Bayesian Analysis of Structural Equation Models With Nonlinear Covariates and Latent Variables

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Traditional structural equation models (SEMs) often assume linearity.
• Handling nonlinearities and diverse covariate types in SEMs presents analytical challenges.

Purpose of the Study:

• To develop a nonlinear structural equation model (SEM) accommodating covariates in measurement and structural equations.
• To implement a Bayesian approach with Markov chain Monte Carlo (MCMC) methods for parameter estimation and uncertainty quantification.

Main Methods:

• Formulation of a nonlinear SEM allowing continuous/discrete covariates and nonlinear terms.
• Development of Bayesian estimation using MCMC, including standard errors, HPD intervals, and PP p-values.
• Validation through two simulation studies and illustration with a real-world example.

Main Results:

• The proposed Bayesian method demonstrates empirical performance in analyzing complex nonlinear SEMs.
• The methodology effectively handles violations of the normal assumption for exogenous latent variables.
• Detailed interpretation of interaction terms is provided, enhancing model understanding.

Conclusions:

• The developed nonlinear SEM and Bayesian analysis provide a flexible and robust framework for complex statistical modeling.
• The method is suitable for diverse data types and model specifications, including interaction effects.
• The approach offers a valuable tool for researchers in various fields requiring advanced SEM techniques.