Fitting two-level structural equation models to summary statistics: Leveling up meta-analytic structural equation...

Standard two-level structural equation models (SEMs) require access to raw data. In this study, we propose a method for fitting two-level SEMs using meta-analytic structural equation modeling (MASEM) on summary statistics. Although our focus is on the meta-analytic case of individuals nested in studies, the approach could be applied to any two-level structure. An illustration using empirical data showed that fitting a two-level model on individual data versus fitting a two-level model using summary statistics produces essentially identical results. One advantage of the MASEM approach is that it is straightforward to model heterogeneity in the within-cluster covariances. Using simulated data, we demonstrated that the MASEM method performed well in such heterogeneous conditions. In contrast, two-level SEM analyses resulted in inflated Type I errors based on the test statistic and a significant underestimation of the parameters' standard errors. Through an empirical example, we show how two-level SEM through the MASEM method can be employed to evaluate measurement invariance across all studies and how the model can be expanded to incorporate study-level variables that explain some of the variation in parameters across studies. Implications and limitations of the proposed method are discussed, and directions for future research are provided. (PsycInfo Database Record (c) 2026 APA, all rights reserved).