# How we can select suitable Variance Influence Factor (VIF) critical value to detect collinearity?

In Variance Influence Factor(VIF) we should use a critical value. A rule of for this value is 10. Is this a good value for detecting collinear based one VIF? How we can select suitable factor for every case?

You cant. A VIF of 10 implies that the standard errors are larger by a factor of $\sqrt{10}$ than would otherwise be the case, if there were no inter-correlations between the predictor of interest and the remaining predictor variables included in the multiple regression analysis.

I have yet to see a compelling argument, as as VIF of 10 could be fine if you have a (very) large sample.

Bottom line: Do you have a insignificant variable? If so look at the VIF, and determine if you have a correlation problem. What happens if you remove one of the highly correlated variables? Let your [reserach area]-intuition guide you

As per you comment: The variance of the OLS estimator is:

$$Var(\hat{\beta_j}) = \frac{\sigma^2}{\Sigma^n_{i=1}(x_{ij} - \bar{x}_j)^2} \cdot VIF$$

The more observations you add, the larger $\Sigma^n_{i=1}(x_{ij} - \bar{x}_j)^2$ will get. And thus the variance will tend to 0, if n tends to infinity - regardless of how large the VIF is. But I would not think that 800 is large.

• Thank you for answer. You mentioned (very) large sample. How many samples we have in a (very) large data-set? My samples are between 250~800 Commented Jul 1, 2015 at 14:36
• (+1) The sample size plays a role only insofar as it affects the standard errors. As Repmat has emphasized, you need to focus on the standard errors. If they are acceptably small for your purposes, then maybe you are worrying about nothing.
– whuber
Commented Jul 1, 2015 at 14:39
• Thank you @whuber . I should not worry about collinearity because of low sample size? I didn't get you purpose. Commented Jul 1, 2015 at 14:45
• Let me repeat: sample size is not the issue. Standard errors are the concern.
– whuber
Commented Jul 1, 2015 at 14:46
• @whuber Can you mention the steps I need? Currently I'm using financial ratios as inputs (Logically we have collinearity between financial ratios). First I check VIF values (and correlation matrix) and remove variables which have higher than 10 VIP. After that I will investigate p-values of regression (I'm estimating logistic regression) and remove inputs that aren't statistically significant Commented Jul 1, 2015 at 15:26