Postselection Inference in Structural Equation Modeling.

Area of Science:

• Statistics
• Psychological Science
• Econometrics

Background:

• Traditional statistical inference assumes a pre-specified model.
• Data-driven model selection introduces randomness, invalidating naive inference.
• This can lead to incorrect conclusions and contribute to the reproducibility crisis.

Purpose of the Study:

• To evaluate three state-of-the-art postselection inference methods for structural equation modeling (SEM).
• To compare these valid methods against the commonly used naive procedure.
• To assess their performance under model selection using L1-penalized SEM.

Main Methods:

• Simulation study comparing data splitting (DS), postselection inference (PoSI), and the polyhedral (PH) method.
• Analysis of L1-penalized SEM for model selection events.
• Application to real-world data examples.

Main Results:

• The naive inference method frequently produced incorrect statistical conclusions.
• Valid postselection inference methods generally controlled coverage rates effectively.
• Each valid method exhibited distinct advantages and disadvantages.

Conclusions:

• Naive inference methods are unreliable when applied after data-driven model selection in SEM.
• Valid postselection inference methods (DS, PoSI, PH) offer statistically sound alternatives.
• These valid methods are practical for real-world research using L1-penalized SEM.