# Contribution of variables on axis in PCoA

I am trying to analyze data using Principal Coordinates Analysis (Classical Multidimensional Scaling (CMDS)) in R. I've tried some different ways (i.e., pcoa {ape}, cmdscale, capscale {vegan}).

I've found that the results are the same and the plots look fine. But, I need some numbers saying how much does every original variable contribute to my axis (principle coordinates). So I am asking how the new dimensions relate to the original variables?

I've learned that:

Information concerning the original variables cannot be recovered.This is because PCoA takes a (dis)similarity matrix derived from the original data as input and not the original variables themselves. However, object scores along the PCoA axes may be correlated with object scores along each original variable's axis, assuming the these are either quantitative or dummy variables. This may be used as a measure of the original variables' contribution to a given PCoA axis.

But I am still not sure how to do it. Can you help me with this?

I am using this code for PCoA:

res3 <- capscale(data~1, distance="gower")


My data looks like this (F and width are continuous, vol and obj are binary, and rt is a multi-level categorical variable):

place    F     width  vol  obj  rt
A       -0.05   17.1  1    0    2
B        0.03   13.5  1    0    0
C        0.13   62.2  1    1    1
D        0.43   9.5   1    0    2

• Do you need the locations of the points in the new coordinate system, or are you asking how the new dimensions relate to the original variables? Can you provide a small example dataset for people to work with? – gung - Reinstate Monica Aug 2 '17 at 12:27
• I added how the data looks like. And I am trying to find out how the new dimensions relate to the original variables. – Terka Dračková Aug 2 '17 at 13:09
• What are these variables? You list that you are using Gower's distance, so I'm guessing that some of these are continuous, & some are categorical, etc. – gung - Reinstate Monica Aug 2 '17 at 13:47
• Yes, the first two columns are continuous, vol and obj are binary and rt is categorical. Now I am thinking about using NMDS, because I read that Gower isn't metric. But I am not sure about it and my question remains. – Terka Dračková Aug 2 '17 at 14:04
• I'm having a similar issue, did you solve this? – Matias Andina Oct 11 '18 at 20:54