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Register a new userVCBART: Bayesian trees for varying coefficients
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Added by
Sameer Deshpande
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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Many studies have reported associations between later-life cognition and socioeconomic position in childhood, young adulthood, and mid-life. However, the vast majority of these studies are unable to quantify how these associations vary over time and with respect to several demographic factors. Varying coefficient (VC) models, which treat the covariate effects in a linear model as nonparametric functions of additional effect modifiers, offer an appealing way to overcome these limitations. Unfortunately, state-of-the-art VC modeling methods require computationally prohibitive parameter tuning or make restrictive assumptions about the functional form of the covariate effects. In response, we propose VCBART, which estimates the covariate effects in a VC model using Bayesian Additive Regression Trees. With simple default hyperparameter settings, VCBART outperforms existing methods in terms of covariate effect estimation and prediction. Using VCBART, we predict the cognitive trajectories of 4,167 subjects from the Health and Retirement Study using multiple measures of socioeconomic position and physical health. We find that socioeconomic position in childhood and young adulthood have small effects that do not vary with age. In contrast, the effects of measures of mid-life physical health tend to vary with respect to age, race, and marital status. An R package implementing VC-BART is available at https://github.com/skdeshpande91/VCBART
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Bayesian Additive Regression Trees (BART) are non-parametric models that can capture complex exogenous variable effects. In any regression problem, it is often of interest to learn which variables are most active. Variable activity in BART is usually measured by counting the number of times a tree splits for each variable. Such one-way counts have the advantage of fast computations. Despite their convenience, one-way counts have several issues. They are statistically unjustified, cannot distinguish between main effects and interaction effects, and become inflated when measuring interaction effects. An alternative method well-established in the literature is Sobol indices, a variance-based global sensitivity analysis technique. However, these indices often require Monte Carlo integration, which can be computationally expensive. This paper provides analytic expressions for Sobol indices for BART posterior samples. These expressions are easy to interpret and are computationally feasible. Furthermore, we will show a fascinating connection between first-order (main-effects) Sobol indices and one-way counts. We also introduce a novel ranking method, and use this to demonstrate that the proposed indices preserve the Sobol-based rank order of variable importance. Finally, we compare these methods using analytic test functions and the En-ROADS climate impacts simulator.
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