Identifiability and Cognitive Diagnosis Models

Abstract

Cognitive Diagnosis Models (CDMs) are popular statistical tools in cognitive diagnosis assessment. CDMs can be viewed as restricted latent class models with constraints introduced by the Q-matrix and assumptions of how skill variables that are assigned to items via the Q-Matrix interact in the item function. As many other latent variable models do, the CDMs often suffer from nonidentifiability. This chapter focuses on the identifiability issue of the CDMs and present conditions to ensure identifiability, which can be directly applied to most of the CDMs.