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    Rights statement: This is the author’s version of a work that was accepted for publication in Tourism Management. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Tourism Management, 71, 2019 DOI: 10.1016/j.tourman.2018.09.008

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Diagnosing and correcting the effects of multicollinearity: Bayesian implications of ridge regression

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<mark>Journal publication date</mark>04/2019
<mark>Journal</mark>Tourism Management
Volume71
Number of pages8
Pages (from-to)1-8
Publication StatusPublished
Early online date3/10/18
<mark>Original language</mark>English

Abstract

When faced with the problem of multicollinearity most tourism researchers recommend mean-centering the variables. This procedure however does not work. It is actually one of the biggest misconceptions we have in the field. We propose instead using Bayesian ridge regression and treat the biasing constant as a parameter about which inferences are to be made. It is well known that many estimates of the biasing constant have been proposed in the literature. When the coefficients in ridge regression have a conjugate prior distribution, formal selection can be based on the marginal likelihood. In the non-conjugate case, we propose a conditionally conjugate prior for the biasing constant, and show that Gibbs sampling can be employed to make inferences about ridge regression parameters as well as the biasing constant itself. We examine posterior sensitivity and apply the techniques to a tourism data set.

Bibliographic note

This is the author’s version of a work that was accepted for publication in Tourism Management. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Tourism Management, 71, 2019 DOI: 10.1016/j.tourman.2018.09.008