A straightforward approach to Markov Chain Monte Carlo methods for item response models

Richard J. Patz and Brian W. Junker


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 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 and Junker, 1997b).

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