The analysis of measurement invariance of latent constructs is important in research across groups, or across time. By establishing whether factor loadings, intercepts and residual variances are equivalent in a factor model that measures a latent concept, we can assure that comparisons that are made on the latent variable are valid across groups or time. Establishing measurement invariance involves running a set of increasingly constrained structural equation models, and testing whether differences between these models are significant. This paper provides a step-by-step guide to analysing measurement invariance.

Van de Schoot, R., Lugtig, P., & Hox. J. (2012). A checklist for testing measurement invariance. European Journal of Developmental Psychology, 9(4), 486-492.