CAS Exam MAS-II Fall 2018, Question 15
Study guide: Exam MAS-II
You are given Model 1 for the SCORE of STUDENT_ID i in CLASS_ID j.
| Model | Model Specification |
|---|---|
| 1 | SCORE_{ij} = \beta_0 + \beta_1 \times SEX_{ij} + \beta_2 \times SCORE\_PRE_{ij} + \beta_3 \times METHOD\_R_j + \beta_4 \times METHOD\_S_j + u_j + \varepsilon_{ij} |
The following assumptions apply to Model 1 and the models listed under A – E:
u_j \sim N(0, \sigma_{\text{class}}^2)\varepsilon_{ij} \sim N(0, \sigma^2)- All
u_j, \varepsilon_{ij}are mutually independent
For hierarchical models:
- Level 1 is Student
- Level 2 is Classroom
Determine which of the following four hierarchical models is equivalent to Model 1.
- A) Level 1:
SCORE_{ij} = b_{0j} + \beta_1 \times SEX_{ij} + \beta_2 \times SCORE\_PRE_{ij} + u_j + \varepsilon_{ij}; Level 2:b_{0j} = \beta_0 + \beta_3 \times METHOD\_R_j + \beta_4 \times METHOD\_S_j + u_j - B) Level 1:
SCORE_{ij} = b_{0j} + \beta_1 \times SEX_{ij} + \beta_2 \times SCORE\_PRE_{ij} + \varepsilon_{ij}; Level 2:b_{0j} = \beta_0 + \beta_3 \times METHOD\_R_j + \beta_4 \times METHOD\_S_j + u_j - C) Level 1:
SCORE_{ij} = b_{0j} + \beta_1 \times SEX_{ij} + \beta_2 \times SCORE\_PRE_{ij} + \beta_3 \times METHOD\_R_j + \beta_4 \times METHOD\_S_j + \varepsilon_{ij}; Level 2:b_{0j} = \beta_0 + u_j - D) Level 1:
SCORE_{ij} = b_{0j} + \beta_1 \times SEX_{ij} + \beta_2 \times SCORE\_PRE_{ij} + \beta_3 \times METHOD\_R_j + \beta_4 \times METHOD\_S_j + u_j; Level 2:b_{0j} = \beta_0 + u_j - E) None of (A), (B), (C), or (D) are equivalent to Model 1.
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