[R] VIF estimation in R

[peter dalgaard]

It does say "may". You could take it as a recommendation to make sure you know exactly what it means for your case.

Strange things happen in no-intercept models (especially if factors are involved, which is not the case here), and VIFs depend on R^2 which also has complications in those cases.

Generically with two variables, the VIF is 1/(1-R^2), with the R^2 being the squared "correlation" between the predictors.  This is also the case when the intercept is absent, but the correlation is based on sum(x1*x2) without first centering the variables. 

If you view the VIF as an extra multiplier in the expression for Var(betahat_i), that is still true without the intercept. However (with or without intercept) you have the issue that the colloquial interpretation (adding variables increases variance of betahat) ignores the fact that adding a variable may reduce the residual variation. 

A better interpretation could be to compare Var(betahat_i) to what it could have been in an optimal design where the predictors are orthogonal. But without centering, it is difficult to have orthogonality between two positive variables. 

-pd


> On 17 Nov 2025, at 14.42, Brian Smith <briansmith199312 using gmail.com> wrote:
> 
> I have below model
> 
> library(car)
> 
> data(Duncan)
> vif(lm(prestige ~ income + education - 1, data=Duncan))
> 
> With this, I am getting a warning message
> 
> Warning message:
> 
> In vif.default(lm(prestige ~ income + education - 1, data = Duncan)) :
> 
>  No intercept: vifs may not be sensible.
> 
> 
> Why for model with no intercept, vifs may not be sensible?
> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
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Office: A 4.23
Email: pd.mes using cbs.dk  Priv: PDalgd using gmail.com