Exam MAS-I Practice Question 122
Study guide: Exam MAS-I
An actuary fits a gamma GLM with a log link to homeowners claim severity. The predictors are building age (a single linear term), construction type (four levels) and protection class (ten levels). Three marginal model plots are drawn, each overlaying a smooth of the observed severities (the data smooth) and a smooth of the fitted values (the model smooth):
- Against building age: the data smooth falls steeply over the first five years and is nearly flat after that. The model smooth declines gently and steadily across the whole range, so it lies above the data smooth for buildings aged roughly 3 to 12 and below it for the newest buildings.
- Against protection class: the two smooths are indistinguishable.
- Against the linear predictor: the two smooths are close over the whole range.
Determine which of the following statements are true.
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I. The plot against building age indicates that a single linear term misstates how severity changes with building age; a banded or spline term for building age is worth trying.
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II. Dropping protection class from the model would leave the data smooth in the building-age plot unchanged.
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III. Because the smooths agree in the plot against the linear predictor, the model needs no change.
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A) I only
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B) I and II only
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C) I and III only
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D) II and III only
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E) The answer is not given by (A), (B), (C), or (D)
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