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Using Data Augmentation and Markov Chain Monte Carlo for the Estimation of Unfolding Response Models

Baruch College, City University of New York

Brian W. Junker

Carnegie Mellon University

Unfolding response models, a class of item response theory (IRT) models that assume a unimodal item response function (IRF), are often used for the measurement of attitudes. Verhelst and Verstralen (1993)and Andrich and Luo (1993) independently developed unfolding response models by relating the observed responses to a more common monotone IRT model using a latent response model (LRM; Maris, 1995). This article generalizes their approach, and suggests a data augmentation scheme for the estimation of any unfolding response model. The article introduces two Markov chain Monte Carlo (MCMC) estimation procedures for the Bayesian estimation of unfolding model parameters; one is a direct implementation of MCMC, and the second utilizes the data augmentation method. We use the estimation procedure to analyze three data sets, one simulated, and two from real attitudinal surveys.

Key Words: data augmentation • latent response model • Markov chain Monte Carlo • unfolding response models

Journal of Educational and Behavioral Statistics, Vol. 28, No. 3, 195-230 (2003)
DOI: 10.3102/10769986028003195


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