

Model selection — fit 5-6 candidate GLMs on a sample dataset and compare with AIC and deviance LRT.

Day 4

Residual diagnostics in R — plot Pearson and deviance residuals; identify problematic points.

Day 5

Practice writing the GLM section of a full mock report; include interpretation and validation.

Day 6

Mixed practice — run an end-to-end GLM model on a fresh dataset against a 90-minute timer.

Day 7

Re-do flagged areas and refine your GLM report template.

How exclam.ai helps you master Generalized Linear Models

Flashcards from your manual

Upload your ACTEX Exam PA digital edition, scanned ASM pages, TIA handouts, or your own notes. exclam.ai extracts the Generalized Linear Models sections and generates flashcards automatically, tuned to the exam traps above.

Worked-example drilling

Each per-objective approach above maps to a quiz template. exclam.ai re-surfaces missed items until you can recall both the setup and the key identity from cold.

FSRS spaced repetition

Because Generalized Linear Models is 30–40% of your exam, losing it during review costs you. FSRS brings it back at the optimal moment.

Generalized Linear Models in the Exam PA context

SOA Exam PA has 4 topic areas. Generalized Linear Models is weighted at approximately 30–40% of the exam, here is where it sits relative to the other topics.

Topic areaWeight
Problem Framing and Data Preparation15–25%
→ Generalized Linear Models30–40%
Decision Trees and Ensemble Methods20–30%
Model Validation and Business Communication15–25%

Other Exam PA topics

Problem Framing and Data Preparation

15–25%

Translating a business problem into a predictive modeling question, exploratory data analysis, and feature engineering.

Study this topic

Decision Trees and Ensemble Methods

20–30%

Fitting and tuning decision trees, random forests, and gradient boosting models in R.

Study this topic

Model Validation and Business Communication

15–25%

Cross-validation, test set performance, sensitivity analysis, and communicating results to non-technical stakeholders.

Study this topic

Start practicing Generalized Linear Models today

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