Markov Chain Monte Carlo Estimation of Item Parameters for the Generalized Graded Unfolding Model

Abstract

The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response options, and sample size were manipulated. Results indicate that the two methods are comparable in terms of item parameter estimation accuracy. Although the MML estimates exhibit slightly smaller bias than MCMC estimates, they also show greater variability, which results in larger root mean squared errors. Of the two methods, only MCMC provides reasonable standard error estimates for all items.