Improved LM Test for Robust Model Specification Searches in Covariance Structure Analysis

TL;DR

This paper introduces an improved Lagrange Multipliers test with stepwise bootstrapping for covariance structure analysis, enhancing model specification detection especially in small samples and complex models.

Contribution

It presents a novel LM test method that improves model specification searches in SEM by incorporating stepwise bootstrapping, addressing limitations of existing approaches.

Findings

Enhanced detection of omitted parameters in small samples.

Improved model fit in high degrees of freedom models.

Validated effectiveness through simulations and empirical data.

Abstract

Covariance Structure Analysis (CSA) or Structural Equation Modeling (SEM) is critical for political scientists measuring latent structural relationships, allowing for the simultaneous assessment of both latent and observed variables, alongside measurement error. Well-specified models are essential for theoretical support, balancing simplicity with optimal model fit. However, current approaches to improving model specification searches remain limited, making it challenging to capture all meaningful parameters and leaving models vulnerable to chance-based specification risks. To address this, we propose an improved Lagrange Multipliers (LM) test incorporating stepwise bootstrapping in LM and Wald tests to detect omitted parameters. Monte Carlo simulations and empirical applications underscore its effectiveness, particularly in small samples and models with high degrees of freedom, thereby enhancing statistical fit.