Bayesian Q Matrix Estimation of Saturated Diagnostic Classification Models Using NIMBLE

Abstract

Diagnostic classification models (DCMs) constitute a subset of restricted latent class models in which latent classes are constrained by an expert-specified $\mathit{Q}$ matrix reflecting students’ mastery of the psychological attributes associated with items. In instances where uncertainty exists in the attribute elements of items specified by the $\mathit{Q}$ matrix, the accurate estimation of the $\mathit{Q}$ matrix is imperative for ensuring accurate person and item estimates. This paper investigates the application of the open-source NIMBLE (Numerical Inference for Hierarchical Models Using Bayesian and Likelihood Estimation) package in R software to infer the $\mathit{Q}$ matrix while incorporating model constraints. Snippets of NIMBLE code illustrate the $\mathit{Q}$ matrix estimation in DCMs, followed by parameter-recovery simulation studies and empirical data analyses. The research findings show a high degree of parameter recovery in simulation studies and provide insightful analyses of empirical data. This paper demonstrates that researchers can now effectively engage with DCMs using NIMBLE, particularly in scenarios where the $\mathit{Q}$ matrix is uncertain. This eliminates the need to laboriously develop and code intricate parameter estimation algorithms, thus enabling researchers to confidently prioritize model development and statistical analysis.