Title: Bayesian estimation of the four-parameter IRT model using Gibbs sampling

Authors: Yanyan Sheng

Addresses: Department of Counseling, Quantitative Methods, and Special Education, Southern Illinois University, Carbondale, IL 62901, USA

Abstract: The four-parameter item response model is theoretically appealing but received little attention in the psychometric literature because of the difficulty in estimation using conventional methods. This study focuses on the fully Bayesian approach and shows that the MCMC procedure for such models is straightforward. However, with an additional item parameter, the four-parameter model is more complicated than conventional unidimensional models in that additional care has to be taken in specifying prior densities for the slope and intercept parameters. Although the four-parameter model can be shown to be more general than the simpler two- and three-parameter models, it performs better and is preferred only when the actual upper asymptote is not one.

Keywords: item response theory; four-parameter IRT model; normal ogive functions; Markov chain Monte Carlo; MCMC; Gibbs sampling; Bayesian estimation; psychometrics.

DOI: 10.1504/IJQRE.2015.071736

International Journal of Quantitative Research in Education, 2015 Vol.2 No.3/4, pp.194 - 212

Received: 06 Nov 2014
Accepted: 19 May 2015
Published online: 16 Sep 2015 *

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