# Detect multicollinearity in maximum likelihood scenarios

I'm estimating a binary logit discrete choice model with BIOGEME and want to check for multicollinearity of my predictors. BIOGEME uses maximum likelihood estimation (MLE) and not ordinary least square (OLS) method.

In OLS regression models, one can use $VIF = \frac{1}{1-R^2}$ to assess for multicollinearity.

My questions are:

1. Can I use VIF in the context of MLE as well?
2. In case, that yes: McFaddens $R^2$ is defined exactly the same as $\rho^2 = 1- \frac{L_1}{L_0}$, where $L_1$ is the estimated model and $L_0$ the nullmodel. Can I then derive: $VIF = \frac{1}{1-\rho^2}$ ?
3. If not: are there any other measures for multicollinearity in MLE models?

Obviously, I check for correlations in between the independent variables before the modelling. However, I'd like to have an indicator for my final model as well.

• Thanks for your comment and the clarification. I indeed missed that $R^2$ is for the independent variables and has nothing to do with the dependent variable. Thanks also for the link, I'll have a look into CI, too! – Klaster Jul 30 '15 at 15:28