A comparison of pseudo-Bayesian and joint maximum likelihood procedures for estimating item parameters in the three-parameter IRT model

Abstract

This study compared pseudo-Bayesian and joint maximum likelihood procedures for estimating item parameters for the three-parameter logistic model in item response theory. Two programs, ASCAL and LOGIST, which employ the two methods were compared using data simulated from a three-parameter model. Item responses were generated for sample sizes of 2,000 and 500, test lengths of 35 and 15, and examinees of high, medium, and low ability. The results showed that the item characteristic curves estimated by the two methods were more similar to each other than to the generated item characteristic curves. Pseudo-Bayesian estimation consistently produced more accurate item parameter estimates for the smaller sample size, whereas joint maximum likelihood was more accurate as test length was reduced. Index terms: ASCAL, item response theory, joint maximum likelihood estimation, LOGIST, parameter estimation, pseudo-Bayesian estimation, three-parameter model.