A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models
- 1 June 1999
- journal article
- Published by American Educational Research Association (AERA) in Journal of Educational and Behavioral Statistics
- Vol. 24 (2) , 146-178
- https://doi.org/10.3102/10769986024002146
Abstract
This paper demonstrates Markov chain Monte Carlo (MCMC) techniques that are particularly well-suited to complex models with item response theory (IRT) assumptions. MCMC may be thought of as a successor to the standard practice of first calibrating the items using E-M methods and then taking the item parameters to be known and fixed at their calibrated values when proceeding with inference regarding the latent trait, in contrast to this two-stage E-M approach, MCMC methods treat item and subject parameters at the same time; this allows us to incorporate standard errors of item estimates into trait inferences, and vice versa. We develop a MCMC methodology, based on Metropolis-Hastings sampling, that can be routinely implemented to fit novel IRT models, and we compare the algorithmic features of the Metropolis- Hastings approach to other approaches based on Gibbs sampling. For concreteness we illustrate the methodology using the familiar two-parameter logistic (2PL) IRT model; more complex models are treated in a subsequent paper (Patz & Junker, in press).Keywords
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