Evaluating sensitivity of parameters of interest to measurement invariance in latent variable models

Latent variable models can only be compared across groups when these groups exhibit measurement equivalence or "invariance," since otherwise substantive differences may be confounded with measurement differences. This article suggests examining directly whether measurement differences present could confound substantive analyses, by examining the expected parameter change (EPC)-interest. The EPC-interest approximates the change in parameters of interest that can be expected when freeing cross-group invariance restrictions. Monte Carlo simulations suggest that the EPC-interest approximates these changes well. Three empirical applications show that the EPC-interest can help avoid two undesirable situations: first, it can prevent unnecessarily concluding that groups are incomparable, and second, it alerts the user when comparisons of interest may still be invalidated even when the invariance model appears to fit the data. R code and data for the examples discussed in this article are provided in the electronic appendix.