In Example 3.9 (political involvement), compare predictive accuracy, DIC and LPML between the proportional odds logistic model

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In Example 3.9 (political involvement), compare predictive accuracy, DIC and LPML between the proportional odds logistic model and a model allowing the regression effect to differ by response category,

\[\gamma_{i j}=\operatorname{Pr}\left(y_{i} \leq j\right)=P\left(\theta_{j}-X_{i} \beta_{j}\right), \quad j=1, \ldots, K-1 .\]

Data from Example 3.9

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