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

Abstract

When faced with the problem of multicollinearity most tourism researchers recommend meancentering 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.

Impact of the Regularization of Regression Models on the Results of the Mass Valuation of Real Estate

“…There is a plethora of studies regarding the regularization of regression models. Some of them concern research related to improvements in classical forms of regularization (Lipovetsky, 2010;Toker, Kaçiranlar, 2013;Hurvich, Simonov, Tsai, 1998;Durage 2014, Assaf, Tsionas, Tasiopoulos, 2019. Studies related to regularization also concern the methods of determining the level of regularization hyperpameter (Golub, Heath, Wahba, 1979;Khalaf, Shukur, 2005;Ohishi, Yanagihara, Fujikoshi, 2020).…”

Quantitative research in tourism and hospitality: an agenda for best-practice recommendations

“…In other words, mean centering does not increase or alleviate the multicollinearity problem. 3-Third, it is important to emphasize that dropping highly correlated variables from the model does not also seem to be a good solution to address the multicollinearity problem, as shown in recent simulation evidence (Assaf et al 2019b). Dropping variables from the model also introduces the risk of misspecifying the regression model.…”

“…The use of Bayesian regression has not been so far highly common in the tourism literature. In a recent paper, Assaf et al (2019b) have demonstrated the power of Bayesian ridge regression in effectively handling the multicollinearity problem, using evidence from both simulated and real datasets. It is also less well known that multicollinearity may indicate endogeneity in the sense that certain explanatory variables may be statistically related as well as related to the dependent variable of the model.…”

“…In such cases, multicollinearity is a problem of specification, rather than a mere cause of inflated standard errors associated with otherwise consistently estimated parameters. We refer the reader to Assaf et al (2019b) for more technical details.…”

Application of Gis Technology for Tourism Flow Modelling in the United Kingdom

“…The findings of meta-analysis will be useful wherever an understanding of the drivers of tourism demand is critically important. Assaf et al (2019) studied the multi-co linearity by Bayesian inference in conjugate and non-conjugate ridge regression models for tourism data set. They found that the Bayesian ridge regression generates better results than a Bayesian regression with diffused prior (Assaf et al, 2019).…”