Dealing with multicollinearity in logistic regresson model

Question

I have 5 quantitative predictor variables in my logit model, and when I use the cor function in R on those 5 variables, I see that $x_{1}$ and $x_{2}$ have correlation coefficient $r_{12}=0.718$ and $x_{3}$ and $x_{4}$ have $r_{34}=0.654$. The VIF values are all less than or equal to 2. So does this suggest that there's no multicollinearity in my model? If there is, my question is how can I deal with multicollinearity? Should I create interaction terms? Or would factor analysis/principal component analysis be applicable here? I'm not familiar with those concepts but I can definitely read up on them.

Answer 1

I wouldn't put any stock in the correlations, since multicollinearity can appear among more than two variables, which pairwise correlations won't pick up. VIFs are better. VIFs below 2 should usually not be a problem.

This of course depends on your sample size. As always, larger VIFs can appear more easily with smaller datasets. You can play around with simulated data to get a feeling for the VIFs you can expect for your $n$, e.g.:

library(car)
n <- 30
foo <- data.frame(y=rnorm(n),x1=rnorm(n),x2=rnorm(n),
  x3=rnorm(n),x4=rnorm(n),x5=rnorm(n))
vif(lm(y~.,foo))

I'll often get VIFs up to 1.3 using this approach. You could create some slight correlations between your variables and look how extreme you need to get to get VIFs around 2.