Distributionally weighted least squares in structural equation modeling

Area of Science:

• Statistics
• Quantitative Psychology
• Econometrics

Background:

• Real-world data in structural equation modeling (SEM) often deviates from normal distribution.
• Ignoring non-normality can lead to unreliable parameter estimates, standard errors, and model fit statistics from methods like Maximum Likelihood (ML) and Generalized Least Squares (GLS).
• Asymptotically Distribution-Free (ADF) estimators avoid distributional assumptions but may lack efficiency in smaller samples.

Purpose of the Study:

• To propose a novel Distributionally Weighted Least Squares (DLS) estimator for SEM.
• To enhance the performance of existing generalized least squares methods by integrating normal theory and ADF approaches.
• To provide a more robust estimation and inference method for SEM with non-normally distributed data.

Main Methods:

• Development of the Distributionally Weighted Least Squares (DLS) estimator.
• Utilizing a model-implied covariance-based version of DLS (DLSM).
• Employing computer simulations to compare DLS with existing methods (ML, GLS, Ridge GLS).
• Implementing a bootstrap procedure for tuning parameter selection in a real data example.

Main Results:

• The DLSM estimator demonstrated relatively accurate and efficient parameter estimates, as measured by Root Mean Square Error (RMSE).
• Empirical standard errors, relative biases of standard error estimates, and Type I error rates using the Jiang-Yuan rank adjusted model fit test statistic (TJY) were competitive with classical methods.
• The performance of DLSM is influenced by its tuning parameter 'a', which can be optimized using bootstrapping.

Conclusions:

• The proposed DLSM estimator offers a promising alternative for SEM analyses with non-normally distributed data.
• DLSM provides competitive accuracy and efficiency compared to traditional methods like ML and GLS.
• The study demonstrates a practical approach to implementing and optimizing DLSM using real data and bootstrapping.