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

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.