Exact and Bayesian Approximate Measurement Invariance

Cross-cultural research is concerned with comparisons of substantive variables across cultures, countries, or other types of socially relevant groups and contexts (Davidov, Schmidt, & Billiet, 2017). However, the properties of the measurements of substantive variables that are gathered from surveys may sometimes preclude valid and meaningful comparisons. Response characteristics of scales to assess latent variables may change across groups (or time), and it may not be clear if the same concepts are actually being analyzed. For example, mean levels of latent variables representing concepts like ethics, values, attitudes, and social or political trust may be incomparable, because their meaning and understanding is substantially different across national cultures, regional contexts, or time points. Hence, comparisons may be impossible