Modified Likelihood-Based Item Fit Statistics for the Generalized Graded Unfolding Model

Abstract

Orlando and Thissen (2000) developed an item fit statistic for binary item response theory (IRT) models known as S - X ². This article generalizes their statistic to polytomous unfolding models. Four alternative formulations of S - X ² are developed for the generalized graded unfolding model (GGUM). The GGUM is a unidimensional IRT model for unfolding polytomous responses. It yields single-peaked, nonmonotonic item characteristic curves that predict a higher item score to the extent that an individual is located close to an item on the underlying latent continuum. A simulation was performed to examine the characteristics of these new item fit indices under the GGUM, as well as a traditional likelihood ratio χ² test (G ²). All variants of S - X ² exhibited reasonable Type I error rates, but that for G ² was more erratic. The new indices exhibited variable power to detect misfit. Two new item fit tests are recommended for use based on simulation results.