Abstract: Evaluation of Test Statistics for Robust Structural Equation Modeling With Nonnormal Missing Data.

Area of Science:

• Statistics
• Quantitative Psychology
• Econometrics

Background:

• Traditional structural equation modeling (SEM) struggles with nonnormal and incomplete datasets, common in practical applications.
• Existing robust methods by Yuan and Zhang (2011a) address nonnormal missing data but require further evaluation with robust statistics.

Purpose of the Study:

• To systematically evaluate parameter estimation accuracy and test statistic performance for a linear growth curve model under nonnormal and incomplete data conditions.
• To compare robust statistics against traditional normal distribution-based methods in SEM.

Main Methods:

• A simulation study was conducted using the R package 'rsem' (Yuan & Zhang, 2011b).
• Data were generated with varying levels of nonnormality, missingness (MCAR, MAR), and outliers.
• Five test statistics were evaluated: Maximum Likelihood (ML), Satorra-Bentler scaled chi-square (RML), mean- and variance-adjusted chi-square (AML), Yuan-Bentler residual-based (CRADF), and Yuan-Bentler residual-based F (RF).

Main Results:

• Robust methods provided significantly more accurate parameter estimates for nonnormal data compared to traditional normal distribution-based methods.
• Parameter estimate bias decreased with larger sample sizes and lower missing rates or outlier counts.
• The ML test statistic performed poorly with nonnormal or missing data; robust statistics (RML, AML, CRADF, RF) showed better performance.
• For nonnormal complete data, CRADF and RF outperformed RML and AML.
• For missing completely at random (MCAR) data, RML and AML generally performed better than CRADF and RF.
• For nonnormal missing at random (MAR) data, CRADF and RF demonstrated superior performance over AML.

Conclusions:

• Robust statistical approaches are essential for accurate SEM with nonnormal and incomplete data.
• The choice of test statistic depends on the data characteristics, specifically the presence of nonnormality and missingness patterns (MCAR vs. MAR).
• The performance of robust methods is not significantly affected by the symmetry of outliers.