Module 27: Markov Chain Monte Carlo Methods for Item Response Theory Models

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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

Jee-Seon Kim

Professor of Department of Educational Psychology, University of Wisconsin, Madison

Jee-Seon Kim is Professor in the Department of Educational Psychology and is also affiliated with the Interdisciplinary Training Program in the Education Sciences and the Center for Health Enhancement Systems Studies at the University of Wisconsin-Madison. Her research focuses on developing and applying statistical models to address practical issues in the behavioral sciences. Her research interests include multilevel modeling, imputation of missing data, longitudinal data analysis, latent variable modeling, and propensity score analysis. She has been a fellow of the Spencer Foundation, consulting editor for Psychological Methods, and book review editor for Psychometrika.

Daniel M. Bolt

Professor of Department of Educational Psychology, University of Wisconsin, Madison

Dr. Bolt joined the department in the spring of 1999, coming from the Laboratory for Educational and Psychological Measurement at the University of Illinois. In addition to his own research, he collaborates on various projects related to the development and statistical analysis of educational and psychological tests. Dr. Bolt teaches courses in test theory, factor analysis, and hierarchical linear modeling.

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Module 27: Estimating Item Response Theory Models Using Markov Chain Monte Carlo Methods
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