# canonical correlation:results (fwd)

From: Agustin Lobo (alobo@ija.csic.es)
Date: Tue Jan 19 1999 - 16:18:01 MET

I'm not geting too many answers to this message
in the ordnews list, maybe somebody in the ADElist
could be interested?

Dr. Agustin Lobo
Instituto de Ciencias de la Tierra (CSIC)
Lluis Sole Sabaris s/n
08028 Barcelona SPAIN
tel 34 93409 5410
fax 34 93411 0012
alobo@ija.csic.es
http://pangea.ija.csic.es/alobo

---------- Forwarded message ----------
Date: Fri, 8 Jan 1999 18:18:36 +0100 (MET)
From: Agustin Lobo <alobo@ija.csic.es>
To: ordnews@colostate.edu
Subject: canonical correlation:results (fwd)

Hi!

Although I'm also reading the papers
suggested by Warren Sarle on
"maximum redundancy analysis", "principal
components of instrumental variables", or "simultaneous linear
prediction." and plan to
use this approach as well, I'm now using canonical
correlation analysis in the following way. Please

I have a set of p "predictor variables" in a matrix X,
and a set of q "response variables" in a matrix Y
with p < q
and for n observations (n >>> p).

I run a canonical analysis in Splus (using cancor, actualy
I have to review that function)

which yields two transformation matrices
which I use to obtain the transformed matrices
X.can and Y.can

I verify that the inverse transformation yields
the original X and Y (o.k, kind of paranoic).

I also verify that the inverse transformation
with only the first 3 components of Y.can produces
a reasonable estimation of Y.

My goal is to predict another set of
responses, Y', from another set of observed
variables, X', according to the following path:

1. Calculate X.can and Y.can as explained above.
2. Calculate the linear regresions between X.can
and Y.can
3. Calculate X'.can by applying the transform to X'.
4. Estimate Y'.can from the regression lines calculated in 2.
5. Calculate Y' by applying the inverse transform to Y'.can

Opinions?

The result is not great. I think this is because only the
first X.can and Y.can (Y.can[,1] and X.can[,1]) have a good
linear correlation, and thus the rest of Y'.can
(Y´can[,2:q]) are not well estimated.

My feeling is that I could do much better because
the cancor approach also implies that the eigenvalues
from whence the transforms for X.can and Y.can come
are the same, but how to use that information?. I mean that somehow
regressions from X.can to Y.can.

Dr. Agustin Lobo
Instituto de Ciencias de la Tierra (CSIC)
Lluis Sole Sabaris s/n
08028 Barcelona SPAIN
tel 34 93409 5410
fax 34 93411 0012
alobo@ija.csic.es
http://pangea.ija.csic.es/alobo

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