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.
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