Soft Bayesian Additive Regression Trees (SBART) for correlated survey response with non-Gaussian error.

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Complex survey data are vital across social sciences, public health, and market research.
• Traditional regression methods struggle with unknown covariate effects, interactions, and non-Gaussian response distributions (heavy-tailed, skewed).
• Nonparametric Bayesian regression, particularly for quantile regression and skewed clustered complex survey data, remains underexplored.

Purpose of the Study:

• Introduce the Soft Bayesian Additive Regression Trees (SBART) framework.
• Address limitations of parametric regression for complex survey data.
• Provide a method for quantile regression and modeling skewed, heavy-tailed response distributions in clustered survey data with weights.

Main Methods:

• Developed the Soft Bayesian Additive Regression Trees (SBART) framework.
• Applied SBART to clustered survey data with subject-specific survey weights.
• Utilized simulation studies and real-world data analysis (National Health and Nutrition Examination Survey).

Main Results:

• SBART effectively performs quantile regression on complex survey data.
• The framework successfully models heavy-tailed and skewed response distributions.
• Demonstrated advantages of SBART through simulations and analysis of periodontal data.

Conclusions:

• SBART offers a robust nonparametric Bayesian approach for complex survey data analysis.
• The method enhances modeling capabilities for quantile regression and skewed distributions.
• SBART provides a valuable tool for researchers in public health, social sciences, and beyond.