New testing procedures for Structural Equation Modeling

TL;DR

This paper presents new hypothesis testing procedures for Structural Equation Modeling that are robust under weak assumptions, include existing methods as special cases, and utilize bootstrap techniques for improved accuracy and robustness assessment.

Contribution

It introduces a new class of testing procedures for SEM, including bootstrap-based methods for p-value approximation and robustness evaluation, extending and generalizing existing approaches.

Findings

New p-value approximation methods perform well under nonnormality.

Bootstrap procedures effectively assess asymptotic robustness.

Large samples are needed for certain bootstrap tests to be reliable.

Abstract

We introduce and evaluate a new class of hypothesis testing procedures for moment structures. The methods are valid under weak assumptions and includes the well-known Satorra-Bentler adjustment as a special case. The proposed procedures applies also to difference testing among nested models. We prove the consistency of our approach. We introduce a bootstrap selection mechanism to optimally choose a p-value approximation for a given sample. Also, we propose bootstrap procedures for assessing the asymptotic robustness (AR) of the normal-theory maximum likelihood test, and for the key assumption underlying the Satorra-Bentler adjustment (Satorra-Bentler consistency). Simulation studies indicate that our new p-value approximations performs well even under severe nonnormality and realistic sample sizes, but that our tests for AR and Satorra-Bentler consistency require very large sample sizes to work well.