Improved LM test for robust model specification searches in covariance structure analysis: application in political science research

Covariance structure analysis or structural equation modeling 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 multiplier (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.