Hello Matteo,

Assuming matlab offers ordinary least squares regression, you could (for each IV in your intended model):

1. Use it as a DV in OLS regression, and use all other IVs as independent variables.

2. Take 1 - Rsquared as the tolerance for that specific variable. Very low values of tolerance suggest the potential for problems due to multicollinearity.

How low a threshold depends on your source. A lot of texts suggest that values below 0.1 are small enough to warrant concern. Decades ago, several statistics packages internally adopted a threshold of 0.001 as the cut-off for automatic variable deletion (or, in the case of some packages, throwing an error message and halting execution).

For what it's worth, Variance Inflation Factor (VIF) is the reciprocal of tolerance (and vice versa): VIF = 1 / tolerance; tolerance = 1 / VIF. Large values of VIF suggest the potential for problems with multicollinearity.

Good luck with your work.

David Morse Thank you very much for your answer.

I have implemented a VIF computational tool in my algorithm, which works with the help of correlation indexes matrix. One last thing: if the some among the VIF values results over my discretionary threshold, but, the p-values result to be all significant at low levels, have I to handle multicollinearity, or can I ignore it?

IMO never ignore it because multicollinearity actively works to change your p-values by changing your estimates of parameter variances which affects Wald statistics just as it does t statistics. see:

Article The small sample performance of the Wald test in the sample ...

Wald tests are used in logistic regression see: https://en.wikipedia.org/wiki/Wald_test

Best wishes, D. Booth

David Eugene Booth thank you so much.

What is the acceptable range or value of Variance Inflation Factor (VIF) in Multinomial Regression? kindly help