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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).
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