Note . The items from 1 to 12 correspond to the P scale; those from 12 to 24 belong to the E scale; and the rest is associated with the N scale. The color of the heat map shows intensity of an item relation in absolute value. In Figure 2 relative locations of the observed log-likelihood values are indicated in histograms of the empirical distributions under each GDCM and DCM. The results suggest that the GDCM fit the given data fairly well whereas the DCM tended to suffer from lack of model fit due conceivably to local item dependence. Specifically, the (unnormalized) log-likelihood observed under the GDCM was 8605.41, corresponding to a p-value 0.792 in the empirical distribution. The DCM displayed the log-likelihood 4169.73 with a p-value 0.012. Recall that the main difference between the two models is the presence of a Markov network, which is designed to account for local item dependence. The substantial improvement in the model fit implies that some of the questionnaire items may interact with each other beyond the latent variable. After including the Markov network, however, such item dependency seemed to be adequately taken into account while the psychometric model remained the same. To provide a graphical representation of the item interactions, a heat map is plotted and pre- sented in Figure 3. The heat map portrays pairwise associations of the items by indicating the 6.3 Results Figure 3: Heat Map of Estimated Design Matrix 23