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Bayesian one-sided variable selection
Gu,Xin Hoijtink,Herbert Mulder,Joris
Gu,Xin
Hoijtink,Herbert
Mulder,Joris
Abstract
This paper presents a novel Bayesian variable selection approach that accounts for the sign of the regression coefficients based on multivariate one-sided tests. We propose a truncated g prior to specify a prior distribution of coefficients with anticipated signs in a given model. Informative priors for the direction of the effects can be incorporated into prior model probabilities. The best subset of variables is selected by comparing the posterior probabilities of the possible models. The new Bayesian one-sided variable selection procedure has higher chance to include relevant variables and therefore select the best model, if the anticipated direction is accurate. For a large number of candidate variables, we present an adaptation of a Bayesian model search method for the one-sided variable selection problem to ensure fast computation. In addition, a fully Bayesian approach is used to adjust the prior inclusion probability of each one-sided model to correct for multiplicity. The performance of the proposed method is investigated using several simulation studies and two real data examples.
Description
Funding Information: Funding : This work was supported by Grant NWO 024.001.003 from the Netherlands Organization for Scientific Research, Grant NWO Vidi 452-17-006 from the Netherlands Organization for Scientific Research, and Grant 2019ECNU-XFZH015 from the East China Normal University.
Date
2022
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Publisher
Research Projects
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Keywords
Fully Bayesian approach, INEQUALITY, MCMC model search, MODEL, PRIORS, SHRINKAGE, one-sided variable selection, prior model probabilities, truncatedgprior
Citation
Gu, X, Hoijtink, H & Mulder, J 2022, 'Bayesian one-sided variable selection', Multivariate Behavioral Research, vol. 57, no. 2-3, pp. 264-278. https://doi.org/10.1080/00273171.2020.1813067