Bayesian testing of linear versus nonlinear effects using Gaussian process priors

TL;DR

This paper introduces a Bayesian method using Gaussian process priors to test whether the effect of a predictor is linear or nonlinear, providing a scale-invariant Bayes factor for model comparison and effect directionality.

Contribution

It develops a novel Bayesian testing framework with Gaussian process priors for assessing linear versus nonlinear effects, including one-sided tests for effect directionality.

Findings

Effective in quantifying evidence for linear vs. nonlinear effects.

Applicable across diverse fields like social networks and education.

Provides a scale-invariant Bayes factor for model comparison.

Abstract

A Bayes factor is proposed for testing whether the effect of a key predictor variable on the dependent variable is linear or nonlinear, possibly while controlling for certain covariates. The test can be used (i) when one is interested in quantifying the relative evidence in the data of a linear versus a nonlinear relationship and (ii) to quantify the evidence in the data in favor of a linear relationship (useful when building linear models based on transformed variables). Under the nonlinear model, a Gaussian process prior is employed using a parameterization similar to Zellner's $g$ prior resulting in a scale-invariant test. Moreover a Bayes factor is proposed for one-sided testing of whether the nonlinear effect is consistently positive, consistently negative, or neither. Applications are provides from various fields including social network research and education.