CAS Exam MAS-II Fall 2018, Question 12
Study guide: Exam MAS-II
Height measurements were taken on the same 90 individuals for three consecutive years and a Linear Mixed Model is built using Sex and Age to model the Height of each individual.
The following summary statistics are provided from the data:
Analysis Variable: Height
| Sex | Age | Number of Observations | Mean | Standard Deviation | Minimum | Maximum |
|---|---|---|---|---|---|---|
| F | 12 | 45 | 156.89 | 4.32 | 148 | 166 |
| F | 13 | 45 | 158.96 | 4.48 | 148 | 168 |
| F | 14 | 45 | 160.84 | 5.19 | 148 | 173 |
| M | 12 | 45 | 152.58 | 4.97 | 138 | 163 |
| M | 13 | 45 | 159.29 | 7.64 | 144 | 177 |
| M | 14 | 45 | 166.20 | 8.55 | 147 | 181 |
Determine which of the following equations specifies the Linear Mixed Model for a given subject i measured at time t with the greatest number of possible random effects.
- A)
HEIGHT_{ti} = \beta_0 + \beta_1 \times SEX_{ti} + \beta_2 \times AGE_{ti} + \beta_3 \times SEX_{ti} \times AGE_{ti} + u_{0i} + \varepsilon_{ti} - B)
HEIGHT_{ti} = \beta_0 + \beta_1 \times SEX_{ti} + \beta_2 \times AGE_{ti} + \beta_3 \times SEX_{ti} \times AGE_{ti} + u_{0i} + u_{1i} \times SEX_{ti} + \varepsilon_{ti} - C)
HEIGHT_{ti} = \beta_0 + \beta_1 \times SEX_{ti} + \beta_2 \times AGE_{ti} + \beta_3 \times SEX_{ti} \times AGE_{ti} + u_{0i} + u_{2i} \times AGE_{ti} + \varepsilon_{ti} - D)
HEIGHT_{ti} = \beta_0 + \beta_1 \times SEX_{ti} + \beta_2 \times AGE_{ti} + \beta_3 \times SEX_{ti} \times AGE_{ti} + u_{0i} + u_{2i} \times AGE_{ti} + u_{3i} \times SEX_{ti} \times AGE_{ti} + \varepsilon_{ti} - E)
HEIGHT_{ti} = \beta_0 + \beta_1 \times SEX_{ti} + \beta_2 \times AGE_{ti} + \beta_3 \times SEX_{ti} \times AGE_{ti} + u_{0i} + u_{1i} \times SEX_{ti} + u_{2i} \times AGE_{ti} + u_{3i} \times SEX_{ti} \times AGE_{ti} + \varepsilon_{ti}
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