Christian Welzel Gave a Talk on Rethinking Measurement In-Equivalence
On April 10th Christian Welzel gave a lecture on “Rethinking Measurement In-Equivalence: Or Why We Should Forget about MGCFA” at the 8th LCSR International Workshop. During the presentation he addressed the issues of measurement invariance required by confirmatory factor analysis when it is performed on the data coming from different groups. Measurement invariance is an assumption that all indicators and parameters used in a factor model are equal among the groups. Factor loadings, intercepts, and mean values have to be equal in all groups to make a conclusion that the model is invariant and, therefore, the results may be compared among the groups.
However, as Christian Welzel showed, the evidence of non-invariance is a methodological artifact that is not related to theoretical constructs. Factor models, including multi-group factor models, are based on the analysis of variances and correlations among manifest variables. Nonetheless, the values of variance and correlation depend on the mean values of the analyzed variables. With the regard to emancipative values, it was illustrated that variance and, then, correlation, is lower when the majority of answers belong to the same category. Likewise, it becomes higher when the answers are polarized (when one-half of the respondents chooses the lowest category and the other half chooses the highest one). Moreover, Chris Welzel suggests looking at the differences in factor loadings among the countries. The results show that the factor loadings are only dependent on standard deviations of the manifest variable. At this point, Chris Welzel implies, the invariant results are the consequence of the methodological flaws of multi-group confirmatory factor analysis.
Furthermore, theoretical issues were discussed. Christian Welzel states that MGCFA models analyze only mathematical aspects of comparison and do not concern any cultural context, while differences in factor loading and means may signify important cross-cultural dissimilarities. Along with it, as the presenter said, MGCFA proposes misleading causal relations. The models are analyzed as the summary of the attitudes of atomic individuals which later comprise the mean value, whereas, in fact, these individual attitudes are affected by the existing level of attitudes.
Regarding all this, Christian Welzel suggests two ways of solving the problems with MGCFA. First, the method may be rejected with group differences treated as a source of new theoretical insights. Second, pooled multilevel factor analysis may be used instead to consider social and cultural differences among countries.
Violetta Korsunova & Jovana Zafirović