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December 2008 Bayesian multinomial regression with class-specific predictor selection
Paul Gustafson, Geneviève Lefebvre
Ann. Appl. Stat. 2(4): 1478-1502 (December 2008). DOI: 10.1214/08-AOAS188

Abstract

Consider a multinomial regression model where the response, which indicates a unit’s membership in one of several possible unordered classes, is associated with a set of predictor variables. Such models typically involve a matrix of regression coefficients, with the (j, k) element of this matrix modulating the effect of the kth predictor on the propensity of the unit to belong to the jth class. Thus, a supposition that only a subset of the available predictors are associated with the response corresponds to some of the columns of the coefficient matrix being zero. Under the Bayesian paradigm, the subset of predictors which are associated with the response can be treated as an unknown parameter, leading to typical Bayesian model selection and model averaging procedures. As an alternative, we investigate model selection and averaging, whereby a subset of individual elements of the coefficient matrix are zero. That is, the subset of predictors associated with the propensity to belong to a class varies with the class. We refer to this as class-specific predictor selection. We argue that such a scheme can be attractive on both conceptual and computational grounds.

Citation

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Paul Gustafson. Geneviève Lefebvre. "Bayesian multinomial regression with class-specific predictor selection." Ann. Appl. Stat. 2 (4) 1478 - 1502, December 2008. https://doi.org/10.1214/08-AOAS188

Information

Published: December 2008
First available in Project Euclid: 8 January 2009

zbMATH: 1156.62018
MathSciNet: MR2655668
Digital Object Identifier: 10.1214/08-AOAS188

Keywords: Bayesian model averaging , ‎classification‎ , Markov chain Monte Carlo , multinomial models

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.2 • No. 4 • December 2008
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