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


From   "Austin Nichols" <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: z-score as a dependent variable in a linear regression
Date   Wed, 14 Nov 2007 19:46:33 -0500

Dan Weitzenfeld <dan.weitzenfeld@emsense.com>:
Using z-scores or similarly transformed data as a depvar in a linear
regression (etc.) is common in education research.  If you have ever
seen an impact on test scores, it comes from a model like that (almost
all test scores are converted from number right to something like a
z-score, if not actually a z-score).  If you search the web for
"effect size" or "IRT" you may see what I mean.

The only thing that worries me is that you seem to be computing the
mean and standard deviation for each individual from some baseline
data, and depending on your application, that may be problematic.  You
may be better off with a panel model.  Or quantile regression.  Sadly,
there is no -xtqreg- yet. But stay tuned--one may be on the horizon.

On 11/14/07, Dan Weitzenfeld <dan.weitzenfeld@emsense.com> wrote:
> 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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