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

Area of Science:

• Educational and behavioral research
• Statistical modeling
• Psychometrics

Background:

• Structural equation modeling (SEM) is prevalent in research, but testing many paths increases false positives.
• Global fit indices may suggest good fit despite numerous chance findings.
• Existing multiplicity control methods in SEM require practical implementation.

Purpose of the Study:

• To present a workflow for false discovery rate (FDR) adjustment in SEM parameter tests.
• To implement the Benjamini-Yekutieli (BY) procedure for dependence-robust FDR control.
• To provide an R implementation for routine use in SEM analyses.

Main Methods:

• Developed a workflow for FDR adjustment of SEM parameter tests using lavaan objects.
• Implemented the Benjamini-Yekutieli (BY) procedure for controlling false discoveries.
• Conducted a Monte Carlo simulation with 1,000 replications (N=500) to evaluate performance.

Main Results:

• Nominal p < .05 resulted in a 69.3% false positive rate and a mean of 1.182 false positives.
• BY adjustment reduced the mean false positives to 0.073, with a modest decrease in true effect detection.
• BY-FDR demonstrated robustness to parameter dependence, unlike the BH procedure.

Conclusions:

• Dependence-robust FDR adjustment, specifically BY, can be integrated into standard SEM workflows.
• This approach substantially reduces false positives in SEM with minimal impact on true effect detection.
• The R implementation supports routine application, enhancing the reliability of SEM findings.