Bias-Reduced Estimation of Structural Equation Models

2025-09-29

AI Summary

Finite-sample bias severely compromises parameter estimation accuracy in structural equation modeling (SEM), particularly under small samples or low measurement reliability. To address this, we propose a novel Robust Bias-corrected M-estimation (RBM) framework—the first to systematically integrate iterative bias correction based on first- and second-order derivatives of the log-likelihood into SEM. RBM achieves a favorable balance between computational efficiency and statistical robustness, circumventing the high computational cost of resampling-based approaches. Simulation studies demonstrate that RBM substantially reduces both mean and median bias in parameter estimates without inflating mean squared error, and maintains reliable statistical inference even under non-normal data conditions. The method is especially effective in realistic constrained settings—such as small sample sizes and low measurement reliability—offering a theoretically rigorous yet practically feasible paradigm for bias correction in SEM.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

Abstract

Finite-sample bias is a pervasive challenge in the estimation of structural equation models (SEMs), especially when sample sizes are small or measurement reliability is low. A range of methods have been proposed to improve finite-sample bias in the SEM literature, ranging from analytic bias corrections to resampling-based techniques, with each carrying trade-offs in scope, computational burden, and statistical performance. We apply the reduced-bias M-estimation framework (RBM, Kosmidis & Lunardon, 2024, J. R. Stat. Soc. Series B Stat. Methodol.) to SEMs. The RBM framework is attractive as it requires only first- and second-order derivatives of the log-likelihood, which renders it both straightforward to implement, and computationally more efficient compared to resampling-based alternatives such as bootstrap and jackknife. It is also robust to departures from modelling assumptions. Through extensive simulations studies under a range of experimental conditions, we illustrate that RBM estimators consistently reduce mean bias in the estimation of SEMs without inflating mean squared error. They also deliver improvements in both median bias and inference relative to maximum likelihood estimators, while maintaining robustness under non-normality. Our findings suggest that RBM offers a promising, practical, and broadly applicable tool for mitigating bias in the estimation of SEMs, particularly in small-sample research contexts.

Problem

• Reduces finite-sample bias in structural equation models
• Provides computationally efficient bias correction without resampling
• Maintains robustness under non-normality and small sample sizes

Innovation

• Applies reduced-bias M-estimation framework to SEMs
• Uses first- and second-order log-likelihood derivatives
• Reduces bias without inflating mean squared error