Date:         Wed, 23 Feb 2005 20:34:32 -0500
Reply-To:     Talbot Michael Katz <topkatz@MSN.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Talbot Michael Katz <topkatz@MSN.COM>
Subject:      Relative Importance of Explanatory Variables,
              Standardized Coefficients, STB option, etc.

Hi.

I'm gathering opinions, facts, anecdotes, etc., and what better place to
start than with SAS-L?  Today's number one question is this:

What is the "best" way to measure the relative importance of explanatory
variables in a model when the model includes class variables?

Let's start with OLS.  Textbooks often say that the standardized regression
coefficients ("betas") measure the relative importance, and that's an
appealingly intuitive picture; if all the variables are placed on the same
scale, then the betas show the effects of a unit change in any of the
variables.  This is even reasonable for logistic models.  The SAS
regression procedures will output the betas if the STB option is requested
(the Enterprise Miner regression node outputs "Standardized Estimates" as a
matter of course).  However, it is documented in SAS and has been remarked
in other threads here, that betas are not computed for class variables,
which is reasonable because class variables cannot be standardized to the
normal distribution.  But certainly the concept of relative importance
should still apply to class variables, so how do you measure it?  This
question is particularly resonant for Enterprise Miner users, since the
variable selection node tends to turn all significant variables into class
variables.

I have been using the square roots of the Wald chi-square values (I call
them "Wald t values," but I don't know if that's widely accepted
terminology).  For a univariate regression model, I believe this t value is
equal to the beta value, so it seems like a reasonable proxy.  Do you
agree?  Do you have any other ideas?  I found a paper from the journal,
Decision Sciences, that studies this issue in more depth (the authors don't
like the use of betas or t values or p values, etc., for measuring relative
importance): (http://home.wi.rr.com/jjrr/dsj.pdf) "A Framework for
Measuring the Importance of Variables with Applications to Management
Research and Decision Models," E.S. Soofi, J.J. Retzer, M. Yasai-Ardekani,
Decision Sciences, Volume 31, Number 3, Summer 2000.

Thanks!

--  TMK  --
"The Macro Klutz"