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<img src='content_image/303673.jpg'>

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. 

## 5.3 LCDM model simulation 

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. 

<img src='content_image/303682.jpg'>

<img src='content_image/303681.jpg'>

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 

