Section 6 : GLM mini case study

Question 1

You are modeling claim severity for a highly skewed distribution.
Which distribution should you use ?

Answer 1

A: Use the Inverse Gaussian distribution.
Why: It handles strong skewness and long tails better than Gamma, which improves predictive accuracy for severe losses.

Question 2

You’re modeling pure premiums with many zero claims and right-skewed positive values.
What should you do?

Answer 2

A: Use the Tweedie distribution.
Why: It accommodates zero-inflation and skewed losses by combining Poisson frequency and Gamma severity in one model.

Question 3

You detect high correlation between two predictors in your GLM.
What should you do?

Answer 3

Remove one of the variables or use PCA (Principal Component Analysis).
Why: Multicollinearity destabilizes coefficient estimates and inflates standard errors, leading to unreliable interpretations.

Question 4

You need to incorporate deductible relativities already estimated from a separate analysis.
What should you do?

Answer 4

Use an offset term in the GLM.
Why: Offsets let you incorporate pre-specified effects (like deductibles) without re-estimating them, maintaining consistency.

Question 5

You want to validate your model with limited data and avoid overfitting.
What should you do?

Answer 5

Use k-fold cross-validation.
Why: It improves robustness by training and testing on multiple partitions, reducing sensitivity to any one split.

Question 6

You want to compare multiple GLMs using the same dataset and distribution.
What should you do?

Answer 6

Compare log-likelihood or scaled deviance.
Why: These metrics are valid when the model assumptions are consistent and help assess goodness of fit.

Question 7

Your GLM includes a continuous predictor with a nonlinear relationship to the target.
What should you do?

Answer 7

Add polynomial terms, bins, or splines.
Why: These transformations improve fit by capturing curvature or thresholds not modeled by a linear term.