Free CAS MAS-I (Modern Actuarial Statistics I) Extended Linear Models Practice Questions
Extended linear models on CAS Exam MAS-I cover generalized linear models (GLMs), link functions (log, logit, identity), model selection criteria, residual diagnostics, and applied regression for insurance ratemaking and classification (CAS).
Sample Questions
Question 1
Easy
Which of the following statements is TRUE regarding the use of an offset variable in a generalized linear model?
Solution
C is correct. An offset is a known quantity that enters the linear predictor with a coefficient fixed at 1 (rather than being estimated from the data). For a Poisson GLM with log link, the linear predictor is , so the predicted count scales proportionally with exposure. This is the standard mechanism for handling unequal time-at-risk or other normalizing quantities in count and severity models.
Question 2
Medium
A Poisson GLM with a log link was fitted to model auto insurance claim counts. The deviance residual plot is shown below. Based on this plot, which issue is most clearly indicated?
Solution
Choice B is correct.
The residual plot shows a clear funnel (megaphone) pattern: residuals near fitted value 2 are tightly clustered within , but by fitted value 10 they spread to . This increasing spread is the hallmark of heteroscedasticity — the variance of the response is not constant but grows with the mean. For a Poisson GLM, this suggests overdispersion (the actual variance exceeds what the Poisson model assumes). A quasi-Poisson or negative binomial model would be more appropriate.
Question 3
Hard
Determine which one of the following statements about Principal Component Regression (PCR) is FALSE.
Solution
C is correct.
Let us evaluate each statement:
A: TRUE. Standardizing predictors before PCA is recommended because PCA is sensitive to the scale of variables.
D: FALSE. PCR does NOT perform feature selection in the traditional sense. It selects principal components (linear combinations of all original features), but it does not select or exclude individual features. All original variables contribute to each principal component. Feature selection methods like LASSO actually zero out coefficients.
C: TRUE. This is a known limitation/assumption of PCR -- it assumes that the directions of maximum variance in the predictors are the directions most associated with the response.
(B): TRUE. PCR can reduce overfitting by using fewer principal components than original features, effectively reducing dimensionality.
E: TRUE. By definition, the first principal component is the direction of maximum variance in the data.
Let us evaluate each statement:
A: TRUE. Standardizing predictors before PCA is recommended because PCA is sensitive to the scale of variables.
D: FALSE. PCR does NOT perform feature selection in the traditional sense. It selects principal components (linear combinations of all original features), but it does not select or exclude individual features. All original variables contribute to each principal component. Feature selection methods like LASSO actually zero out coefficients.
C: TRUE. This is a known limitation/assumption of PCR -- it assumes that the directions of maximum variance in the predictors are the directions most associated with the response.
(B): TRUE. PCR can reduce overfitting by using fewer principal components than original features, effectively reducing dimensionality.
E: TRUE. By definition, the first principal component is the direction of maximum variance in the data.