# Difference between Variance Inflation Factor (VIF) and kappa in R?

I am running a regression analyis in r:

fit <- lm(Cost ~ Slope + YardDist, data = test)


I want to test the two independent variables for multicollinearity. I tested it with vif() (from the car package) and kappa().

> vif(fit)
Slope YardDist
1.000121 1.000121
> kappa(fit)
[1] 11631.87


VIF tells me there is no multicollinearity and kappa tells me there is very high multicollinearity. What is the difference between both and which one is 'right'?

$$\text{VIF}=\frac{1}{\text{tolerance}}=\frac{1}{1-r^2}$$ On the other hand, kappa, is the condition number; that is: $$\sqrt{\frac{\text{max(eigenvalue(X'X))}}{\text{min(eigenvalue(X'X))}}}$$ One thing that is often recommended with kappa is to center your variables first (note that there is difference of opinion about this recommendation). If your variables are far from 0, the sampling distributions of the $\beta_j$s will be correlated with the sampling distribution of $\beta_0$ (i.e., the intercept). I suspect that's what you are seeing here.
• @user1738154, the upshot is that your SE / 95% CI for the intercept will be inflated / you will have lower power to differentiate your estimated intercept, $\hat\beta_0$, from $0$. This is due to the fact that your $X_j$ values are far from $x_j=0$ & there is some uncertainty about the slopes. However, most people aren't terribly concerned about this. If, OTOH, you are, you will need to run another study where your $X_j$s are centered on $x_j=0$. – gung Jun 30 '13 at 18:52