Characteristics of MML/EAP Parameter Estimates in the Generalized Graded Unfolding Model

Abstract

The generalized graded unfolding model (GGUM) is a very general parametric, unidimensional item response theory model for unfolding either binary or polytomous responses to test items. Roberts, Donoghue, and Laughlin have described a marginal maximum likelihood (MML) approach to estimate item parameters in the GGUM along with an expected a posteriori (EAP) method to estimate person parameters. This article examines the data demands required to produce accurate parameter estimates using these techniques under ideal conditions. It also examines the robustness of parameter estimates under nonideal conditions, in which there are inconsistencies between the prior distribution of person parameters that must be speci.ed when using either the MML or EAP approaches and the true distribution of person parameters. Results from two simulation studies show that accurate item parameter estimates can generally be obtained with approximately 750 to 1,000 respondents. Similarly, responses to approximately 15 to 20, equally spaced, six-category items can yield accurate EAP estimates of person parameters under static testing conditions. The results also suggest that MML item parameter estimates are quite robust to discrepancies between the prior and true distributions of person parameters. EAP parameter estimates are also fairly robust as long as the item response patterns in question are not too extreme. Finally, 20 quadrature points are generally sufficient to integrate over the prior distribution in both the MML and EAP methods when test and sample characteristics are like those simulated. Thus, the MML/EAP approach to parameter estimation in the general graded unfolding model can produce accurate estimates in an ef.cient manner even when there is uncertainty about the true distribution of person parameters.