Model Selection Indices for Polytomous Items

Abstract

This study examines the utility of four indices for use in model selection with nested and nonnested polytomous item response theory (IRT) models: a cross-validation index and three information-based indices. Four commonly used polytomous IRT models are considered: the graded response model, the generalized partial credit model, the partial credit model, and the rating scale model. In a simulation study, comparisons among the four indices suggest that model selection is dependent to some extent on the particular conditions simulated. Overall, the Bayesian information criterion index appears to be most accurate in selecting the correct polytomous IRT model. Results are presented from analysis of a real data set to illustrate the use of the four indices for selecting an appropriate model.