Approximate Invariance Testing in Diagnostic Classification Models in the Presence of Attribute Hierarchies - A Bayesian Network Approach

Abstract

This paper demonstrates the process of invariance testing in diagnostic classification models in the presence of attribute hierarchies via an extension of the log-linear cognitive diagnosis model (LCDM). This extension allows researchers to test for measurement (item) invariance as well as attribute (structural) invariance simultaneously in a single analysis. The structural model of the LCDM is parameterized as a Bayesian network which allows attribute hierarchies to be modeled and tested for attribute invariance via a series of latent regression models. We illustrate the steps for carrying out the invariance analyses through an in-depth case study with an empirical dataset and provide JAGS code for carrying out the analysis within a Bayesian framework. The analysis revealed that a subset of the items exhibit partial invariance and evidence of full invariance was found at the structural level.

Alfonso J. Martinez

Assistant Professor of Psychometrics and Quantitative Psychology

My research interests include generalized latent variable modeling, Bayesian analysis, and computational statistics.