Hypothesis Testing for Nonlinear and Interactive Effects Using Additive Gaussian Processes
Abstract
Real-world data often exhibit nonlinear, interactive associations between predictors and an outcome. For example, in public health studies, environmental exposures and demographic variables can have nonlinear associations with health outcomes and modify the associations of other predictors. Parametric regression models facilitate interpretable inference and hypothesis testing with Type I error rate control, but may be misspecified when associations are nonlinear. In contrast, flexible nonparametric regression models such as Gaussian processes (GPs) can capture complex nonlinearity, but are often more difficult to interpret and do not readily provide hypothesis tests with Type I error rate control. To bridge this gap, we propose a hypothesis testing framework based on additive GPs restricted to pairwise interactions, allowing tests of variable associations and interaction effects with Type I error rate control. We further establish contraction rates for additive GPs, providing theoretical support for their reduced dependence on predictor dimension when higher-order interactions are absent. Through simulations, we show that restricting the model to pairwise interactions can substantially improve testing power relative to methods based on standard GPs. Applications to environmental health studies identify nonlinear associations between metal exposures and health outcomes as well as effect modification by demographic factors.
Related
- R2-GP: Variance-Calibrated Priors for Additive Gaussian Processes
- Bayes Factor Testing of Linear and Nonlinear Effects in Additive Gaussian Process Regression
- Large deviations for additive functionals of one-dimensional zero-range processes
- Scale operators for Cramér--Lundberg type Markov additive processes
- Exit problems for additive-increase and multiplicative-decrease Markov-modulated processes
BibTeX
@misc{wiecha2026hypothesis,
title = {{Hypothesis Testing for Nonlinear and Interactive Effects Using Additive Gaussian Processes}},
author = {Nate Wiecha and Cailee E. Harrington and Ameer Qaqish and Haibo Zhou and Marc Serre and Lauren A. Eaves and Rebecca Fry and Didong Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10907},
eprint = {2610.10907},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10907},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hypothesis Testing for Nonlinear and Interactive Effects Using Additive Gaussian Processes
AU - Nate Wiecha
AU - Cailee E. Harrington
AU - Ameer Qaqish
AU - Haibo Zhou
AU - Marc Serre
AU - Lauren A. Eaves
AU - Rebecca Fry
AU - Didong Li
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10907
UR - https://arxiv.org/abs/2610.10907
AB - Real-world data often exhibit nonlinear, interactive associations between predictors and an outcome. For example, in public health studies, environmental exposures and demographic variables can have nonlinear associations with health outcomes and modify the associations of other predictors. Parametric regression models facilitate interpretable inference and hypothesis testing with Type I error rate control, but may be misspecified when associations are nonlinear. In contrast, flexible nonparametric regression models such as Gaussian processes (GPs) can capture complex nonlinearity, but are often more difficult to interpret and do not readily provide hypothesis tests with Type I error rate control. To bridge this gap, we propose a hypothesis testing framework based on additive GPs restricted to pairwise interactions, allowing tests of variable associations and interaction effects with Type I error rate control. We further establish contraction rates for additive GPs, providing theoretical support for their reduced dependence on predictor dimension when higher-order interactions are absent. Through simulations, we show that restricting the model to pairwise interactions can substantially improve testing power relative to methods based on standard GPs. Applications to environmental health studies identify nonlinear associations between metal exposures and health outcomes as well as effect modification by demographic factors.
ER -