Item G and S estimates mse of G and S φ r1 r2 r3 φ r1 r2 r3 1 0.900 0.189 - - 1e-4 0.001 - - 2 0.902 0.194 - - 2e-4 0.001 - - 3 0.904 0.192 - - 2e-4 0.001 - - 4 0.900 - 0.300 - 2e-4 - 0.001 5 0.900 - 0.291 - 2e-4 - 0.001 6 0.902 - 0.294 - 3e-4 - 0.001 7 0.901 - - 0.395 3e-4 - - 0.001 8 0.901 - - 0.398 3e-4 - - 0.001 9 0.901 - - 0.396 3e-4 - - 0.001 10 0.899 0.491 0.710 - 2e-4 0.002 0.003 - 11 0.896 0.500 0.701 - 2e-4 0.002 0.002 - 12 0.896 0.602 - 0.398 3e-4 0.002 - 0.002 13 0.897 0.597 - 0.400 3e-4 0.002 - 0.002 14 0.899 - 0.500 0.494 3e-4 - 0.002 0.002 15 0.896 - 0.498 0.497 3e-4 - 0.002 0.002 Table 8: The mean and mse of the estimated parameters for reduced NC-RUM model based on 100 simulations. We also use the Silhouette method to cluster item responses probabilities for each item j . The proportion of the correctly estimated item’s partial information structure is 88.0%. We also calculate the frequentist properties of parameters of reduced NU-RUM model. The result is listed in Table 8. In our third simulation setting, we consider a three-attribute LCDM model which is defined as where and λ $_{j}$, η$_{j}$ are prespecified parameters. The Q -matrix and parameters are listed in Table 9. We generate date sets containing 2000 observations. The latent class of attribute profile (1 , 0 , 0) has mixture probability π$_{1}$ , (0 , 1 , 0) has 5.3 LCDM model simulation p$_{j,}$ α = exp( λ T j h ( α , q$_{j}$ ) − η ) 1 + exp( λ T j h ( α , q$_{j}$ ) η$_{j}$ ) , λ T j h ( α , q$_{j}$ ) = K ∑ k =1 λ$_{jk}$ ( α$_{k}$q$_{jk}$ ) + K ∑ k =1 ∑ ˜ k>k λ$_{jk}$$_{˜}$ $_{k}$( α$_{k}$α$_{˜}$ $_{k}$q$_{jk}$ q$_{j}$$_{˜}$ $_{k}$) + · · · , 23