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My study is examining predictors of skin lesions in pigs. I am looking at the effect of predictor variables (including weight at 4 weeks, 9 weeks and 20 weeks) and I have carried out a mixed model analysis with 2 cross-classified random factors (weaning pen and finishing pen) and several predictor variables. I have checked for collinearity using the VIF test in SPSS.

Another author on the paper (who is much more familiar with statistics than me) has commented that the variance inflation factor is not an appropriate measure to use in a multi-level model because 'it assumes the errors are independent identically distributed, with a multi-level model you have clustered errors'. Is this correct? If so, how should collinearity be examined in a mixed model?

I also centred within pen weight as I wanted to look at how variation in weight, in relation to the pen-mean weight, affected skin lesion scores. The second author commented that I should have standardised weight rather than centred it.

Who is correct on these 2 issues?

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First, if you are going with one of the usual methods of testing for collinearity, condition indexes are better than variance inflation factors. This was shown by David Belsley in his two books; I also wrote about it in my dissertation.

Second, I think that the methods used in the perturb package in R are very promising. The idea there is to add small amounts of noise to the data and then see how it affects results. Not only does this make intuitive sense to me, but it allows you to test for collinearity in categorical variables and makes no assumptions about the model.

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  • $\begingroup$ Thanks Peter. Is it actually wrong to use VIF or just inferior? $\endgroup$ Jan 22, 2016 at 12:14
  • $\begingroup$ In general, it's just inferior to condition indexes. In this particular case, I think both of those methods may be inappropriate. $\endgroup$
    – Peter Flom
    Jan 22, 2016 at 12:19
  • $\begingroup$ what method would you suggest in this case? $\endgroup$ Jan 22, 2016 at 12:31
  • $\begingroup$ Like I said, I think perturb is the way to go. $\endgroup$
    – Peter Flom
    Jan 22, 2016 at 12:35

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