Bayesian Estimation of Graded Response Multilevel Models Using Gibbs Sampling: Formulation and Illustration

Abstract

The present study presents the formulation of graded response models in the multilevel framework (as nonlinear mixed models) and demonstrates their use in estimating item parameters and investigating the group-level effects for specific covariates using Bayesian estimation. The graded response multilevel model (GRMM) combines the formulation of graded response models with the discrimination parameter fixed at one for all items by Tuerlinckx and Wang and of two parameter models by Rijmen and Briggs to offer graded response models with item-specific discrimination parameters. Apart from the contribution to the body of knowledge by formulating GRMMs, the significance of the present study includes providing a meeting point between psychometrics and statistics, overcoming the Neyman—Scott problem by using Bayesian estimation, estimation of abilities of persons with extreme scores, and demonstration of general purpose software for estimating item response theory parameters. Data from the emotional functioning scale on 11,158 healthy and chronically ill children and adolescents were used from the PedsQL 4.0 Generic Core Scales database to illustrate the model. Estimates for the item parameters from WINBUGS using Bayesian priors and Multilog were compared for the GRMM and the ordinary graded response models, respectively.