CAS Exam MAS-II Spring 2019, Question 24
Study guide: Exam MAS-II
You are building a model to understand student test scores. Your model is as follows:
y_{ij} = \beta_0 + x_{ij}\beta_1 + \tau_i + \epsilon_{ij}\begin{align*}
\beta_0 &\sim \text{Normal}(\mu, \sigma_0^2) \\
\beta_1 &\sim \text{Normal}(0, \sigma_1^2) \\
\tau_i &\sim \text{Normal}(0, \sigma_2^2) \\
\mu &\sim \text{Normal}(0, \sigma_3^2) \\
\epsilon_{ij} &\sim \text{Normal}(0, \sigma_4^2)
\end{align*}where student j in classroom i has a final exam score of y_{ij} and a midterm score of x_{ij}.
You feel that the classroom data is not dependable and, therefore, you want to shrink the classroom-specific effects toward the overall mean.
Determine how you would adjust the hyperparameters for this model.
- A) Reduce the value of
\sigma_0^2 - B) Reduce the value of
\sigma_1^2 - C) Reduce the value of
\sigma_2^2 - D) Reduce the value of
\sigma_3^2 - E) Reduce the value of
\sigma_4^2
Answer this question and see the worked solution