Compare the suitability of ordinal logistic and ordinal probit regression for the political involvement data using the posterior predictive criteria

\[\operatorname{Pr}\left(z_{\text {rep }, i}>z_{i} \mid y\right) .\]

The \(z\) and \(z_{\text {rep }}\) are readily obtained using the likelihood command

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y[i] dcat.aux (theta [1: KM], z[i],1), where KM K-1=3 is one less than the number of categories, and with z[i] ~dnorm (eta[i], 1), for ordinal probit regression with regression term eta[i] excluding an intercept, and z[i] dlogis (eta[i], 1), for ordinal logit regression. Specifically one may obtain a tally of poorly fitted cases, where either Pr(Zrepi > Zily) < 0.1 or Pr(zrepi > Zily) > 0.9.