Evaluating differences in latent means across studies: Extending meta-analytic confirmatory factor analysis with the...

Meta-analytic confirmatory factor analysis (CFA) is a type of meta-analytic structural equation modeling (MASEM) that is useful for evaluating the factor structure of measurement scales based on data from multiple studies. Modeling the factor structure is just one example of the many potentially interesting research questions. Analyzing covariance matrices allows for the evaluation of measurement properties across studies, such as whether indicators are functioning the same across studies. For example, are some indicators more indicative of the common factor in certain types of studies than in others? The additional analysis of means of the observed variables opens up many other research questions to consider such as: "Are there mean differences in mental health between clinical and non-clinical samples?" To answer such questions, it is necessary to analyze both the covariance and the mean structure of the indicators. In this paper, we present, illustrate, and evaluate a method to incorporate the means of variables in the MASEM analyses of such datasets. We focus on meta-analytic CFA, with the aim of testing differences in latent means across studies. We provide illustrations of the comparison of latent means across groups of studies using two empirical datasets, for which data and analysis scripts are provided online. The performance of the new model was tested in a small-scale simulation study. The results showed adequate performance under the tested conditions. Finally, we discuss how the proposed method relates to other analysis options such as multigroup or multilevel structural equation modeling.