CAS Exam 8 Fall 2018, Question 7
Study guide: Exam 8
An actuary is planning to add a credit-based insurance score to a model that estimates the probability of a policy having a claim. The actuary has decided to offset all of the current model variables before fitting the new variable.
Given the following:
- The current model (without the insurance score variable) is a logit-link binomial GLM (logistic regression).
- The logit link function is defined as
g(\mu) = \ln\left(\frac{\mu}{1-\mu}\right) - The insurance score is a continuous variable having a value between 1 and 100.
- The current fitted values and insurance score for three policies as well as regression results from the fit of the insurance score variable are given below:
| Policy Number | Fitted Probability Without Insurance Score | Insurance Score |
|---|---|---|
| 1 | 1.3% | 78 |
| 2 | 20.3% | 92 |
| 3 | 2.5% | 35 |
| Variable | Parameter Estimate |
|---|---|
| Intercept | 1.250 |
| Insurance Score | -0.020 |
Part a (0.5 points)
Calculate the offset term to be used in the regression for each of the three policies above.
Part b (0.75 points)
Calculate the revised fitted probability of having a claim for each of the three policies above.
Part c (0.5 points)
Identify the range of:
i. the logit function
ii. the logistic function
Part d (0.25 points)
Briefly explain why logistic regression is often used to model probabilities.
Part e (0.5 points)
Identify and briefly describe one situation in which the use of an offset is preferable to (re)fitting all variables.
Answer this question and see the worked solution