Multigroup CFA and SEM as unbiased tests of differences in latent means and relations between concepts
Social and political scientists generally rely on composite scores, such as means or additive scores, to test whether groups (e.g., countries, cohorts, occupational groups) differ in some dimensions of interest. Differences (or lack of differences) in these scores are interpreted as reflecting ‘real’ group differences (or ‘real’ lack of differences). However, methodological artefacts, such as inaccurate translations or a tendency to respond towards the middle of the scale, have the potential to affect the measurement, which may result in biased findings (e.g., artificial mean differences). For this reason, it is strongly advised to establish measurement equivalence by means of Multigroup Confirmatory Factor Analyses (MGCFA). Based on two Swiss examples, this presentation will illustrate the necessary steps to perform and interpret multigroup analyses. First, the different levels of measurement equivalence and the criteria to decide whether a level is reached will be exemplified. Second, we will discuss the solutions to undertake (e.g., verifying whether the substantive findings are affected, discarding an item) when MGCFA reveal non-equivalent parameters. Finally, if measurement is considered as sufficiently equivalent, composite scores can be created and used in inferential analysis (e.g., regressions). However, it is also possible to test for group differences (in means or in relations between concepts) with MGCFA and Multigroup Structural Equation Modeling (MGSEM). As we will illustrate in a last step, these methods have the advantage of taking into account measurement error.
Sarrasin, O., Green, E. G. T., Berchtold, A., & Davidov, E. (2012) 'Measurement equivalence across subnational groups: An analysis of the conception of nationhood in Switzerland', International Journal of Public Opinion Research: Advance Online publication.
Chen, Fang Fang (2008) 'What happens if we compare chopsticks with forks? The impact of making inappropriate comparisons in cross-cultural research', Journal of personality and social psychology 95(5): 1005-1018.