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Similar to the DINA model, the positive response probability is 

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The DINO model is the dual model of the DINA model. The DINO model is often used in the application of psychiatric assessment, for which the positive response to a diagnostic question (item) could be due to the presence of one disorder (attributes) among several. 

Example 5 (C-RUM model) The GLM-type parametrization with a logistic link function is used for the compensatory reparameterized unified model (C-RUM), that is 

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The corresponding item parameter vector is ( β j k : j = 1 , · · · , J, k = 0 , · · · , K ) . The C-RUM model is a compensatory model and one can recognize (6) as a structure in multidimensional IRT model or in factor analysis. 

## 2.3 Identifiability of model parameters 

We discuss the identifiability for two types of parameters separately: 1. item parameters and the attribute distribution, 2. item partial information and the Q -matrix. Let θ denote the vector of all item parameters and the attribute distribution. Its identifiability is defined as follows. 

Definition 1 The parameter θ is said to be identifiable if, for any θ ′ ̸ = θ , the resulting marginal distributions of the responses Y in (1) are distinct. 

If the parameter θ is identifiable, then, thanks to the entropy inequality [16] and under very mild conditions, the maximum likelihood estimator is consistent. 

The identifiability of the Q -matrix is different from that of the regular item parameters. In what follows, we provide some discussions on the estimation of the Q -matrix for a generic diagnostic clas- sification model. One may view this problem from different perspectives. The most straightforward 

