# Multicolinearity Test for Multiple Multivariate Regression

I have multiple independent variables and multiple dependent variables, some categorical and some quantitative. I have created a data sheet with dummy columns appropriate to each categorical variable.

My team and I have ran various tests with our data, including Multivariate Multiple Regression, and will need to re-do all of them in light of a multicolinearity test that will surely eliminate some variables. This is our last step before writing up a manuscript, so all and any help is deeply appreciated.

I have access to SPSS, SAS and R (though no experience with R). Multicolinearity tests are simple enough for multiple regression with SPSS, but I'm lost when it comes to multiple multivariate regression.

Any suggestions for how to test for multicolinearity for multivariate multiple regression?

Here is a link to some of our data:

I have used the vif function from the car package in R to obtain the Variance Inflation Factor (VIF), which is a measure of multi-collinearity. You should be able to do the same with your multivariate analysis. Basically, once you obtain your multivariate model, you'll need to load the car package, simply write vif(name_of_your_model) in R and you'll obtain the VIF for each of your explanatory variable. Note that according to Zuur et al. (2009) Mixed Effects Models and Extensions in Ecology with R, if a predictor variable as a VIF ­> 5 it means that there's a multi-collinearity issue. You would have to exclude the predictor variable with the highest VIF, redo the vif test on the updated model and repeat these steps until all your predictor variables have a VIF < 5.