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I am considering to do a multiple regression in which some of the predictive variables are PCA (principal components) axes whereas others are NMDS (nonmetric muliple dimension scaling) axes. I would like to know if this is incorrect and why.

I'm considering this because I have two groups of many variables that I want to reduce before analyzing the relative effects of each of these groups over another variable. The first group is composed by anatomical variables from several species which are best represented by a Phylogenetic PCA. The second group is a bunch of environmental variables which are very non-normal and that I can't normalize through transformation (I tried several and the variables remained with exponential distribution).

What would be a correct way to reduce all variables before doing the multiple regression via generalized least squares?

ttnphns
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Agus Camacho
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  • Non-normality of variables doesn't preclude them from PCA. So why did you decide to use NMDS and how did it help? – ttnphns Apr 07 '14 at 08:33
  • I thought(maybe erroneusly or unnacurately) that normal data would be better described by a PCA by correlation because a line could better represent the variance carried on a normal distribution than on another one(e.g. exponential). Thus the representation in a line of correlated variables would make sense. However, i saw here: http://stats.stackexchange.com/questions/32105/pca-of-non-gaussian-data. that the real problem with data reduction is not normality but the representation of the variance of the variables contained by each one of the PCs. – Agus Camacho Apr 07 '14 at 13:08
  • Notwithstanding, the loadings obtained for the variables were different in each approach, higher for NMDS in most cases. I would use NMDS for all the groups of variables, but in the anatomical setup, literature tells me i need to take into account the phylogeny of the studied species – Agus Camacho Apr 07 '14 at 13:13

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