[R] RDA and trend surface regression

[Gavin Simpson]

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:

Dray, S., P. Legendre, and P. R. Peres- Neto. 2006. Spatial modeling: a
comprehensive framework for principal coordinate analysis of neighbor
matrices (PCNM). Ecological Modelling, in press.

Griffith, D. A., and P. R. Peres- Neto. 2006. Spatial modeling in
ecology: the flexibility of eigenfunction spatial analyses. Ecology, in
press.

HTH

G

> 
> If you want a quadratic model, I would suggest that you use QDA with the
> predictors in the original units (or see Hastie's book for a good
> example of using higher order terms with LDA). 
> 
> Looking at your email, you want a "a variation partitioning analyses".
> RDA works best as a classification technique. Perhaps a multivariate
> ANOVA model may be a more direct way to meet your needs. There is a
> connection between LDA and some multivariate linear models, but I don't
> know of a similar connection to RDA.
> 
> Max
> 
> -----Original Message-----
> From: MORLON [mailto:morlon.helene at gmail.com] 
> Sent: Tuesday, February 27, 2007 12:53 PM
> To: 'Jari Oksanen'; r-help at stat.math.ethz.ch
> Cc: Kuhn, Max
> Subject: RE: [R] RDA and trend surface regression
> 
> Thanks a lot for your answers,
> 
> I am concerned by your advice not to use polynomial constraints, or to
> use
> QDA instead of RDA. My final goal is to perform variation partitioning
> using
> partial RDA to assess the relative importance of environmental vs
> spatial
> variables. For the spatial analyses, trend surface analysis (polynomial
> constraints) is recommended in Legendre and Legendre 1998 (p739). Is
> there a
> better method to integrate space as an explanatory variable in a
> variation
> partitioning analyses? 
> 
> Also, I don't understand this: when I test for the significant
> contribution
> of monomials (forward elimination)
> 
> >anova(rda(Helling ~ I(x^2)+Condition(x)+Condition(y)))
> 
> performs the permutation test as expected, whereas 
> 
> >anova(rda(Helling ~ I(y^2)+Condition(x)+Condition(y)))
> 
> Returns this error message:
> 
> Error in "names<-.default"(`*tmp*`, value = "Model") : 
>         attempt to set an attribute on NULL
> 
> Thanks again for your help
> Kind regards,
> Helene
> 
> Helene MORLON
> University of California, Merced
> 
> -----Original Message-----
> From: Jari Oksanen [mailto:jarioksa at sun3.oulu.fi] 
> Sent: Monday, February 26, 2007 11:27 PM
> To: r-help at stat.math.ethz.ch
> Cc: morlon.helene at gmail.com
> Subject: [R] RDA and trend surface regression
> 
> 
> > 'm performing RDA on plant presence/absence data, constrained by
> > geographical locations. I'd like to constrain the RDA by the "extended
> > matrix of geographical coordinates" -ie the matrix of geographical
> > coordinates completed by adding all terms of a cubic trend surface
> > regression- . 
> > 
> > This is the command I use (package vegan):
> > 
> >  
> > 
> > >rda(Helling ~ x+y+x*y+x^2+y^2+x*y^2+y*x^2+x^3+y^3) 
> > 
> >  
> > 
> > where Helling is the matrix of Hellinger-transformed presence/absence
> data
> > 
> > The result returned by R is exactly the same as the one given by:
> > 
> >  
> > 
> > >anova(rda(Helling ~ x+y)
> > 
> >  
> > 
> > Ie the quadratic and cubic terms are not taken into account
> > 
> 
> You must *I*solate the polynomial terms with function I ("AsIs") so that
> they are not interpreted as formula operators:
> 
> rda(Helling ~ x + y + I(x*y) + I(x^2) + I(y^2) + I(x*y^2) + I(y*x^2) +
> I(x^3) + I(y^3))
> 
> If you don't have the interaction terms, then it is easier and better
> (numerically) to use poly():
> 
> rda(Helling ~ poly(x, 3) + poly(y, 3))
> 
> Another issue is that in my opinion using polynomial constraints is an
> Extremely Bad Idea(TM).
> 
> cheers, Jari Oksanen
> 
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