Use of Multi-Group Confirmatory Factor Analysis in Examining Measurement Invariance in Counseling Psychology Research

Hui Xu, Terence J. G. Tracey


The purpose of this article is to introduce the theoretical implications and analytic strategies of measurement invariance. The article is focused on three important invariance conditions, consisting of configural invariance, metric invariance, and scalar invariance. Configural invariance refers to a qualitatively invariant measurement pattern of latent constructs across groups. Metric invariance refers to a quantitatively invariant measurement model of latent constructs across groups. Scale invariance refers to invariant mean levels of latent constructs across groups. While each invariance condition depicts one aspect of the relation between latent constructs with manifest observations, a progressive statistical strategy of measurement invariance was introduced based on multi-group confirmatory factor analysis. The article also provided a case example illustrating how to apply and examine measurement invariance in counseling psychology, with detailed theoretical implications and analytic decision-makings in each step. Application of measurement invariance in measurement comparison across multiple groups (e.g., gender, developmental stages, and national boundaries) was discussed and recommended.


measurement invariance; multiple groups; confirmatory factor analysis; configural invariance; metric invariance; scalar invariance