Correction for measurement error in invariance testing: An illustration using SQP

With the increasing availability of cross-national data, more attention has been given to the issue of comparability. But while a lot of emphasis has been directed to the assessment of measurement invariance, there has been substantially less concern on how measurement error can affect the results of measurement invariance testing. In this study, we show how correction for measurement error can be applied to measurement invariance analysis. We illustrate this using the concept of "Perceived ethnic threat" measured in the European Social Survey Round 3 (2006). The measurement invariance results before and after correction for measurement error are compared. We show that correction for measurement error offers a viable way to ensure that non-invariant parameters are actually caused by differences in the data and not caused by the measurement method.