Parameter Recovery for the Four-Parameter Item Response Theory Model: A Comparison of Marginal Maximum Likelihood and Markov Chain Monte Carlo Approaches

• In Event: Advances in Item Response Theory Modeling and Application

Abstract

This study assessed the parameter recovery accuracy of MML with EM algorithm and two MCMC methods, Gibbs and HMC, under the four-parameter unidimensional binary item response function. Data were simulated under the fully crossed design with three sample size levels (1000, 2500 and 5000 respondents) and two latent trait distributions (normal and negatively skewed). Results indicated that Gibbs and HMC offered nearly identical outcomes and produced lower total errors than MML across all conditions. Overall, MML was more extensively affected by θ skewness but had more appreciable accuracy improvement in conjunction with sample size increase than MCMC. Guidelines for measurement practitioners regarding estimation method selection, sample size requirement and consideration of the tenability of latent trait normality assumption are provided.

Authors

• Hoan Do, Ohio University

• Gordon P. Brooks, Ohio University