A Bayesian Approach to Estimating Reciprocal Effects with the Bivariate STARTS Model

Area of Science:

• Psychometrics
• Statistical Modeling
• Quantitative Psychology

Background:

• The bivariate Stable Trait, AutoRegressive Trait, and State (STARTS) model is valuable for analyzing reciprocal effects over time.
• Maximum Likelihood (ML) estimation of the bivariate STARTS model often encounters convergence issues, limiting its practical application.

Purpose of the Study:

• To introduce and implement a Bayesian approach for estimating the bivariate STARTS model.
• To address parameterization challenges and suggest appropriate prior distributions for model parameters.

Main Methods:

• Implementation of the bivariate STARTS model using Bayesian inference in Stan software.
• Proposal of the four-parameter beta distribution as a flexible prior for autoregressive and cross-lagged effects.
• Conducting a simulation study to compare Bayesian and ML estimation accuracy.

Main Results:

• The Bayesian approach demonstrated more accurate parameter estimates compared to ML estimation, particularly in challenging data configurations.
• The proposed method effectively stabilizes parameter estimates for the bivariate STARTS model.

Conclusions:

• The Bayesian approach offers a robust and accurate alternative for estimating the bivariate STARTS model, overcoming limitations of ML.
• This method enhances the reliability of analyzing reciprocal relationships in longitudinal data.