Evaluating Sensitivity of Parameters of Interest to Measurement Invariance in Latent Variable Models

Latent variable models are common in the social sciences to measure ideal points of U.S. Senators, countries’ “level of democracy” or the relationships between latent attitudes and values across countries, for instance. Because differences in measurement parameters can be confounded with substantively interesting differences, measurement invariance or “equivalence” is a prerequisite for cross-group comparisons of parameters of interest. The practice of “invariance testing” attempts to rule out confounding by testing equality-constrained models. However, some tests may be rejected due to slight violations of invariance that are inconsequential for the comparison of interest. Conversely, even when the invariance hypothesis fits “closely”, measurement inequivalence may still bias comparisons of interest substantially. This article explores an alternative approach: evaluating directly whether parameters of interest are affected by possibly misspecified measurement invariance restrictions. A sensitivity measure, the ”EPC-interest”, is shown to provide valuable insight in whether groups can be considered equivalent