Exam MAS-I Practice Question 154
Study guide: Exam MAS-I
Commercial auto policies are cross-classified by territory T (3 levels), vehicle use U (2 levels: service, delivery) and whether a claim was made in the year Y (2 levels), giving 12 cells. Poisson log-linear models are fitted with these results:
| Model | Deviance | Degrees of freedom |
|---|---|---|
T + U + Y |
48.2 | 7 |
T + UY |
22.8 | 6 |
TU + Y |
31.5 | 5 |
TU + UY |
6.1 | 4 |
TU + TY |
25.9 | 3 |
TU + TY + UY |
2.3 | 2 |
TUY (saturated) |
0.0 | 0 |
The 95th percentiles of the chi-squared distribution are 3.841 (1 df), 5.991 (2 df), 7.815 (3 df), 9.488 (4 df), 11.070 (5 df), 12.592 (6 df) and 14.067 (7 df).
The actuary's criteria are: a model must fit (its deviance is not significant at the 5% level), and a term is kept only if dropping it raises the deviance significantly at the 5% level.
Which model and interpretation should the actuary choose?
- A)
TU + Y, because adding theTUterm to complete independence lowers the deviance significantly - B)
TU + UY, under which territory and claim occurrence are independent once vehicle use is known - C)
TU + UY, under which claim occurrence is independent of both territory and vehicle use - D)
TU + TY + UY, since it has the lowest deviance of the unsaturated models - E)
TUY, since its deviance of zero means it reproduces every cell count exactly
Answer this question and see the worked solution
Concepts tested
- Log-Linear Model
- Deviance
- Likelihood Ratio Test
- Chi-Squared Distribution
- Interaction
- Model Selection