Exam MAS-II Practice Question 25
Study guide: Exam MAS-II
An actuary models the annual loss ratios of 60 agencies over five years with a linear mixed model that has a random intercept for each agency. She wants to know whether AGENCY_SIZE (three levels: small, medium and large, with small as the reference level) is needed as a fixed effect. Both models below have the same random intercept and residual variance, and each is fitted to the same data by both REML and ML:
| Model | Fixed effects | -2 \times REML log-likelihood |
-2 \times ML log-likelihood |
|---|---|---|---|
| Full | Intercept, YEAR, AGENCY_SIZE | 1,851.3 | 1,842.6 |
| Reduced | Intercept, YEAR | 1,861.1 | 1,847.2 |
Using a likelihood ratio test at the 5% significance level, which conclusion is correct?
- A) Keep AGENCY_SIZE: the REML test statistic, 9.8, exceeds 5.99, the 95th percentile of
\chi^2_2 - B) Keep AGENCY_SIZE: the full model has the smaller
-2 \timeslog-likelihood under both methods - C) Keep AGENCY_SIZE: the ML test statistic, 4.6, exceeds 3.84, the 95th percentile of
\chi^2_1 - D) Drop AGENCY_SIZE: the ML test statistic, 4.6, is below 5.99, the 95th percentile of
\chi^2_2 - E) Keep AGENCY_SIZE: the REML statistic, 9.8, is significant against a 50:50 mixture of
\chi^2_1and\chi^2_2
Answer this question and see the worked solution
Concepts tested
- Variable Selection
- Likelihood Ratio Test
- Restricted Maximum Likelihood
- Maximum Likelihood Estimation
- Fixed Effects
- Linear Mixed Model