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

Standard two-level SEM models require access to raw data. In this study we propose a method for fitting two-level SEMs using meta-analytic structural equation modelling (MASEM) on sum-mary 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 PISA 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 da-ta, 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 ex-ample, 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 pro-vided.