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the CPRs were reasonably high while the FPRs were well under control. We note that the overall level of the RMSD observed in Table 3 is greater than that of Table 1 because, in contrast to the guessing and slipping parameters whose values are bounded by [0, 1], the value of φ$_{jj}$ ′ is defined on a continuum with no bounds. Table 3 indicates that, despite the wider support, the suggested estimation method can recover the true φ$_{jj}$ ′ values with the distance less than 0.2 units. Also presented in Table 3 are the FPRs calculated as the proportion of edges that were erroneously flagged for conditional dependence. The table shows that the overall false alarm rates remained at an acceptable level, ranging from 2.84% to 5.82% on average. The CPR in Table 3 denotes the proportion of nonzero edges that were correctly identified for a given design matrix. Note that a direct comparison of FPRs or CPRs across the different Φ cases lends little meaning because the number of (non)zero edges varies in each simulated condition. On the whole, it can be concluded that the GDCM served well the purpose of identifying the presence of local item dependence. Applying the cutoff 0.8 (Cohen, 1992), the framework demonstrated moderate recovery when the sample size was 500 and showed excellent recovery as the sample size was greater than 1000. In Table 3 the sample size seemed to be the most influential factor affecting the recovery of Φ . The trends in the results indicate that the larger the sample, the smaller the RMSDs and FPRs, and the greater the CPRs. 

Table 4 presents the average pairwise distance of the estimated π s from the true values. It suggests that the proposed algorithm recovered the underlying prior distributions with minimal errors. Across the simulation conditions, the smallest estimation error was associated with the smaller K , the largest N , and the simplest Φ . This pattern is in line with the expectation that π is 

<img src='content_image/312406.jpg'>

Note . FPR=false positive rate. CPR=correct positive rate. 

