6.3 Global identifiability of general CDMs

It should be noted that identifiability is a property of both CDM and the Q-matrix. The following theorem is related to more general models, such as R-RUM, A-CDM and G-DINA model.

Identifiability Conditions #2

For any CDM, the following conditions are sufficient (but not necessary) for global model identification (G. Xu, 2019).

  1. The Q-matrix has the following forms, where \(I_K\) is an identity matrix. \[ Q=\begin{pmatrix} I_K \\ I_K \\ Q' \end{pmatrix} \]
  2. There exist at least one item in \(Q'\) such that students with \(\alpha=\mathbf{e}_k\) have different positive response probability from that of students with \(\alpha=\mathbf{0}\).

Based on the above theorem, we can have the following sufficient conditions:

Identifiability Conditions #3

For any CDM, the following condition is sufficient (but not necessary) for global model identification:

The Q-matrix consists of three identity matrices. \[ Q=\begin{pmatrix} I_K \\ I_K \\ I_K \\ Q' \end{pmatrix} \]

References

Xu, G. (2019). Identifiability and Cognitive Diagnosis Models (M. von Davier & Y.-S. Lee, Eds.; pp. 333–357). Springer International Publishing. http://link.springer.com/10.1007/978-3-030-05584-4_16