# How to detect multicollinearity in a logistic regression where all the independent variables are categorical and binary?

I'm doing a multivariate logistic regression where all my independent variables are categorical and binary. I have transformed all my categorical variables into dummies in order to have reference groups and interpret my odds-ratios. However, I would like to check if there are eventually multicollinearity issues.

I plan to calculate Spearman correlation between my independent variables and calculate VIF too. Nevertheless, I have several questions: Is Vif appropriate in this case? Do I have to calculate VIF and Spearman correlation on my categorical variables or their associated dummies?

I have tested other ways to detect multicollinearity (I check if the coefficients vary a lot if I increase my sample size or drop or add variables) and I'm pretty sure there is not a collinearity issue but I would like to have a "quantitative" proof.

• Several small confusions here: Multivariate logit strictly means several response variables. Your title says "dependent variables", your text says "independent variables": you probably mean the second. The confusion is further evidence for those like myself who think both terms are better avoided. Aug 10 '16 at 9:22
• Why Spearman correlation? There is precisely no reason to prefer its use here to Pearson correlation for investigating multicollinearity although in practice if all variables are binary, Spearman gives exactly the same answer, as 0 and 1 are just replaced by two distinct mean ranks, which is a linear transformation. Aug 10 '16 at 9:27