Testing Measurement Invariance on Zero-Inflated Measures with Two-Part Factor Model and MGCFA

Abstract

Measurement invariance justifies using observed variables to identify group differences on the latent construct because it indicates that there is no systematic measurement bias between the observed and the latent variables across groups. Using structural equation modeling, multi-group confirmatory factor analysis (MGCFA) is a commonly used tool for testing measurement invariance. However, to date, the usefulness of MGCFA for testing measurement invariance on zero-inflated variables has not been studied. Due to the non-normality of zero-inflated data, flexible modeling to handle zero-inflation and extending the two-part model to factor analysis (two-part factor model) is possible. Therefore, we examined how different levels of zero-inflation affected the measurement invariance tests with the two-part factor model and the MGCFA and suggested the appropriate factor analysis model when zero-inflated variables are the target measures. Study I compared the performance of the two-part factor model and the MGCFA on testing measurement invariance of empirical zero-inflated data. The two models led to different measurement invariance results on the target variables. Thus, applying a different factor model to test measurement invariance brought different conclusions when the measures were zero-inflated. Study II evaluated the performances of the two-part factor model and the MGCFA across different simulation conditions: sample size, level of non-invariance, and extent of zero-inflation. Both models showed acceptable Type I error rates except for some conditions, and the two-part factor model outperformed MGCFA in terms of its power to detect non-invariance on the zero-inflated variable. However, the two models had low power and difficulty in identifying correct partial invariance models when the zero-inflation was extreme (90%).