12.4 Repeat the latent trait analysis in Example 12.5 but apply the posterior predictive check procedure proposed by Ansari and Jedidi (2000). This involves 45 correlations based on odds ratios ω = ad/(bc) where a and d are the diagonal frequencies and b and c are the off diagonal frequencies in the (all 1077 subjects) contingency table for each pair

( j, k) of the 10 binary items. A correlation coefficient based on the C-type distribution of Mardia (1967) is approximated by T ( j, k) = (ω0.74 − 1)/(ω0.74 + 1). The T statistics are compared between observed and replicated data. What implications are there from these pairwise comparisons regarding the conditional independence assumptions of the model?