CAS Exam MAS-II Spring 2019, Question 15
Study guide: Exam MAS-II
You are fitting a Linear Mixed Model on a clustered dataset and considering the following two models:
Model I
Y_{ij} = \beta_0 + \beta_1 X_{ij}^{(1)} + \beta_2 X_{ij}^{(2)} + \beta_3 X_{ij}^{(3)} + u_j + \varepsilon_{ij}u_j follows a normal distribution with mean 0 and variance \sigma_c^2; \varepsilon_{ij} follows a normal distribution with mean 0 and variance \sigma^2; all \varepsilon_{ij} are independent.
Model II
Y_{ij} = \beta_0 + \beta_1 X_{ij}^{(1)} + \beta_2 X_{ij}^{(2)} + \beta_3 X_{ij}^{(3)} + \varepsilon_{ij}\varepsilon_{ij} follows a normal distribution with mean 0 and variance \sigma^2; all \varepsilon_{ij} are independent.
The fit statistics are as follows:
| Model I | Model II | |
|---|---|---|
| -2 log-likelihood | 401.1 | 489.9 |
You are using the test statistic to choose between Model I and Model II. Determine which of the following statements are true:
- A) Based on referring the test statistic to a chi-squared distribution with 1 degree of freedom, we select Model I at a confidence level of 0.005
- B) Based on referring the test statistic to an average of chi-squared distributions with 0 and 1 degrees of freedom, we select Model I at a confidence level of 0.005
- C) Based on referring the test statistic to a chi-squared distribution with 1 degree of freedom, we select Model II at a confidence level of 0.005
- D) Based on referring the test statistic to an average of chi-squared distributions with 0 and 1 degrees of freedom, we select Model II at a confidence level of 0.005
- E) The correct answer is not given by (A), (B), (C), or (D)
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