Free SOA Exam PA (Predictive Analytics) Generalized Linear Models Practice Questions
Generalized linear models are the largest topic on SOA Exam PA. Tasks test distribution and link function selection, coefficient interpretation, offsets and weights, regularization, and model validation and comparison, argued in writing from provided R output.
Sample Questions
Question 1
Easy
In a regularized GLM, what happens to the fit as the penalty is set to a very large value?
Solution
C is correct. Increasing strengthens the penalty, driving coefficients toward zero so the model relies mostly on the intercept. This produces an underfit model with high bias and low variance, the opposite extreme from no penalty.
Question 2
Medium
By default glmnet leaves the intercept term unpenalized. Why is this the standard choice?
Solution
C is correct. The intercept captures the baseline level of the response; shrinking it toward zero would tie the fit to the arbitrary origin/scale of the response variable, which is undesirable. Leaving it unpenalized ensures the penalty acts only on the predictor effects, so predictions are not distorted by the response's location.
Question 3
Hard
For grouped binomial data (each row summarizes many trials), which two R model specifications yield IDENTICAL coefficient estimates?
Solution
E is correct. For a binomial GLM, supplying the observed proportion as the response with prior weights equal to the number of trials is mathematically equivalent to supplying cbind(successes, failures). The prior weights encode how many trials each proportion is based on, reproducing the same likelihood and hence the same coefficients.