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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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Diagnosing and correcting the effects of multicollinearity
T2 - Bayesian implications of ridge regression
AU - Assaf, A.G.
AU - Tsionas, M.
AU - Tasiopoulos, A.
N1 - 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
PY - 2019/4
Y1 - 2019/4
N2 - 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.
AB - 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.
KW - Bayesian analysis
KW - Gibbs sampling
KW - Multicollinearity
KW - Ridge regression
U2 - 10.1016/j.tourman.2018.09.008
DO - 10.1016/j.tourman.2018.09.008
M3 - Journal article
VL - 71
SP - 1
EP - 8
JO - Tourism Management
JF - Tourism Management
SN - 0261-5177
ER -