Comment on “A Note on Collinearity Diagnostics and Centering” by Velilla (2018)

Gómez, Rafael Briones; García, Celia Prados; Pérez, José Garcı́a

doi:10.1080/00031305.2019.1635527

Cited by 5 publications

(6 citation statements)

References 17 publications

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“…This paper analyzes the detection of essential and nonessential multicollinearity from auxiliary centered and noncentered regressions, obtaining two complementary measures between them that are able to detect both kinds of multicollinearity. The relevance of the results is that they are obtained within an econometric context, encompassing the distinction between centered and noncentered models that is not only accomplished from a numerical perspective, as was the case presented, for example, in Salmerón Gómez et al [12] or Salmerón Gómez et al [10]. An undoubtedly interesting point of view of this situation is the one presented by Spanos [38] that stated: It is argued that many confusions in the collinearity literature arise from erroneously attributing symptoms of statistical misspecification to the presence of collinearity when the latter is misdiagnosed using unreliable statistical measures.…”

Section: Discussionmentioning

confidence: 96%

“…Thus, the VIFnc coincides with the expression given by Stewart [9] for the VIF and is denoted as k 2 j , that is, V IFnc(j) = k 2 j . However, recently, Salmerón Gómez et al [12] showed that the index presented by Stewart has been misleadingly identified as the VIF, verifying the following relation between both measures:…”

Section: Noncentered Variance Inflation Factormentioning

confidence: 97%

“…However, in Salmerón Gómez et al [12] it is shown that the VIF and the index of Stewart are not the same measure. This paper analyzes in what cases use one measure or another, focusing on the initial distinction between centered and noncentered models.…”

Section: Introductionmentioning

confidence: 94%

“…This paper analyzes in what cases use one measure or another, focusing on the initial distinction between centered and noncentered models. Thus, the algebraic contextualization provided by Salmerón Gómez et al [12] will be complemented from an econometric point of view. This question was also presented by Jensen and Ramirez [13], striving to commit to a clarification of the misuse given to the VIF over decades since its first use, who insinuated: To choose a model, with or without intercept, is substantive, is specific to each experimental paradigm and is beyond the scope of the present study.…”

Section: Introductionmentioning

confidence: 99%

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Detection of Near-Nulticollinearity through Centered and Noncentered Regression

2020

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This paper analyzes the diagnostic of near-multicollinearity in a multiple linear regression from auxiliary centered (with intercept) and noncentered (without intercept) regressions. From these auxiliary regressions, the centered and noncentered variance inflation factors (VIFs) are calculated. An expression is also presented that relates both of them. In addition, this paper analyzes why the VIF is not able to detect the relation between the intercept and the rest of the independent variables of an econometric model. At the same time, an analysis is also provided to determine how the auxiliary regression applied to calculate the VIF can be useful to detect this kind of multicollinearity.

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Section: Discussionmentioning

confidence: 96%

Section: Noncentered Variance Inflation Factormentioning

confidence: 97%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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Detection of Near-Nulticollinearity through Centered and Noncentered Regression

2020

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“…Although Stewart identified this index with the VIF, both measures only coincide if the variable where they are calculated has a mean of zero (see Salmerón Gómez et al (2020) for more detail). Another interesting aspect that makes the S 2 i measure different from the VIF is that it can be obtained for i = 1 (i.e., for the intercept).…”

Section: A New Definition For the Vif And Its Thresholds: A Test For ...mentioning

confidence: 99%

Overcoming the inconsistences of the variance inflation factor: a redefined VIF and a test to detect statistical troubling multicollinearity

Gómez¹,

García²,

Garcı́a³

2020

Preprint

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Multicollinearity is relevant to many different fields where linear regression models are applied, and its existence may affect the analysis of ordinary least squares (OLS) estimators from both the numerical and statistical points of views.Thus, multicollinearity can lead to incoherence in the statistical significance of the independent variables and the global significance of the model. The variance inflation factor (VIF) is traditionally applied to diagnose the possible existence of multicollinearity, but it is not always the case that detection by VIF of a troubling degree of multicollinearity corresponds to negative effects on the statistical analysis. The reason for the lack of specificity of VIF is that there are other factors, such as the size of the sample and the variance of the random disturbance, that can lead to high values of the VIF but not to problematic variance in the OLS estimators (see O'brien (2007)). This paper presents a new variance inflation factor (TVIF) that consider all these additional factors. Thresholds for this new measure and from the index provided by Stewart Stewart (1987) are also provided. These thresholds are reinterpreted and presented as a new statistical test to diagnose the existence of statistical troubling multicollinearity. The contributions of this paper are illustrated with two real data examples previously applied in the scientific literature.

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