[R] RDA and trend surface regression

[Jari Oksanen]

On 27 Feb 2007, at 20:55, Gavin Simpson wrote:

> On Tue, 2007-02-27 at 13:13 -0500, Kuhn, Max wrote:
>> Helene,
>>
>> My point was only that RDA may fit a quadratic model for the terms
>> specified in your model. The terms that you had specified were already
>> higher order polynomials (some cubic). So a QDA classifier with the
>> model terms that you specified my be a fifth order polynomial in the
>> original data. I don't know the reference you cite or even the
>> subject-matter specifics. I'm just a simple cave man (for you SNL 
>> fans).
>> But I do know that there are more reliable ways to get nonlinear
>> classification boundaries than using x^5.
>
> I doubt that Helene is trying to do a classification - unless you
> consider classification to mean that all rows/samples are in different
> groups (i.e. n samples therefore n groups) - which is how RDA
> (Redundancy Analysis) is used in ecology.
>
> You could take a look at multispati in package ade4 for a different way
> to handle spatial constraints. There is also the principle coordinates
> analysis of neighbour matrices (PCNM) method - not sure this is coded
> anywhere in R yet though. Here are two references that may be useful:
>
Stéphane Dray has R code for finding PCNM matrices. Google for his 
name: it's not that common. I also have a copy of his function and can 
send it if really needed, but it may be better to check Dray's page 
first. Stéphane Dray says think that not all functions need be in CRAN. 
May be true, but I think it might help many people.

There are at least three reasons why not use polynomial constraints in 
RDA. Max Kuhn mentioned one: polynomials typically flip wildly at 
margins (or they are unstable in more neutral speech). Second reason is 
that they are almost impossible to interpret in ordination display. The 
third reason is that RDA (or CCA) avoid some ordination artefacts 
(curvature, horseshoe, arc etc.) just because the constraints are 
linear: allowing them to be curved allows curved solutions. These 
arguments are not necessarily valid if you only want to have variance 
partitioning, or if you use polynomial conditions ("partial out" 
polynomial effects in Canoco language). In that case it may make sense 
to use quadratic (or polynomial) constraints or conditions.

cheers, Jari Oksanen