| Summary: | This article offers a gentle introduction to the measurement invariance (MI) literature with a focus on its relevance to comparative political research. It reviews 1) the conceptual foundations of MI; 2) standard procedures of testing for MI in practical applications within the multiple-group confirmatory factor analysis (MGCFA) paradigm; and 3) two novel approaches to MI, Bayesian approximate measurement invariance, and MGCFA alignment optimization, which are especially suitable for dealing with extremely heterogeneous data from large-scale comparative surveys typical for modern political science. It then provides an empirical illustration of the key concepts and methods from the MGCFA-MI literature by applying them to testing for MI of two recently introduced measures of democracy attitudes, so-called liberal and authoritarian notions of democracy, across 60 countries in the sixth round of the World Values Survey. These analyses show that both measures can be considered reliable comparative measures of democratic attitudes, although for different reasons. Finally, this study emphasizes that some survey-based constructs, e.g., authoritarian notions of democracy, do not follow the reflective (correlation-based) logic of construct development. These alternative measures, known as formative measures, do not assume strong correlations between their indicators, for which reason it is inappropriate to test their comparability using the reflective MGCFA approach. Instead, their comparability can be tied to their correlations with theoretically relevant external variables.
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