[R-sig-eco] Data transformation prior to RDA

[Jari Oksanen]

Dear Devoto Mariano,

On 20/04/10 02:02 AM, "Devoto Mariano" <mdevoto at agro.uba.ar> wrote:

> Dear all,
> I'm trying to do a redundancy analysis. I'm following Legendre & Legendre's
> (1998) tips to prepare the data prior to the analysis, and I´m hoping to do
> the analysis using package 'vegan'.
> I've already centered and standardized my explanatory and response
> variables,

You do not need to do this in vegan. Vegan uses methods that cope nicely
with non-centred constraints in original scale. Pierre Legendre explains the
"projection matrix" method where centring is necessary and standardization
useful, but vegan uses different methods (QR decomposition).
 
> but I'm having trouble at deciding whether or not (and how) data
> should be transformed "to linearise the relationships and make the
> distributions more symmetric". Is there a way to find the best possible
> transformation for each variable but considering at the same time its
> linearity to the other ones? Please tell me if I'm not even asking the right
> question here...

This is a difficult question, and there is no easy answer. RDA is basically
a linear method and linear combination scores (LC scores) indeed are linear
combinations of constraints. Nonlinear transformation will change the LC
scores and hence the ordination. Selecting an optimal transformation for
multivariate explanatory variables (constraints) for multivariate response
(species) is a tricky thing, and people usually do not try to do this. I
have no idea how to do this. For instance, I have no idea what would be a
criterion of "good" model -- the only thing I'm sure is that goodness of fit
(eigenvalue) is not a good criterion. What you may be do is to inspect the
constraints by pairs() plots, and see if there are some strange distribution
patterns in pairwise panels. It is a completely different question than
having a good linear relationship between your joint constraints
simultaneously to all species simultaneously, though.

If you intended to ask about transformation of species data, read the other
answers.

Cheers, Jari Oksanen