Multiplicity Control for Structural Equation Modeling in lavaan : A Practical Workflow for False Discovery Rate Adjustment

Abstract

Structural equation modeling (SEM) is widely used in educational and behavioral research, but applied SEM often involves simultaneous tests of many structural paths. When many coefficients are evaluated at nominal thresholds, the probability of false positives and the expected number of false discoveries can be substantial even when global fit indices indicate close fit, encouraging substantive interpretation of chance findings. Building on prior work on multiplicity control in SEM, this article presents a practical workflow for false discovery rate (FDR) adjustment of families of SEM parameter tests obtained from fitted lavaan model objects, including the dependence-robust Benjamini-Yekutieli (BY) procedure, and provides an R implementation to support routine use. In a Monte Carlo study (1,000 replications; N = 500) with nine latent factors, a correctly specified measurement model, and an overspecified structural model with 33 candidate regressions (8 non-zero), nominal p < .05 produced at least one false positive in 69.3% of samples and a mean of 1.182 false-positive paths. BY adjustment reduced the mean number of false positives to 0.073, while the mean number of detected true effects declined from 6.358 to 5.857. A sensitivity analysis across three dependency conditions indicated that BY-FDR was more robust to the direction and magnitude of parameter dependence, whereas BH’s false-positive control weakened under negative dependence. These results suggest that dependence-robust FDR adjustment can be integrated into a standard SEM workflow with lavaan in R, and may substantially reduce false positives with a modest reduction in detected true effects.