On the Identifiability of Q-matrix Based CDM's

Abstract:

There has been growing interest in recent years in using cognitive diagnosis models (CDMs) for diagnostic measurement, i.e., classification according to multiple discrete latent traits. However, many CDMs suffer from issues of identifiability, limiting their application. We begin by describing necessary and sufficient conditions for identifiability in two popular CDM’s. Depending on the area of application and the researcher’s degree of control over the experiment design, fulfilling these conditions may be difficult. Thus, we also propose new methods for parameter estimation and respondent classification for use with non-identifiable models. In addition, our framework allows consistent estimation of the severity of the non-identifiability problem, in terms of the proportion of the population affected by the issue.