Revision: Variance Inflation in Regression

Jensen, D. R.; Ramirez, D. E.

Revision: Variance Inflation in Regression

dc.contributor.author	Jensen, D. R.	en
dc.contributor.author	Ramirez, D. E.	en
dc.contributor.department	Statistics	en
dc.date.accessioned	2017-09-18T09:47:37Z	en
dc.date.available	2017-09-18T09:47:37Z	en
dc.date.issued	2013-02-25	en
dc.date.updated	2017-09-18T09:47:37Z	en
dc.description.abstract	Variance Inflation Factors (VIFs) are reexamined as conditioning diagnostics for models with intercept, with and without centering regressors to their means as oft debated. Conventional VIFs, both centered and uncentered, are flawed. To rectify matters, two types of orthogonality are noted: vector-space orthogonality and uncorrelated centered regressors. The key to our approach lies in feasible Reference models encoding orthogonalities of these types. For models with intercept it is found that (i)uncentered VIFs are not ratios of variances as claimed, owing to infeasible Reference models; (ii) instead they supply informative angles between subspaces of regressors; (iii) centered VIFs are incomplete if not misleading, masking collinearity of regressors withthe intercept; and (iv) variance deflation may occur, where ill-conditioned data yield smaller variances than their orthogonal surrogates. Conventional VIFs have all regressors linked, or none, often untenable in practice. Beyond these, our models enable the unlinking of regressors that can be unlinked, while preserving dependence among those intrinsically linked. Moreover, known collinearity indices are extended to encompass angles between subspaces of regressors. To reaccess ill-conditioned data, we consider case studies ranging from elementary examples to data from the literature.	en
dc.description.version	Published version	en
dc.format.mimetype	application/pdf	en
dc.identifier.citation	D. R. Jensen and D. E. Ramirez, “Revision: Variance Inflation in Regression,” Advances in Decision Sciences, vol. 2013, Article ID 671204, 15 pages, 2013. doi:10.1155/2013/671204	en
dc.identifier.doi	https://doi.org/10.1155/2013/671204	en
dc.identifier.uri	http://hdl.handle.net/10919/78993	en
dc.language.iso	en	en
dc.publisher	Hindawi	en
dc.rights	Creative Commons Attribution 4.0 International	en
dc.rights.holder	Copyright © 2013 D. R. Jensen and D. E. Ramirez. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.	en
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	en
dc.title	Revision: Variance Inflation in Regression	en
dc.title.serial	Advances in Decision Sciences	en
dc.type	Article - Refereed	en
dc.type.dcmitype	Text	en