[19226] in s-news-athena
Re: [S] Comparing the fit of least squares models
daemon@ATHENA.MIT.EDU (Viswanath Devanarayan)
Tue Sep 14 18:36:14 1999
Date: Tue, 14 Sep 1999 17:31:23 -0500
From: Viswanath Devanarayan <DEVANARAYAN_VISWANATH@lilly.com>
To: jay <jay@v4.wustl.edu>
Cc: s-news@wubios.wustl.edu
Message-Id: <052567EC.007BB676.00@aammta1.d51.lilly.com>
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The simplest approach would be to use the concordance-correlation-coefficient
(of the fitted versus observed values) as described in the book by Vonesh and
Chinchilli (Linear and Nonlinear Models for the Analysis of Repeated
Measurement
Data, Marcel-Dekker, 1997). It is a non-likelihood based approach, and is a
nice
and quick way to compare goodness of fits. This can be easily implemented
in Splus.
Devan
jay <jay@v4.wustl.edu> on 09/14/99 02:07:54 PM
To: jay@v4.wustl.edu, s-news@wubios.wustl.edu
cc:
Subject: [S] Comparing the fit of least squares models
Hi,
I have a question of how to evaluate the fits of several
linear and non-linear models to the same data set. In particular,
I'd like to compare the outputs of the S+ functions lm(), lme()
and nls(), all of which use the least squares method.
The data in question are responses of nerve cells to visual
stimulation at two different levels of brightness, as shown by the
following dummy data:
Responses at Brightness Level
__________________________________
B1 B2
__________________________________
Stimulus
S1 12.6 27.9
S2 17.0 30.1
S3 14.3 44.5
S4 19.9 35.7
. . .
. . .
. . .
Sn 14.2 48.9
Both S and B are continuous variables. I have the full data
set for N number of (mutually independent) cells. I'd like to determine,
for each cell INDIVIDUALLY, which of the following three models best
describes the relationship between B1 and B2:
Model #1. lm(B2 ~ B1)
Model #2. lme(B2 ~ B1, cluster = Stimulus)
Model #3. nls(B2 ~ B1*exp(x), start=list(x=2))
In Model #2 above, clustering according Stimulus is justifiable for
reasons that are quite involved.
Now my problems are as follows:
(1) What's a good QUANTITATIVE way of deciding which of the
above models, if any, best fits the behavior of A GIVEN CELL?
(2) Since all of the above are least-squares methods, I'd
naively think that comparing the corresponding multiple R-squared terms
is a good way (when appropriate F-values etc. check out) of comparing the
fit by different models. Is that correct?
(3) Are there any good references on this specific issue of
comparing the fit of different models to the same data set?
Thank you very much.
Jay Hegde
Washington University School of Medicine
St. Louis, MO 63110
jay@v1.wustl.edu
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