Exam MAS-I Practice Question 94

Study guide: Exam MAS-I

A commercial auto insurer will specify a GLM for claim frequency. The modelling file has one record per vehicle per accident year, 2021 to 2025, with these fields:

Field	Description
`n_claims`	number of claims on the vehicle in the year
`veh_years`	earned vehicle-years, between 0.05 and 1.00
`acc_year`	accident year, 2021–2025
`weight_class`	light, medium, heavy, extra-heavy
`territory`	nine rating regions, stored as the integers 1–9
`drv_exp`	the driver's years of commercial driving experience

The rating plan will vary by weight class, territory and driver experience. It will not vary by accident year, but frequency rose over 2021–2025 while the book's mix shifted toward heavier vehicles. Write $v$ for a record's earned vehicle-years. Specify the model one decision at a time.

Part a (1 point)

Choose the response distribution and link.

A) Normal, identity link
B) Poisson, log link
C) Gamma, log link
D) Binomial, logit link
E) Tweedie with power $p$ between 1 and 2, log link

Part b (1 point)

Choose how earned vehicle-years enter the model.

A) As a predictor, $\ln v$ , whose coefficient is estimated
B) As an offset equal to $v$ itself
C) Not at all, since every record is a single vehicle
D) As an offset equal to $\ln v$
E) As the response, replacing the claim count

Part c (1 point)

Choose how accident year enters the model.

A) As a categorical predictor whose effect is estimated, then left out when the rating relativities are extracted
B) Not at all, because accident year will not be a rating variable
C) As an offset, with its coefficient fixed at 1
D) As a categorical predictor whose relativities are multiplied into the rates
E) As a prior weight, so that recent years count for more

Part d (1 point)

Choose how territory enters the model.

A) As a single numeric predictor taking the values 1–9
B) As an offset of the territory code
C) As nine indicator columns plus the intercept
D) As the logarithm of the territory code
E) As eight indicator columns, against a base territory

Part e (1 point)

Write the linear predictor of the model you have specified, naming each term, and state how weight class and driver experience should enter it.

Answer this question and see the worked solution