Can compositional data (percentages) be used in the explanatory data matrix of an RDA or CCA?

Question

I would like to know if compositional data (percentage) can be used in the explanatory data matrix of a redundancy analysis (RDA) or canonical correspondance analysis (CCA) (not to be confused with canonical correlation analysis). I appologize if this question has already been asked but I have searched the web far and wide and have yet to find an answer...

Here is a little background info: My objective is to determine which environmental variables explain my species abundances. So there is one response matrix and one explanatory matrix.

My first matrix is composed of species abundance (that I plan to transform using the Hellinger transfomration as suggested by Legendre & Legendre 2012). This is my response matrix, it has sites as rows, and species as columns. My second matrix contains the proportions of every habitat type found in a 100m buffer around my sampling sites (my explanatory matrix). Here the rows are once again the sites, but the columns are the proportions of the different habitat types.

I've read that centered log ratio transformation might be the way to go to eliminate problems of colinearity within my environmental data (Aitchison, 1986) but I still haven't read anywhere that this is a valid method for RDA or CCA. Also if this is a valid method can I include other environmental variables in my analysis?

Any hints will be appreciated.

Answer 1

Yes, you can use "compositional" or percentage data as explanatory variables in your explanatory matrix for RDA or CCA. And yes, you can introduce other environmental variables in your analysis, all you need to do is center and scale your matrices (i.e. both your explanatory and response matrix has to have mean zero and variance 1, see van den Wollenberg, 1977 and Legendre, 2012).

You may want to consider using the package sRDA for R which centers and scales your matrices automatically.

My first matrix is composed of species abundance (that I plan to transform using the Hellinger transfomration as suggested by Legendre & Legendre 2012). This is my response matrix, it has sites as rows, and species as columns. My second matrix contains the proportions of every habitat type found in a 100m buffer around my sampling sites (my explanatory matrix). Here the rows are once again the sites, but the columns are the proportions of the different habitat types.

Since your rows are the sites in both matrices, with RDA you will show the variance explained in the species (your response variables) by the proportions of the different habitat types (your explanatory variables).

Good luck!

References

• Legendre, P. & Legendre, L., 2012. Numerical ecology
• van den Wollenberg, A.L., 1977. Redundancy analysis an alternative for canonical correlation analysis. Psychometrika, 42(2), pp.207–219.