The Q -matrix was designed such that there exist at least three items measuring unique attribute or else the row vectors were randomly sampled from { 0 , 1 } K \ 0 . Every simulation condition was implemented with a total of 100 repetitions consisting of unique sets of item and person parameters. Given the parameters generated, Gibbs sampler was implemented to obtain binary item responses. Let x ( t ) 1 , . . . , x ( t ) J denote a set of draws available from the t -th iteration for a simulee. A response in the next iteration, x ( t +1) j , is then drawn from the Bernoulli distribution with the success probability To ensure that the sample observations come from the appropriate stationary distribution, the study collected samples from a chain after 300 burn-ins. The generated response data were then calibrated as presented in Sections 3 and 4, and the resulting item parameters were transformed to the DINA parameters as discussed in Section 2. The accuracy of the estimated item parameters was evaluated via root mean square deviation (RMSD) and biasedness from the true values. The RMSD for the guessing parameter was calculated as the square root of the mean square error E [(ˆ g − g $^{∗}$) $^{2}$], where ˆ g is the estimated value and g ∗ is the generating parameter value. The biasedness was computed as the absolute deviation of ˆ g from g ∗ in order to avoid the cancellation between positive and negative biases. The RMSDs and absolute biases for the slipping parameter were calculated likewise. A similar criterion was used to evaluate the closeness of the design matrix. In addition to the RMSD as a distance measure, the false positive rate (FPR) and correct positive rate (CPR) were considered as follows: 5.2 Evaluation Criteria P ( t +1) j = exp $^{(}$β ⊤ j α + ∑ j $^{′}$̸ = j φ$_{jj}$ ′ x ( t ) j ′ ) 1 + exp $^{(}$β ⊤ j α + ∑ j $^{′}$̸ = j φ$_{jj}$ ′ x ( t ) j ′ $_{)}$. FPR = ∣ $_{∣}${ ( j, j $^{′}$) : j < j $^{′}$, ˆ φ$_{jj}$ ′ = 0 and φ ∗ jj ′ = 0 } ∣ ∣ ∣ $_{∣}${ ( j, j $^{′}$) : j < j $^{′}$, φ ∗ jj ′ = 0 } ∣ ∣ , 16