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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:

  1. Does anyone know where this "rule of thumb" of r < 0.6 could have emerged (a reference)?
  2. 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.
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    $\begingroup$ how long is a piece of string? see e.g. Graham 2003 Ecology $\endgroup$ – Ben Bolker Oct 7 '15 at 21:15
  • $\begingroup$ Knowing that you have 3 predictors, which formula are you using to calculate the correlation coefficient? $\endgroup$ – aloha Oct 8 '15 at 14:32
  • $\begingroup$ I calculated Pearson's r for each pair of predictors. $\endgroup$ – Gavin M. Jones Oct 8 '15 at 15:02
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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.

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