Type I Error Rates for Generalized Graded Unfolding Model Fit Indices

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Type I error rates were examined for several fit indices available in GGUM2000: extensions of Infit, Outfit, Andrich’s χ2, and the log-likelihood ratio χ2. Infit and Outfit had Type I error rates much lower than nominal α. Andrich’s χ2 had Type I error rates much higher than nominal α, particularly for shorter tests or larger sample sizes. The log-likelihood χ2 had Type I error rates near or below nominal α for small samples or longer tests but had inflated error rates with large samples and shorter tests. For conditions in which the log-likelihood ratio χ2 did not perform well, alternative fit indices or modifications to these procedures should be considered in future studies.