A comparison of mixed and partial membership diagnostic classification models with multidimensional item response models

Diagnostic classification models (DCM) are latent structure models with discrete multivariate latent variables. Recently, extensions of DCMs to mixed membership have been proposed. In this article, ordinary DCMs, mixed and partial membership models, and multidimensional item response theory (IRT) models are compared through analytical derivations, three example datasets, and a simulation study. It is concluded that partial membership DCMs are similar, if not structurally equivalent, to sufficiently complex multidimensional IRT models.