Parameter estimation with mixture item response theory models: A Monte Carlo comparison of maximum likelihood and Bayesian methods

Abstract

The Mixture Item Response Theory (MixIRT) can be used to identify latent classes of examinees in data as well as to estimate item parameters such as difficulty and discrimination for each of the groups. Parameter estimation via maximum likelihood (MLE) and Bayesian estimation based on the Markov Chain Monte Carlo (MCMC) are compared for classification accuracy and parameter estimation bias for difficulty and discrimination. Standard error magnitude and coverage rates were compared across number of items, number of latent groups, group size ratio, total sample size and underlying item response model. Results show that MCMC provides more accurate group membership recovery across conditions and more accurate parameter estimates for smaller samples and fewer items. MLE produces narrower confidence intervals than MCMC and more accurate parameter estimates for larger samples and more items. Implications of these results for research and practice are discussed. © 2012 JMASM, Inc.