Bias and Efficiency in Structural Equation Modeling: Maximum Likelihood Versus Robust Methods.

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Maximum Likelihood (ML) is the standard for structural equation modeling (SEM) due to its claimed asymptotic unbiasedness and efficiency.
• Deviations from normality or presence of outliers can compromise the performance of ML estimators, leading to bias and inefficiency.
• Robust methods exist to mitigate outlier effects, but their statistical properties, especially standard errors, lack systematic investigation.

Purpose of the Study:

• To systematically compare the bias and efficiency of two robust SEM methods against the traditional ML method.
• To evaluate the performance of robust methods under varying data distributions, including non-normality and outliers.
• To develop and validate a formula for consistent standard errors (SEs) for robust estimators.

Main Methods:

• Confirmatory Factor Analysis (CFA) model was used for comparison.
• Extensive simulations were conducted to assess bias and efficiency of ML and robust estimators.
• A real-world dataset (Cross Racial Identity Scale) was analyzed for illustration.

Main Results:

• Robust methods yield results comparable to ML when data are normally distributed.
• Under heavy-tailed data or with outliers, robust methods produced significantly less biased and more efficient estimators than ML.
• A novel formula for consistent SEs for one robust method was developed and validated; formula-based SEs closely matched empirical SEs.

Conclusions:

• Robust methods are recommended for SEM when data deviate from normality or contain outliers.
• The developed formula provides reliable standard errors for robust estimation, enhancing their practical utility.
• The findings support the use of robust methods for more accurate and dependable results in SEM analyses.