Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons

It is frequently stated in the literature that measurement invariance is a prerequisite for the comparison of group means or standard deviations of the latent variable in factor models. This article argues that measurement invariance is not necessary for meaningful and valid comparisons across groups. There is unavoidable ambiguity in how researchers can define comparisons if measurement invariance is violated. Moreover, there is no support for preferring the partial invariance approach over competing approaches, such as invariance alignment, robust linking, or Bayesian approximate invariance. Furthermore, we also argue why an intentionally misspecified multiple-group factor model with invariant item parameters can be justified if measurement invariance is violated.