Measurement Invariance and Sensitivity of Delta Fit Indexes in Non-Normal Data: A Monte Carlo Simulation Study

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  In Roundtable Session: Measurement Complexity in SEM: Cross-Loading, Invariance, and Heterogeneity

Abstract

The primary objective of this research is to examine how commonly used delta fit indexes of measurement invariance respond under conditions of non-normality. The present research was built upon Cao and Liang (2022a)’s study to test the sensitivities of a series of delta fit indexes, and further scrutinizes how non-normal data distributions affect fit cutoffs. Data sets with varying degrees of skewness and kurtosis were generated. These data were examined using multi-group confirmatory factor analysis (MGCFA). Delta fit index performance including Delta Comparative Fit Index (ΔCFI), Delta Standardized Root Mean Square residual (ΔSRMR) and Delta Root Mean Square Error of Approximation (ΔRMSEA) were assessed. These findings have significant implications for professionals and scholars in psychology and education.

Authors

• Meixi Yu, University of Central Florida

• Stephen A. Sivo, University of Central Florida

• Parul Acharya, Columbus State University