Evaluating Fit Indices for Multivariate t-Based Structural Equation Modeling with Data Contamination.

Area of Science:

• Statistics
• Psychometrics
• Data Analysis

Background:

• Conventional structural equation modeling (SEM) using normal-theory maximum likelihood (ML-Normal) is susceptible to bias and inefficiency from data outliers.
• Robust estimation methods are needed to mitigate the impact of outliers in SEM.
• Multivariate-t-based SEM offers a promising alternative for handling contaminated data.

Purpose of the Study:

• To introduce and demonstrate the application of maximum likelihood estimation with a multivariate-t model (ML-t) in SEM for outlier detection.
• To evaluate the performance of ML-t compared to ML-Normal in the presence of data contamination.
• To assess the effectiveness of fit indices and information criteria in identifying data contamination.

Main Methods:

• Applied ML-t estimation to the Holzinger and Swineford (1939) dataset with artificially introduced outliers.
• Conducted a simulation study comparing ML-Normal and ML-t under varying degrees of outlier presence.
• Examined the behavior of standard fit indices and information criteria in both estimation methods.

Main Results:

• Fit indices deteriorated significantly for ML-Normal with increasing outliers, while remaining stable for ML-t.
• Information criteria effectively differentiated between uncontaminated data (favoring ML-Normal) and contaminated data (favoring ML-t).
• The effectiveness of information criteria was particularly pronounced with sample sizes of 200 or more.

Conclusions:

• ML-t provides a robust estimation strategy for SEM in the presence of outliers, outperforming ML-Normal.
• Information criteria serve as valuable tools for model selection, guiding the choice between ML-Normal and ML-t based on data contamination.
• Researchers should consider ML-t for SEM analyses where data outliers are suspected or present, especially with adequate sample sizes.