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

Richard J. Patz and Brian W. Junker

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 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).

Here is the full postscript text for this technical report. It is 6356097 bytes long.