Approximate measurement invariance

This chapter focuses on a practical analysis of the Bayesian approximate measurement invariance model using standard software. It introduces the concept of approximate measurement invariance and illustrates the use of its most basic variant. The chapter discusses the use of measurement invariance testing in latent variable measurement models. In such models, the response functions are estimated through presumed conditional independence assumptions, and investigation of measurement invariance proceeds through restrictions on the parameters of these estimated functions. The most common model for this test is the confirmatory factor model, but this framework also includes item response theory (IRT) models, latent class models, and generalized multitrait‐multimethod models. The chapter focuses on a multigroup confirmatory factor analysis (MGCFA). The methodological literature on cross‐cultural and cross‐country analysis has recommended testing for measurement equivalence to guarantee that differences across groups are due to substantive true differences and not methodological artifacts