Linear regression multicollinearity

Question

I run linear regression with Posttest scores as DV and Pretest scores and Group as IVs. Collinearity Statistics Tolerance shows .998 both for Pretest and Group (VIF 1.002). Is this one of the situations where violating Collinearity might be ignored?

Answer 1

I think you are misinterpreting what tolerance means. Much like in real life, in statistics you want high tolerance. Tolerance is $1-R^2$ where $R^2$ is the squared correlation of the two variables being compared (in your case pretest scores and group assignment). Thus, .998 means there is almost no multicollinearity. It means that your variables have a correlation ($r$) of about .04, which is rather low. Also for future reference, if you didn't know, $VIF=\frac{1}{tolerance}=\frac{1}{1-R^2}$.

Lastly, you ask about times when you can ignore multicollinearity. You can do this always if you aren't interpreting your coefficients and only care about having a high $R^2$ of your model (this is rare unless you are merely making a prediction model). Other than that it depends on the situation, and what you mean by high. Any multicollinearity changes how you interpret your coefficients. So make sure you understand that coefficients are marginal effects and interpret them thusly. Very high multicollinearity essentially means two variables are effectively measuring the same thing. You can ignore it in cases like when the collinearity is between an $X$ variable and $X^2$ in a quadratic model. Here are a few others.

Answer 2

The rule of thumb for VIF in regards to mulitcollinearity is when VIF > 10, so having a VIF of 1.002 is nowhere close to violating any assumptions. See the wiki page for more detail on VIF.

Even on the more conservative side, an article by Paul Allison states "Personally, I tend to get concerned when a VIF is greater than 2.50, which corresponds to an R2 of .60 with the other variables." Again, your VIF of 1.002 is far below this conservative threshold.

Lastly, this article may be an interesting read for you, if you still don't feel comfortable with a VIF = 1.002.