The paper further examines the association among the items, especially if the model can explain the odds ratios corresponding to the responses to pairs of items. Finally, in an effort to examine the issue of differential item functioning (DIF), this paper suggests a version of the Mantel-Haenszel statistic (Holland, 1985), which uses "matched groups" based on equivalence classes, as a discrepancy measure with posterior predictive model checking. Limited simulation studies and a real data application examine the effectiveness of the suggested model diagnostics.
