So currently running a logistic regression and as a precursor i run some pairwise correlation tests and find that some variables are correlated >.7.
I then run a multicollinearity test and get all tolerance values greater than 0.4 and all VIF values were between 1 and 3 suggesting no multicollinearity?
Does this mean that I can continue my logistic regression?
Thank you
These VIF values don't mean there is no multicollinearity, just that there isn't enough to be worried about. In the simplest multiple regression case with only two regressors, the VIF is exactly equal to $\frac{1}{1-r^2}$, where $r$ is the correlation between the two regressors. So if you go with the rule of thumb that VIFs > 10 are cause for concern, then with a little algebra you can work out that this approximately corresponds to $r>0.95$. So it may be surprising how much collinearity you can actually "get away with". (Of course if you have more than two regressors, the math is a bit different; then 0.95 is basically the limit on the sum of the partial correlations between the regressors.)
Also, note that multicollinearity doesn't mean the results of the regression won't be valid. Your confidence in the estimated coefficients will be lower compared to a situation with no multicollinearity, but this will be reflected in the standard error estimates on those coefficients. So your statistics (including, for example, p-values) don't become biased or anything like that. You do lose some statistical power, though, and how much power you lose is reflected in the VIFs.
