In my field of study (wildlife ecology), a correlation coefficient of r = 0.6 is a commonly-used threshold for identifying collinearity among pairs of predictor variables. In other words, predictors with a correlation above r = 0.6 are generally not included in the same model.
I recently wrote in the draft of a manuscript: "There was no strong collinearity detected among the predictor variables (all r < 0.6)…" We only had 3 predictors. A colleague reviewed the draft and posited: "r < 0.6 seems like a high threshold, can you briefly justify that?"
I don't have a good reference supporting the r < 0.6 threshold, but there are several posts on this site where r < 0.6 is mentioned in passing when members have discussed possible collinearity in their data or lack thereof (here, here, and here). In other places (in a former stats class, as well as here), I've heard that VIF = 10 is an appropriate threshold, which corresponds approximately with r = 0.95 (i.e., for only two variables $VIF = 1/(1-0.95^2$).
All things considered, I think r = 0.6 may be a relatively conservative (low) threshold, rather than a high threshold as my colleague suggested. I plan on responding by saying that r = 0.6 is a conservative threshold for collinearity that gives us relatively good confidence that collinearity among predictors is not affecting our inference.
My question is:
- Does anyone know where this "rule of thumb" of r < 0.6 could have emerged (a reference)?
- If the cutoff is more or less arbitrary, do you think it is too low (conservative) or high (liberal)? Compared to when VIF = 10 (r = 0.95), it appears conservative.
Best Answer
There is recent work showing that collinearity becomes a more serious problem (inflating the variance of estimated regression coefficients, and therefore not necessarily finding the 'significant' ones correctly) at r>0.7;
Dormann, C. F., J. Elith, S. Bacher, et al. 2013. Collinearity: a review of methods to deal with it and a simulation study evaluating their performance. Ecography 36:27–46.