The Effect of Among-Group Dependence on the Invariance Likelihood Ratio Test

Abstract

When comparing latent variables among groups, it is important to first establish the equivalence or invariance of the measurement model across groups. Confirmatory factor analysis (CFA) is a commonly used methodological approach to examine measurement equivalence/invariance (ME/I). Within the CFA framework, the chi-square goodness-of-fit test and chi-square difference tests are used to evaluate ME/I, and these tests rely on the assumption of independence among groups. Limitations in the study design can hinder the practicality of the independence among groups assumption. This article illustrates, algebraically, the effects of violations independence on the chi-square goodness-of-fit and chi-square difference test statistics in a multigroup CFA.

Notes

¹This is equivalent to the expression given by Satorra and Saris (1985), but we use the notation N/G to denote the sample size for each group.

²Release 9.2 of SAS includes an experimental procedure, PROC TCALIS, which allows for multiple group comparisons, but requires the standard assumption of independence among the groups.