Bayesian Semiparametric Inference on Functional Relationships in Linear Mixed Models

Abstract

Regression models with varying coefficients changing over certain underlying covariates offer great flexibility in capturing a functional relationship between the response and other covariates. This article extends such regression models to include random effects and to account for correlation and heteroscedasticity in error terms, and proposes an efficient new data-driven method to estimate varying regression coefficients via reparameterization and partial collapse. The proposed methodology is illustrated with a simulated study and longitudinal data from a study of soybean growth.