Relating the One-Parameter Logistic Diagnostic Classification Model to the Rasch Model and One-Parameter Logistic Mixed, Partial, and Probabilistic Membership Diagnostic Classification Models

Author:

Robitzsch Alexander12ORCID

Affiliation:

1. IPN–Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, 24118 Kiel, Germany

2. Centre for International Student Assessment (ZIB), Olshausenstraße 62, 24118 Kiel, Germany

Abstract

Diagnostic classification models (DCMs) are statistical models with discrete latent variables (so-called skills) to analyze multiple binary variables (i.e., items). The one-parameter logistic diagnostic classification model (1PLDCM) is a DCM with one skill and shares desirable measurement properties with the Rasch model. This article shows that the 1PLDCM is indeed a latent class Rasch model. Furthermore, the relationship of the 1PLDCM to extensions of the DCM to mixed, partial, and probabilistic memberships is treated. It is argued that the partial and probabilistic membership models are also equivalent to the Rasch model. The fit of the different models was empirically investigated using six datasets. It turned out for these datasets that the 1PLDCM always had a worse fit than the Rasch model and mixed and partial membership extensions of the DCM.

Publisher

MDPI AG

Subject

Applied Mathematics,General Mathematics

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