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st: z-score as a dependent variable in a linear regression


From   "Dan Weitzenfeld" <dan.weitzenfeld@emsense.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: z-score as a dependent variable in a linear regression
Date   Wed, 14 Nov 2007 16:10:29 -0800

Dear Stata Users and Abusers,

In general, is it kosher to use a z-score as a dependent variable in a
linear regression?  Is it "better" to use some sort of ratio
measurement?

I've reviewed the assumptions of OLS, etc., and I can't find a glaring
objection to using a z-score as a dependent variable in a linear
regression.  However, it feels strange, especially because the units
of a z-score are not uniform, in that the difference in probability
between a z-scores 0 and .5 is not the same as the difference in
probability beween z-scores .5 and 1.  In other words, I feel that by
using the z-score, I am not giving adequate weight to observations
with very high and very low z-scores.

Why not use the underlying measurement that was used to derive
z-score, you ask?  Each individual has a unique baseline and
variation, so in order to compare individual responses to my stimuli,
I need to put everybody on the same scale.

Any feedback or direction to reading material would be helpful.

Thank you,
Dan
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