Detect multicollinearity in maximum likelihood scenarios

Question

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.

Answer 1

The variance-inflation factor (VIF) represents relations among the independent variables rather than their relations to the dependent variable. So provided that you analyze the relations among the independent variables with standard linear regression, it doesn't matter whether the overall model uses OLS or MLE to estimate the relations of those independent variables to the dependent variable.

You might, however, want also to consider a different approach, rather than VIF, for evaluating multicollinearity, and generalized VIF if your independent variables include categorical factors.