# Re: How do I run RDA and pCCA?

From: Jean Thioulouse (Jean.Thioulouse@biomserv.univ-lyon1.fr)
Date: Tue Apr 03 2001 - 15:45:57 MEST

Leonard.Sandin@ma.slu.se wrote:
>I have started using ADE-4 which seems like an eccellent program for
>multivariate analysis of Ecological data. Since my french unfortunately is
>non existent I have a couple of "stupid" questions that I really hope that
>anyone can give me some short answers to. I have managed to run CCA in ADE
>and I understand that it is possible to run both RDA and partial CCA using
>the PCAIV module, I just canīt figure out how to do it. I have tried to
>understand what it says in the "Ordination sous contraintes" on page 28 and
>onwards but even if I know spanish I canīt figure it out.

First, did you read the Projectors module documentation (in english) ?

Partial CCA and RDA are fairly difficult methods, and not very often used.
The general principle is as follows:

We have a table X, with a first-level analysis :
- PCA: Correlation matrix PCA --> X.cnta
- COA: COrrespondence Analysis --> X.fcta
- MCA: Multiple Correspondence Analysis --> X.cmta
etc.

We want to do this analysis with a constraint. This constraint can be
positive (we want to see what is linked to the constraint) or negative
(removing an effect : we do not want to see what is linked to the constraint).

For exemple, we want to see what depends on time, or what is independent
from time. Or what depends on a second table Y, or what does NOT depend
on the variables of Y.
Or what depends on time but not on space, or on space and not on time.
etc.

This constraint comes from a table Y0 of artificial variables that form
an orthonormal basis of a subspace of Rn. Such tables can come from :

- a qualitative variable : Projectors: One Categ Var->Orthonormal Basis

- a raw table : Projectors: Table->Orthonormal Basis

- a first level analysis : Projectors: Triplet->Orthonormal Basis

- two qualitative variables : Projectors: Two Categ Var->Orthonormal Basis

- two tables Projectors: Intersection of 2 Subspaces
etc.

When the first table and the constraint are chosen, one can do two analyses :

- 1/ Projectors: PCA on Instrumental Variables to introduce a positive
constraint (analyse X to see what is linked to Y).

- 2/ Projectors: Orthogonal PCAIV to introduce a negative constraint
(analyse X after removing what is linked to Y).

Back to RDA and pCCA :

- RDA is the particular case where X is analysed by a Correlation matrix PCA,
with a positive constraint coming from the Correlation matrix PCA of Y.

- CCA is the particular case where X is analysed by correspondance analysis
(COA), with a positive constraint coming from the Correlation matrix PCA of Y.

- partial CCA is the particular case where X is analysed by correspondance
analysis (COA), with a positive constraint coming from the analysis of one
table, plus a negative constraint coming from the analysis of a second table.

- between and within class analyses (Discrimin: Between analysis: Run and
Discrimin: Within Analysis: Run) are particular cases of positive (between)
or negative (within) constraints coming from one qualitative variable.

See the exemples in the Projectors module documentation.

ADE-4 allows you to freely combine any number of positive and negative
constraints, starting from any kind of data table. Of course, only a very
small part of these possibilities corresponds to known methods... and for
unknown methods, you are on your own.

```--
Jean Thioulouse - Laboratoire de Biometrie et Biologie Evolutive
Universite Lyon 1 - Bat  711 - 69622 Villeurbanne Cedex - France
Fax: (33) 4 78 89 27 19              Tel/Fax: (33) 4 72 43 27 56
```

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