CAS Exam MAS-II Fall 2019, Question 20
Study guide: Exam MAS-II
Three hierarchal Bayesian regression models, Model I, Model II, and Model III, are fit to the same dataset. The dataset contains information that relates whether or not an insurance policy sale was completed and includes four potential covariates:
- region, i, of the sales office where
i \in \{1, 2, \ldots, 7\} - The type of product, j, sold where
j \in \{1, 2, \ldots, 6\} - The experience level of the insurance sales representative
- Whether the sale attempt was made as part of a bundle of other products or made in isolation
All three models' fits include experience and bundle as covariates. Model II also includes region and Model III also includes both region and product.
Model III is specified as follows:
\begin{align*}
y_i &\sim \text{Bernoulli}(p_i) \\
\text{logit}(p_i) &= b + b_{region[i]} + b_{product[j]} + (b_1 + b_2 \ast x_{bundle}) \ast x_{experience} \\
b_{region} &\sim \text{Normal}(0,\ \sigma_{region}) \\
b_{product} &\sim \text{Normal}(0,\ \sigma_{product}) \\
b &\sim \text{Normal}(0, 10) \\
b_1 &\sim \text{Normal}(0, 10) \\
b_2 &\sim \text{Normal}(0, 10) \\
\sigma_{region} &\sim \text{HalfCauchy}(0, 1) \\
\sigma_{product} &\sim \text{HalfCauchy}(0, 1)
\end{align*}You are given the following comparison between Model I and Model II.
| Model | WAIC | pWAIC | dWAIC | Weight | SE | dSE |
|---|---|---|---|---|---|---|
| Model I | 682.4 | 2.9 | 151.2 | 0.0 | 9.45 | 18.59 |
| Model II | 531.2 | 8.1 | 0.0 | 1.0 | 19.43 | NA |
You are also provided the posterior means and 90% Bayesian credible intervals for the parameters in Model III in the graphic below.
Determine the most likely value of pWAIC for Model III.
- A) 5.0
- B) 8.0
- C) 11.0
- D) 14.0
- E) 17.0
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