A Mixture Rasch Model With a Covariate: A Simulation Study via Bayesian Markov Chain Monte Carlo Estimation

Mixtures of item response theory (IRT) models have been proposed as a technique to explore response patterns in test data related to cognitive strategies, instructional sensitivity, and differential item functioning (DIF). Estimation proves challenging due to difficulties in identification and questions of effect size needed to recover underlying structure. In particular, the impact of covariates for examinees in estimation has not been systematically explored. The goal of this study is to carry out a systematically designed simulation study to investigate the performance of mixture Rasch model (MRM) under Bayesian estimation. Insights and suggestions on model application and model estimation are discussed. The foci of this study are to use a flexible logistic regression structure to include examinees' covariate in MRM, to study Markov chain Monte Carlo (MCMC) estimation behavior in light of effect size, and to provide an effective and applicable method for dealing with chain switching.