Why Measurement Invariance is Important in Comparative Research. A Response to Welzel et al. (2021)

Welzel et al. (2021) claim that non-invariance of instruments is inconclusive and inconsequential in the field for cross-cultural value measurement. In this response, we contend that several key arguments on which Welzel et al. (2021) base their critique of invariance testing are conceptually and statistically incorrect. First, Welzel et al. (2021) claim that value measurement follows a formative rather than reflective logic. Yet they do not provide sufficient theoretical arguments for this conceptualization, nor do they discuss the disadvantages of this approach for validation of instruments. Second, their claim that strong inter-item correlations cannot be retrieved when means are close to the endpoint of scales ignores the existence of factor-analytic approaches for ordered-categorical indicators. Third, Welzel et al. (2021) propose that rather than of relying on invariance tests, comparability can be assessed by studying the connection with theoretically related constructs. However, their proposal ignores that external validation through nomological linkages hinges on the assumption of comparability. By means of two examples, we illustrate that violating the assumptions of measurement invariance can distort conclusions substantially. Following the advice of Welzel et al. (2021) implies discarding a tool that has proven to be very useful for comparativists