Properties and performance of the one-parameter log-linear cognitive diagnosis model

Abstract

Diagnostic classification models (DCMs) are psychometric models that yield probabilistic classifications of respondents according to a set of discrete latent variables. The current study examines the recently introduced one-parameter log-linear cognitive diagnosis model (1-PLCDM), which has increased interpretability compared with general DCMs due to useful measurement properties like sum score sufficiency and invariance properties. We demonstrate its equivalence with the Latent Class/Rasch Model and discuss interpretational consequences. The model is further examined in a DCM framework. We demonstrate the sum score sufficiency property and we derive an expression for the cut score for mastery classification. It is shown by means of a simulation study that the 1-PLCDM is fairly robust to model constraint violations in terms of classification accuracy and reliability. This robustness in combination with useful measurement properties and ease of interpretation can make the model attractive for stakeholders to apply in various assessment settings.