-------- Original Message --------
Subject: Re: multiple correlated variables
Date: Mon, 25 Feb 2008 17:16:01 -0800 (PST)
From: Joseph Kunkel <[EMAIL PROTECTED]>
To: [email protected]
CC: Joseph Kunkel <[EMAIL PROTECTED]>
References: <[EMAIL PROTECTED]>
Jason,
The appropriate approach is Analysis of Dispersion which is the
multivariate extension of Analysis of Variance. It allows multiple Yi
observations that may be correlated via a Cov(Yi,Yj) covariance
matrix. These are related to a traditional X design matrix via the
generalized matrix equation Y = XB where Y is n by p for p dependent
characters and sample size n. X is n by k for k design elements or
independent variables. That results in a k by p matrix of parameters,
B, to be estimated.
One can ask the question for design feature q, a portion of the k
design elements:
Given characters say 1 to 10 of the p available, if characters 1-5 are
corrected for characters 6-10 is there any additional information in
1-5 that is significant on the design feature q. This type of
question answers your query of whether one variable or a set of
variables is more important or more predictive than another set and
answers it with an F-test.
I have a set of R-scripts that carry out this analysis if you are
willing to use the Gnu Public R calculation environment and are
somewhat familiar with setting up the X design matrices. I have not
seen another convenient implementation of this although I am sure it
can be found somewhere else.
Analysis of Dispersion is well described in C. Radhakrishna Rao (1965)
Linear Statistical Inference and Its Applications, 1st Edition.
Joe Kunkel
[EMAIL PROTECTED]
On Feb 25, 2008, at 11:30 AM, morphmet wrote:
-------- Original Message --------
Subject: multiple correlated variables
Date: Sun, 24 Feb 2008 04:48:15 -0800 (PST)
From: Jason S <[EMAIL PROTECTED]>
To: [email protected]
Dear all,
I have a quick question, and I'd love to hear any suggestions you
might
have.
I got one dependent variable (body size) and several independent
variables, and I'm trying to figure out which independent variable is
more important in explaining variation in the dependent one
(experiments
are not feasible). The problem is that many of the independent
variables
are themselves highly correlated. I thought about calculating partial
correlation coefficients, but I'm not very confident with that choice.
Any suggestions?
Thanks a lot!
Jason
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Joseph G. Kunkel, Professor
Biology Department
University of Massachusetts Amherst
Amherst MA 01003
http://www.bio.umass.edu/biology/kunkel/
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