Power of Alternative Fit Indices for Multiple Group Longitudinal Tests of Measurement Invariance

Abstract

Measurement invariance testing with confirmatory factor analysis has a long history in social science research, and more recently has increased use and popularity. The current paper begins by reviewing the steps for measurement invariance testing via multiple group confirmatory factor analysis, and synthesizing previous research recommendations for model testing, including the chi-square difference test, and examining change in model fit indices. Previous research on measurement invariance testing has examined change in alternative fit indices such as the CFI, TLI, RMSEA, and SRMR, but these studies had not examined power to detect invariance when more than two groups exist and multiple time points are present. The present study implemented a Monte Carlo simulation to examine the power of change in alternative fit indices to detect two types of measurement invariance, weak and strong, across a variety of manipulated study conditions including sample size, sample size ratio, lack of invariance, location of noninvariance, magnitude of noninvariance, and type of mixed study design.