IDENTIFYING MAIN EFFECTS AND INTERACTIONS AMONG EXPOSURES USING GAUSSIAN PROCESSES

• 成果类型: Article
• 署名作者: Ferrari, Federico; Dunson, David B.
• 署名单位: Duke University
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/20-AOAS1363
• 发表日期: 2020
• 页码: 1743-1758
• 关键词: bayesian variable selection; air-pollution; chemical-mixtures; HEALTH; regression; association; CHILDREN; obesity; metals; models

摘要

This article is motivated by the problem of studying the joint effect of different chemical exposures on human health outcomes. This is essentially a nonparametric regression problem, with interest being focused not on a black box for prediction but instead on selection of main effects and interactions. For interpretability we decompose the expected health outcome into a linear main effect, pairwise interactions and a nonlinear deviation. Our interest is in model selection for these different components, accounting for uncertainty and addressing nonidentifiability between the linear and nonparametric components of the semiparametric model. We propose a Bayesian approach to inference, placing variable selection priors on the different components, and developing a Markov chain Monte Carlo (MCMC) algorithm. A key component of our approach is the incorporation of a heredity constraint to only include interactions in the presence of main effects, effectively reducing dimensionality of the model search. We adapt a projection approach developed in the spatial statistics literature to enforce identifiability in modeling the nonparametric component using a Gaussian process. We also employ a dimension reduction strategy to sample the nonlinear random effects that aids the mixing of the MCMC algorithm. The proposed MixSelect framework is evaluated using a simulation study, and is illustrated using data from the National Health and Nutrition Examination Survey (NHANES). Code is available on GitHub.