  This manuscript presents a novel Bayesian varying coefficient quantile
regression (BVCQR) model designed to assess the longitudinal effects of
chemical exposure mixtures on children's neurodevelopment. Recognizing the
complexity and high-dimensionality of environmental exposures, the proposed
approach addresses critical gaps in existing research by offering a method that
can manage the sparsity of data and provide interpretable results. The proposed
BVCQR model estimates the effects of mixtures on neurodevelopmental outcomes at
specific ages, leveraging a horseshoe prior for sparsity and utilizing a
Bayesian method for uncertainty quantification. Our simulations demonstrate the
model's robustness and effectiveness in handling high-dimensional data,
offering significant improvements over traditional models. The model's
application to the Health Outcomes and Measures of the Environment (HOME) Study
further illustrates its utility in identifying significant chemical exposures
affecting children's growth and development. The findings underscore the
potential of BVCQR in environmental health research, providing a sophisticated
tool for analyzing the longitudinal impact of complex chemical mixtures, with
implications for future studies aimed at understanding and mitigating
environmental risks to child health.
