Informative prior on structural equation modelling with non-homogenous error structure

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Homogeneous error structures in statistical models often unrealistically assume equal variances.
• Heteroscedasticity, or non-equal variances, is a common issue in real-world data.
• Bayesian structural equation modeling (BSEM) offers a flexible framework for complex data analysis.

Purpose of the Study:

• To investigate the impact of informative priors on BSEM with heteroscedastic error structures.
• To evaluate different forms of heteroscedasticity within the BSEM framework.
• To compare Bayesian approaches with classical methods for handling non-equal variances.

Main Methods:

• Four distinct forms of heteroscedastic error structures were analyzed.
• Informative priors were updated to assess their influence.
• Simulations were conducted across various sample sizes (50, 100, 200, 500).

Main Results:

• Both posterior predictive probability (PPP) and log likelihood were significantly influenced by sample size and prior information.
• The linear form of heteroscedastic error structure demonstrated superior performance.
• The chosen Bayesian approach outperformed classical methods reliant solely on sample information.

Conclusions:

• The study successfully addressed heteroscedasticity of known forms using informative priors in BSEM.
• The linear heteroscedastic model is recommended for data violating the homogeneous variance assumption.
• This Bayesian method provides a robust alternative for handling non-equal variances in structural equation models.