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John,

I am not a specialist but there is a place to ask this question, which

is a discussion list specially devoted to multivariate data analysis:

majordomo@biomserv.univ-lyon1.fr to join the list and

adelist@biomserv.univ-lyon1.fr to ask the question

you will find all the details at the web site

http://pbil.univ-lyon1.fr/ADE-4/ (see there how to join the list)

and there is a FREE gorgeous software (in English !!!) with a huge

documentation, datasets and analysed examples. However, it's a whole

world and analysis are not always that simple...

Moreover, these people do like S-Plus !...

Hope this helps,

Renaud

John Balding a écrit :

*>
*

*> The questions I have are only loosely related to S-PLUS, but since I am
*

*> using S-PLUS (4.5R2 for win95) to do the work I thought this might be a
*

*> good place to ask anyways. Answers on this list tend also to be much
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*> more helpful than those on the statistics newsgroups!
*

*>
*

*> I've been left to figure out a consultant's report commissioned in the
*

*> early eighties. This report dealt with the prediction of levels of a
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*> number of stream pollutants from measures of discharge, rainfall, and
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*> other climate variables. Among the techniques employed was canonical
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*> correlation analysis. Because the audience was originally
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*> semi-technical, none of the equations were outlined in the report;
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*> unfortunately the person who authored the report has since passed away.
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*> I am left with the task of trying to see which of the techniques in the
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*> report might be valid for data from a number of watersheds we've since
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*> started monitoring. As luck would have it, I have almost no experience
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*> with CCA at all (although the other methods were relatively easy to
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*> understand).
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*>
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*> Both predictors and predictands were preprocessed using PCA and the
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*> resulting standardized scores used in the CCA. The CCA was performed on
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*> the correlation matrices, not the covariance matrices as seems to be the
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*> default in the S-PLUS cancor() routine. Because of my newness to CCA I
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*> decided to work through an example in Green's Analyzing Multivariate
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*> Data before tackling the report. I think I now have a basic grasp of the
*

*> technique and roughly know what each of the resulting matrices means...
*

*> unfortunately I can't figure out how one goes about predicting values of
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*> the predictands from new values of the predictors. What is the matrix
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*> equation for doing this?
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*>
*

*> I have
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*>
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*> 1) the standardized predictor and predictand variables Xs and Ys
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*> (arranged in columns)
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*> 2) the correlation matrices Rxx, Ryy, Rxy, and Ryx
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*> 3) the matrix product F = Rxx^-1 Rxy Ryy^-1 Ryx
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*> 4) the diagonal matrix of eigenvalues D and the eigenvectors V of F
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*> 5) the diagonal matrix of canonical correlations M (ie. D^0.5)
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*> 6) the canonical weights matrices A and B (scaled such that A' Ryy A =
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*> I, and B' Rxx B = I)
*

*> 7) the canonical loadings G = Ryy A and H = Rxx B
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*> 8) the canonical variate scores T = Ys A and U = Xs B
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*>
*

*> Now how do I get from Xs(new) to Ys(new)? I would also like to be able
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*> to select the number of canonical variates to be used in the final
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*> prediction equation (much like selecting the number of PCs to use, I
*

*> would assume). I know there must be a very simple matrix equation for
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*> predicting values of the predictands from values of the predictors using
*

*> the results of CCA. I just need a little help!
*

*>
*

*> Thank you very much,
*

*>
*

*> John
*

*>
*

*> ______________________________________________________
*

*> Get Your Private, Free Email at http://www.hotmail.com
*

*> -----------------------------------------------------------------------
*

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*

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*

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*

-- Renaud Lancelot ISRA-LNERV BP 2057 Dakar-Hann Senegal tel (00 221) 832 49 02 work (00 221) 824 57 12 home fax (00 221) 821 18 79 (CIRAD) http://www.cirad.fr

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