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From: saswss@hotellng.unx.sas.com (Warren Sarle)
Subject: Re: Input Variable Contribution
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Date: Fri, 28 Jun 1996 02:57:18 GMT
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References: <31C1A2EE.274E@wvu.edu> <31C3B219.4DE0@cs.ucdavis.edu> <31C6F5B7.135C@mail.ddnet.es> <4qiojn$3q@sjx-ixn3.ix.netcom.com> <biocomp.22.02BE9E80@biocomp.seanet.com> <4qtj1g$h1s@yama.mcc.ac.uk>
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In article <4qtj1g$h1s@yama.mcc.ac.uk>, Simon Read <s.read@cranfield.ac.uk> writes:
|> CC: biocomp@biocomp.seanet.com (Carl M. Cook)
|> CC> Thus for each record in a data set, hold all inputs at the values in that 
|> CC> record then step up and down each variable by a user specified percentage
|> CC> and measure the effect. ...
|> -->
|> Interesting. I myself have needed some sort of technique like this.
|> Is there anywhere that the above results are published?

If the steps up and down are small, and you divide the change in the
output by the size of the step, what you get is a finite-difference
approximation to the partial derivative of the output with respect
to the input (see any calculus textbook). In a linear model, these
partial derivatives are equal to the weights (aka regression
coefficients--see any regression textbook). The regression coefficients
are one of numerous measures of input variable contribution--see:

  Darlington, R.B. (1968), "Multiple Regression in Psychological Research
  and Practice," Psychological Bulletin, 69, 161-182.


-- 

Warren S. Sarle       SAS Institute Inc.   The opinions expressed here
saswss@unx.sas.com    SAS Campus Drive     are mine and not necessarily
(919) 677-8000        Cary, NC 27513, USA  those of SAS Institute.
