Revision: variance inflation in regression
type: Item
instance of: scholarly article
title: Revision: variance inflation in regression
zbMATH Open document ID: 1263.62106
DOI: 10.1155/2013/671204
published in: Advances in Decision Sciences
publication date: 2013-05-31T00:00:00Z
review text: Summary: 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 with the 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.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62J20
zbMATH DE Number: 6168877
zbMATH Keywords: ratios of variances
zbMATH Keywords: conventional VIFs
zbMATH Keywords: ill-conditioned data
author: Donald R. Jensen
author: Donald E. Ramirez
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/671204
OpenAlex ID: W2041773590
Wikidata QID: Q57444632
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description: scientific article; zbMATH DE number 6168877