Markov Network for Modeling Local Item Dependence in Cognitively Diagnostic Classification Models

TL;DR

This paper introduces a novel exploratory graphical modeling approach using Markov networks integrated into DCMs to detect and model local item dependencies without prior knowledge of item structure, improving parameter estimation.

Contribution

It develops a new framework combining Markov networks with DCMs for exploratory detection of local item dependence without prior specification.

Findings

Accurately recovers generating parameters in simulations

Produces more reliable item parameter estimates under local dependence

Effectively models local dependence in real assessment data

Abstract

The study presents an exploratory graphical modeling approach for evaluating local item dependency within cognitively diagnostic classification models (DCMs). Current approaches to modeling local dependence require known item structure and have limited utility when such information is not available. In this study, we propose an exploratory approach to modeling local dependence so that items' own interactions can be revealed without dependency specification. The new framework is developed by integrating a Markov network into a generalized DCM. The framework unveils item interactions while performing regular cognitive diagnosis within a unified scheme. The inference on the model parameters is made on the regularized pseudo-likelihood and is implemented by an EM algorithm. Numerical experimentation from Monte Carlo simulation suggests that the proposed framework adequately recovers generating parameters and yields reliable standard error estimates. Compared with the regular DCM, the new model produced more accurate item parameter estimates as items exhibit local dependence. The study demonstrates application of the model using two real assessment data and discusses practical benefits of modeling local dependence.