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?
Solved – How we can select suitable Variance Influence Factor (VIF) critical value to detect collinearity
multicollinearityvariance-inflation-factor
Best Answer
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.