The maximum likelihood alignment approach to testing for approximate measurement invariance: A paradigmatic cross-cultural application

Background: The impracticality of using the confirmatory factor analytic (CFA) approach in testing measurement invariance across many groups is now well known. A concerted effort to addressing these encumbrances over the last decade has resulted in a new generation of alternative methodological procedures that allow for approximate, rather than exact measurement invariance across groups. The purpose of this article is twofold: (a) to describe and illustrate common difficulties encountered when tests for multigroup invariance are based on traditional CFA procedures and the number of groups is large, and (b) to walk readers through the maximum likelihood (ML) alignment approach in testing for approximate measurement invariance. Methods: Data for this example application derive from an earlier study of family functioning across 30 cultures that include responses to the Family Values Scale for 5,482 university students drawn from 27 of these30 countries. Analyses were based on the Mplus 7.4 program. Results: Whereas CFA tests for invariance revealed 108 misspecified parameters that precluded tests for latent mean differences, noninvariant results were well within the acceptable range for the alignment approach thereby substantiating the trustworthiness of the latent mean estimates and their comparison across groups. Conclusion: The alignment approach in testing for approximate measurement invariance provides an automated procedure that can overcome important limitations of traditional CFA procedures in large-scale comparisons.