Sensitivity of Goodness of Fit Indices to Lack of Measurement Invariance with Categorical Indicators and Many Groups

45 Pages Posted: 9 Jul 2019

See all articles by Boris Sokolov

Boris Sokolov

National Research University Higher School of Economics - Laboratory for Comparative Social Research

Date Written: July 9, 2019

Abstract

Using Monte Carlo simulation experiments, this paper examines the performance of popular SEM goodness-of-fit indices, namely CFI, TLI, RMSEA, and SRMR, with respect to a specific task of measurement invariance testing with categorical data and many groups (10-50 groups). Study factors include the number of groups, the level of non-invariance in the data, and the absence/presence of model misspecifications other than non-invariance. In sum, the study design yields a total of 81 conditions. All simulated data sets are analyzed using two popular SEM estimators, MLR and WLSMV. The main contribution of this paper to the methodological literature on cross-cultural survey research is that it produces revised guidelines for evaluating the goodness of fit of invariance MGCFA models with many groups.

Keywords: SEM; MGCFA; measurement invariance; fit indices, simulations

JEL Classification: C15

Suggested Citation

Sokolov, Boris, Sensitivity of Goodness of Fit Indices to Lack of Measurement Invariance with Categorical Indicators and Many Groups (July 9, 2019). Higher School of Economics Research Paper No. WP BRP 86/SOC/2019, Available at SSRN: https://ssrn.com/abstract=3417157 or http://dx.doi.org/10.2139/ssrn.3417157

Boris Sokolov (Contact Author)

National Research University Higher School of Economics - Laboratory for Comparative Social Research ( email )

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