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*>I have been trying to prepare data tables for RLQ analysis. A weighted COA
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*>of my R table (394 rows, 3 columns) using a file.fcpl produced from COA of
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*>the L table repeatedly fails. Introducing a dummy fourth column allows the
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*>weighted COA of R to proceed. So the problem appears to be related to
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*>column number in R. Why?
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*>
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*>We have got round the problem by weighting the R table in Excel and
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*>proceeding with an unweighted COA. Is this valid?
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*>
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*>The attached file contains more information on the data matrices.
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Dear Matthew,

It seems that analysing your table R with a weighted COA is a wrong option.

This table contain quantitative data (decimals and integers) and it should

be analyzed by PCA (normalized if the variance of the three variables are

too different) and weighted by file.fcpl as indicated. Did you try PCA on

this table?

This question is the occasion for reminding some general aspects of what is

called RLQ analysis in ADE-4 which were proposed in a former mail.

Let F be a faunistic table with n rows-samples and p columns-species

Let M be an environmental table with n rows-samples and v columns-variables

Let B be a table that contains some biological information on the species

and and p columns-species

alors il existe un tableau Q croisant les trois avec t lignes-traits et p

colonnes-espèces

If M and B contains dummy variables the matrix Q = BFtM simply contains the

contingency table that crosses the modalities of the environmental

variables and the modalities of the biological traits.

This particular situation was addressed by P. Legendre and coauthors with

the so-called fourth-corner problem (Legendre, P., Galzin, R. &

Harmelin-Vivien, M.L. (1997) Relating behavior to habitat: Solutions to the

fourth-corner problem. Ecology, 78, 547-562). The authors further proposed

some permutation tests to check for the significance of the link between M

and B through F.

In ADE-4, RLQ analysis helps to explore the relationship between M and B

through F using a broader numerical context since M and B may contain

quantitative, dummy or fuzzy variables. Before performing a RLQ analysis,

each table should be processed as follows:

F must be processed by a correspondence analysis (COA)

M can be analysed by any type of one-table analysis (PCA, MCA, FCA) using

the row weight of F

B can be analysed by any type of one-table analysis (PCA, MCA, FCA) using

the column weight of F

RLQ analysis then incorporates the following sequence:

RLQ : Prepare -> to match the three previous analyses

RLQ : RLQ test - Fixed L -> to test the relationship between M and B

through F using random permutations. Note that F remains fixed. Another

option should be to fix M and B and permute randomly F (See Legendre et al.

1997).

RLQ : Diagonalize -> to analyse the fourth corner matrix

RLQ : Coinertia analysis -> to display the scores and various

interpretation aids

The name RLQ is thus justified by using R for a table analysed in R-mode

and Q for a table analysed in Q-mode. L stands for Link (Link table).

All the general theory is available in Dolédec, S., Chessel, D., Ter Braak,

C.J.F. & Champely, S. (1996) Matching species traits to environmental

variables: a new three-table ordination method. Environmental and

Ecological Statistics : 3, 143-166. In this general theory the matching of

two MCAs through a COA (as used in the example of the paper) is considered

a particular case of RLQ thus meaning that this approach is far from being

completed.

All the very best,

Sylvain Dolédec

_____________________________________________

Sylvain Dolédec

Université Claude Bernard - Lyon 1

43 Bd du 11 novembre

Bat 401C - 2ème étage

F-69622 Villeurbanne CEDEX

Tel : +33 4 72 43 13 63

Fax : +33 4 72 43 11 41

_____________________________________________

ADE-4 package is available on the Internet

--> http://pbil.univ-lyon1.fr/ADE-4/

_____________________________________________

**Next message:**Christian Barnabé : "MCA et genetique des populations"**Previous message:**Daniel Chessel: "Re: diagnostics for choosing response models"**Maybe in reply to:**Matthew O'Hare: "Problem: Weighted COA of 3 column file"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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