content_image/309812.jpg content_image/309809.jpg content_image/309810.jpg
Example 2 (NIDA model) The NIDA model admits the following form 

<img src='content_image/309812.jpg'>

The problem solving involves multiple skills indicated by the Q -matrix. For each skill, the student has a certain probability of implementing it: 1 − s$_{j}$ for mastery and g$_{j}$ for non-mastery. The problem is solved correctly if all required skills have been implemented correctly by the student, which leads to the above positive response probability. 

The following reduced NC-RUM model is also a conjunctive model, and it generalizes the DINA and the NIDA models by allowing the item parameters to vary among attributes. 

Example 3 (Reduced NC-RUM model) Under the reduced noncompensatory reparameterized unified model (NC-RUM), we have 

<img src='content_image/309809.jpg'>

where φ$_{j}$ is the correct response probability for subjects who possess all required attributes and r$_{j,k}$ , 0 < r$_{j,k}$ < 1 , is the penalty parameter for not possessing the k th attribute. The corresponding item parameters are ( φ$_{j}$, r$_{j,k}$ : j = 1 , · · · , J, k = 1 , · · · , K ) . 

In contrast to the DINA, NIDA, and Reduced NC-RUM models, the following DINO and C- RUM models assume compensatory (non-conjunctive) relationship among attributes, that is, one only needs to possess one of the required attributes to be capable of providing a positive response. 

Example 4 (DINO model) The ideal response of the DINO model is given by 

<img src='content_image/309810.jpg'>

