Module 27: Markov Chain Monte Carlo Methods for Item Response Theory Models
The purpose of this ITEMS module is to provide an introduction to Markov chain Monte Carlo (MCMC) estimation for item response models. A brief description of Bayesian inference is followed by an overview of the various facets of MCMC algorithms, including discussion of prior specification, sampling procedures, and methods for evaluating chain convergence. Model comparison and fit issues in the context of MCMC are also considered. Finally, an illustration is provided in which a two-parameter logistic (2PL) model is fit to item response data from a university mathematics placement test through MCMC using the WINBUGS 1.4 software. While MCMC procedures are often complex and can be easily misused, it is suggested that they offer an attractive methodology for experimentation with new and potentially complex IRT models, as are frequently needed in real-world applications in educational measurement.
Keywords: Bayesian estimation, goodness-of-fit, item response theory, IRT, Markov chain Monte Carlo, MCMC, model comparison, two-parameter model, 2PL, Winbugs