# Phylogenetic General Least Squares, multivariate regression

I'm working on a biological question, with species data derived from an external database, which has multiple response and predictor variables. As a result, I want to do multivariate regression across a phylogeny to empirically test if my response variables are significantly different in respect to my predictors.

Please refer to source [2] and it's citations for your own investigation of this process.

I know how to do multiple regression via pGLS, but the R package [1] only mentions predictors and response. Furthermore, another source [2] discusses how multivariate regression though pGLS in R can be done, but requires one to transform the data under a Brownian motion model. (Edit: It seems that [2] is a solution...so I'm looking the process).

Sources:

1. The vignette for the pGLS package (pdf)

2. D.C. Adams. 2014. A Method for Assessing Phylogenetic Least Squares Models for Shape and Other High-Dimensional Multivariate Data. Evolution. 68:9 2675-2688. doi: 10.1111/evo.12463

3. Revell, L. J. (2010), Phylogenetic signal and linear regression on species data. Methods in Ecology and Evolution, 1: 319–329. doi: 10.1111/j.2041-210X.2010.00044.x

## migrated from stackoverflow.comOct 20 '14 at 12:28

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• Would it be useful if I added programming and theory for reference? I figured that someone who could help me would already be well versed in the material. But if this is not the case, I'll gladly shorten the text and add more details in depth. – user3834916 Oct 20 '14 at 16:22
• I do not work with pGLS but this problem type could be solved via canonical multivariate approaches or ordination followed by regression on the principal axes. Have you considered that? Also, NTSYSpc seems to have a trial version you could use. – katya Oct 21 '14 at 16:46
• Thank you for your response! I recently found that trial myself and have also located a few other papers that may be of significant use. I'll look into the approaches you recommended as well (but the lack of independence among taxa needs to be accounted for). – user3834916 Oct 23 '14 at 18:11
• Can I ask what your response variable is? It might make sense to use Dean Adams D-PGLS approach, but only if the set of variables actually represents a multidimensional trait (such as shape). If you want to make inferences about how your predictors relate to specific response variables, then you should just do separate PGLS regressions for each response variable. If you do end up using PGLS, I'd recommend checking out the caper package. I'm not familiar with the package you mention there, but caper is very widely used and effective. – Slow loris May 10 '16 at 4:30