Investigating the Sensitivity of Goodness-of-Fit Indices to Detect Measurement Invariance in a Bifactor Model

Abstract

A Monte Carlo simulation study was conducted to evaluate the sensitivities of the likelihood ratio test and five commonly used delta goodness-of-fit (ΔGOF) indices (i.e., ΔGamma, ΔMcDonald’s, ΔCFI, ΔRMSEA, and ΔSRMR) to detect a lack of metric invariance in a bifactor model. Experimental conditions included factor loading differences, location and number of noninvariant items, and sample size. The results indicated all ΔGOF indices held Type I error to a minimum and overall had adequate power for the study. For detecting the violation of metric invariance, only ΔGamma and ΔCFI, in addition to Δχ2, are recommended to use in the bifactor model with values of −.016 to −.023 and −.003 to −.004, respectively. Moreover, in the variance component analysis, the magnitude of the factor loading differences contributed the most variation to all ΔGOF indices, whereas sample size affected Δχ2 the most.