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 - X2. This article generalizes their statistic to polytomous unfolding models. Four alternative formulations of S - X2 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 ( G2). All variants of S - X2 exhibited reasonable Type I error rates, but that for G2 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.