Does cluster-robust estimation provide within-study effects? A comparison of individual participant data methods in MASEM

Researchers conducting meta-analytical structural equation modeling (MASEM) with individual participant data can choose from several methods, including cluster-robust estimation, two-level SEM, multivariate meta-analysis of path coefficients, and One-Stage MASEM (OSMASEM). While two-level SEM and OSMASEM model within- and between-study effects separately, cluster-robust estimation combines them, estimating an overall path coefficient. Despite its popularity, cluster-robust estimation often yields results that differ from other methods. Simulations using factor models and real-world comparisons using path models show that it may not accurately reflect within-study estimates and can produce biased standard errors. This study compares IPD MASEM methods using simulated data, varying intraclass correlations, parameter equality across levels, number of studies, and missing data. Results reveal that cluster-robust estimation frequently misrepresents within-study estimates, produces biased standard errors, and tends to incorrectly reject model fit, highlighting the need for careful method selection in IPD MASEM applications.