The Annals of Applied Statistics
- Ann. Appl. Stat.
- Volume 13, Number 2 (2019), 958-989.
Variable prioritization in nonlinear black box methods: A genetic association case study
The central aim in this paper is to address variable selection questions in nonlinear and nonparametric regression. Motivated by statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel and interpretable way to summarize the relative importance of predictor variables. Methodologically, we develop the “RelATive cEntrality” (RATE) measure to prioritize candidate genetic variants that are not just marginally important, but whose associations also stem from significant covarying relationships with other variants in the data. We illustrate RATE through Bayesian Gaussian process regression, but the methodological innovations apply to other “black box” methods. It is known that nonlinear models often exhibit greater predictive accuracy than linear models, particularly for phenotypes generated by complex genetic architectures. With detailed simulations and two real data association mapping studies, we show that applying RATE enables an explanation for this improved performance.
Ann. Appl. Stat., Volume 13, Number 2 (2019), 958-989.
Received: March 2018
Revised: August 2018
First available in Project Euclid: 17 June 2019
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Crawford, Lorin; Flaxman, Seth R.; Runcie, Daniel E.; West, Mike. Variable prioritization in nonlinear black box methods: A genetic association case study. Ann. Appl. Stat. 13 (2019), no. 2, 958--989. doi:10.1214/18-AOAS1222. https://projecteuclid.org/euclid.aoas/1560758434
- Supplement to “Variable prioritization in nonlinear black box methods: a enetic association case study.”. This file contains supplementary derivations, figures, and tables referenced in the main text.
- Supplementary Table S2. Description of the six quantitative phenotypes analyzed in the Arabidopsis thaliana QTL mapping study.
- Supplementary Table S3. Results for each of the six metabolic traits in the Arabidopsis thaliana QTL mapping study.
- Supplementary Table S5. Results for each of the three quantitative traits in the heterogenous stock of mice dataset.