Marginal Maximum A Posteriori Item Parameter Estimation for the Generalized Graded Unfolding Model

Abstract

A marginal maximum a posteriori (MMAP) procedure was implemented to estimate item parameters in the generalized graded unfolding model (GGUM). Estimates from the MMAP method were compared with those derived from marginal maximum likelihood (MML) and Markov chain Monte Carlo (MCMC) procedures in a recovery simulation that varied sample size, questionnaire length, and number of item response categories. MMAP item parameter estimates were generally the most accurate and had the smallest standard errors on average. In contrast, the accuracy and variability of MML estimates suffered substantially when the number of item response categories was small and the true item locations were extreme. MMAP estimates were also more computationally efficient than corresponding MCMC estimates. Consequently, the MMAP procedure is recommended for estimation of GGUM item parameters.