# VIF values and interactions in multiple regression

I am running a multiple regression of the form y~a+b+c+ab+ac+bc

I have checked the VIF values for the direct effects - should I check them for the interactions?

I am assuming not as that would equate to looking at the multicolinearity between a variable and itself (albeit in an interaction) which will surely be very high?

• @Penguin_Knight (1) Which do you believe is "correct": that the VIF should be checked for interactions or not? (2) Why does low variability of b imply high correlation of bc with c? I don't see how it can, because rescaling b by any amount, large or small, will simply rescale bc by the same amount, which will not change its correlation with anything, including c. Thus the magnitude of variation of b cannot be associated with the correlation between bc and c. – whuber Mar 20 '13 at 20:22
• @whuber (1) I'd probably put keeping the interaction in before checking VIF. VIF hurts the standard error, but the slope estimate of the main effects would still be closer to correct. (2) Thanks for the correction! I'd proceed to delete the comment. – Penguin_Knight Mar 20 '13 at 20:30
• Sarah, concerning your last comment, consider data where $a = (1,1,1,1,-1,-1,-1,-1)$, $b = (1,1,-1,-1,1,1,-1,-1)$, and $c = (1,-1,1,-1,1,-1,1,-1)$. (This often happens with designed experiments.) Then all six variables $a$, $b, \ldots$, $bc$ are mutually orthogonal (and orthogonal to the constant term) and all VIFs equal $1$. Thus, your assumption that interaction terms create high multicollinearity is not generally true. – whuber Mar 20 '13 at 20:36
• Thank you for your comments. The reason for my question is that I've checked the vif values for my maximal model in R. All were less than 6 (the cutoff that I am using - I realise this is subjective) except for two: variable 'a' and variable 'a:b'. These have vif values of 6.5 and 6.8 respectively. Should I be concerned here? I realise now I perhaps should be... – Sarah Mar 21 '13 at 11:54

## 1 Answer

I go with Penguin_Knight. You will check interaction term also for VIF but you can ignore high values of VIFs here when you use interaction. You can further check for the detailed overview here:

http://www.statisticalhorizons.com/multicollinearity