# Logistic regression detection of multicollinearity- is VIF applicable?

#### mtsip

##### New Member
I have a model with a dichotomous DV and IVs both continuous/numerical and dichotomous.
I checked for collinearity with Pearson.
How do I check for multicollinearity in logistic regression?
Could I follow the procedure of rotating my IVs as DVs one at a time against the remaining IVs, and estimate the VIFs? (1/1-Rsquared).
Could I do that for the continuous/numerical IVs, run linear regression and estimate VIFs?
How should I treat the dichotomous IVs? (could I run linear regression as well and see only the VIFs? ignoring the other results?)

Or to test for multicollinearity, I should check the SE of the coefficients (>2)?

Or is there another approach?

I am sorry if the questions are stupid, but econometrics is not my field, and I am trying hard to understand.

Thank you

#### Tarek

##### New Member
Multicolinearity is about the predictors, not the response variable. This means that you are not limited to logistic regression procedures to detect it. Analyze your binary outcome data as if it was a traditional regression and use whatever your normal tools are for assessing variance inflation factors. If you were using SAS, you could use the regression procedure (PROC REG) with the TOL and VIF options (tolerance and variance inflation factors, respectively). Here's what they mean: lets say you have predictors X1 X2 and X3 for your binary outcome Y variable. You regress X1 onto X2 and X3 and calculate the R-squared (the % of the variance in X1 collectively explained by X2 and X3). Now take (1-R-squared), which measures variation in X1 not explained by X2 and X3. This value is the Tolerance of X1, and higher values mean less multicolinearity. I have read that tolerances of less than 0.4 is cause for concern, but things like this may be field or question-specific. The "Variance Inflation Factor" for X1 is just the reciprocal of tolerance. VIF can be interpreted as how 'inflated' the variance of X1 coefficient in your regression relative to what it would be if it was uncorrelated with other model variables. I think a VIF of 8 implies that X1 has 2.8x the standard error it should have if the other model variables weren't there (radical 8=2.83).
I think calculation of VIF/Tolerance is the same for your categorical independent variables. I've only done it in regression, but ANCOVA (linear and categorical predictores), ANOVA, and regression are all general linear models so the smae multicolinearity tests should work for all 3.