Parameter Estimation and Group Classification with Mixture Item Response Theory Models

• Activity Number: 526
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Holmes Finch*+ and Brian French
• Companies: Ball State University and Washington State University
• Keywords: mixture models ; item response theory ; bayesian modeling ; maximum likelihood ; group classification

Abstract

Mixture item response theory models are increasingly popular in psychometrics for identifying (a) differentially functioning items for various item types and (b) latent groups. The two most popular methods for estimating these models are maximum likelihood (MLE) and Markov Chain Monte Carlo Bayesian techniques (MCMC). Although popular, no systematic investigation has examined these methods in terms of the accuracy of grouping individuals or estimates of item difficulty and discrimination parameters for groups. This simulation study compared MLE with MCMC in terms of parameter estimation accuracy as measured by root mean squared error (RMSE) and grouping accuracy for varying sample sizes, number of latent classes, number of items, and degree of group separation. Results reveal that both methods correctly classified more than 90% of cases, with MCMC being slightly more accurate. RMSE for item difficulty estimation was comparable for the two methods. MLE produced lower RMSE values, indicating more accurate estimates, for item discrimination. The complete paper will discuss these results in detail and offer recommendations for practitioners applying these methods.