CAS Exam 8 Fall 2019, Question 6
Study guide: Exam 8
An actuary creates a generalized linear model (GLM) to estimate commercial property claim frequency by occupancy class and amount of insurance (AOI) for sprinklered and non-sprinklered risks. Given the following:
- Occupancy class is a categorical variable with four levels: class 1, 2, 3 and 4.
- Sprinklered status is a categorical variable with two levels: sprinklered and non-sprinklered.
- The natural log of AOI, ln(AOI), is a continuous variable.
- The log link function is selected.
- An interaction variable is included as ln(AOI) for sprinklered and zero otherwise.
- The model results are as follows:
| Parameter | Coefficient |
|---|---|
| Intercept | -8.4607 |
| Occupancy class 2 | 0.2714 |
| Occupancy class 3 | 0.3620 |
| Occupancy class 4 | 0.0395 |
| Sprinklered | 0.7228 |
| ln(AOI) | 0.4311 |
| Sprinklered:Yes, ln(AOI) | -0.0960 |
Part a (0.75 points)
Calculate the ratio of the estimated model frequency of a sprinklered property to that of a non-sprinklered property for AOI = 200,000 and occupancy class 2.
Part b (0.75 points)
Calculate the intercept term if AOI is centered at the base level of 200,000.
Part c (0.5 points)
Briefly describe two advantages of centering variables of a GLM at their base levels.
Answer this question and see the worked solution