Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses

Publication Date

December, 1997

Publication Type

Tech Report

Author(s)

Richard J. Patz and Brian W. Junker

Abstract

Patz and Junker (1997) describe a general Markov chain Monte Carlo (MCMC) strategy, based on Metropolis-Hastings sampling, for Bayesian inference in complex item response theory (IRT) settings. They demonstrate the basic methodology using the two-parameter logistic (2PL) model. In this paper we extend their basic MCMC methodology to address issues such as non-response, designed missingness, multiple raters, guessing behavior and partial credit (polytomous) test items. We apply the basic MCMC methodology to two examples from the National Assessment of Educational Progress 1992 Trial State Assessment in Reading: (a) a multiple item format (2PL, 3PL and generalized partial credit) subtest with missing response data; and (b) a sequence of rated, dichotomous short-response items, using a new IRT model called the generalized linear logistic test model (GLLTM).