Newsgroups: bit.listserv.psycgrad
Date:         Tue, 12 Jan 1993 14:48:25 -0800
              <PSYCGRAD@UOTTAWA.BITNET>
From:         Unabashedly Egregiously Prolix <tbn@UTXVM.CC.UTEXAS.EDU>
Subject:      Re: Regression Question (long)

>Hi, Everyone!
>
>For about a month now, I've been quietly listening in on your
>discussions, and I'd like to introduce myself and request some
>statistics advice.  This is my first year in the organizational behavior
>program at Carnegie-Mellon University (in Pittsburgh).  I did my
>undergrad studies at the University of Washington (Seattle) in
>psychology.  And I don't know nearly enough about statistics yet.
>(But I do think it's important that we become competent in a variety of
>statistical methods).

Yaaay! :-)

>
>My problem is this:  If you have several groups of kids, and you are
>using measures of individual and group performance as predictors of
>subsequent attitudes toward that subject, how do you put them together
>in a regression model?

The way I would attack this problem in regression is to ask myself, "Okay,
what are my central questions? That is, what hypotheses am I most
interested in testing?" If you are willing to assume that the group and
individual predictors are orthogonal (i.e., independent of one another),
then I'd say you were justified in entering each one as separate terms in a
multiple regression analysis. Then you could talk about an effect of group
performance and an effect of individual performance on the attitude DV.

One problem that you may have to tackle is the multicollinearity issue that
John alluded to in his posting. If group performance is somehow *dependent*
on individual performance (or vice versa), then correlated predictors
(multicollinearity) can be a problem, although I seem to remember reading
somewhere or other (Psych Bulletin?) that with modern estimation methods
which the stat programs such as SAS and SPSS employ, unless you have huge
correlations between your predictors, multicollinearity isn't the bugaboo
(problem) it used to be.

>There will be lots of individual scores, but
>only a few group scores.  It doesn't seem quite fair to enter the group
>score for each individual (because you might have five actual group
>scores, but they would go into the regression as thirty observations).

Well, yes, except that each person gets a group score based on his/her
performance (along with everyone else's) to the group, so in effect each
participant does have a "unique group score".

>I can't use dummy variables for group membership because the ratio of
>the scores may be important.

As John said, I find this confusing as well.

>  Has anybody dealt with this kind of
>individual/group analysis problem?  I would really appreciate any
>suggestions.
>
>Thanks a bunch!
>
>Debbie Gibbons

One way you could go about this problem is to treat it from a general
linear modeling perspective and ask yourself, "What specific hypotheses am
I interested in testing?" and construct separate full vs. restricted models
and test them, as one can do with the TEST statement in SAS's PROC REG. For
example, for a full model you could have both the group and the individual
level performance variables included (2 predictor model) and compare that
model to the restricted model of individual level performance (one
predictor model). If you get a statistically significant F-ratio from the
TEST in PROC REG, it tells you that by imposing the restriction of group
level performance equaling zero (i.e., for all practical intents and
purposes, not including it in the model), you've rejected the null
hypothesis that the restricted model (individual level performance only)
works as well as the full model (group *and* individual level performance
predictors included) in the population from which you drew your sample.
That test would answer the question, "Does group level performance add
anything significant to the prediction of attitudes, above and beyond that
contribution made by individual level performance?"

I hope this hasn't been horribly confusing. I guess I like the general
linear modeling approach (even though it gives me headaches sometimes)
because it really forces the investigator to specify the tests/hypotheses
of interest ahead of time before the actual regression models are
constructed.

Best of luck with your analyses!

cheers,

Tor


Tor Neilands
Systems Analyst
Statistical Services Group
Computation Center
University of Texas at Austin

Internet:  TBN@Utxvm.cc.utexas.edu
___________________________________________________

"Should they whisper false of you,
    Never trouble to deny;
 Should the words they say be true,
    Weep and storm and swear they lie".
                                                   --- Dorothy Parker

"Two roads diverged in a yellow wood and I, I took
 the road less traveled by, and that has made all the
 difference".                                 --- Robert Frost
___________________________________________________

Disclaimer:  All of the views expressed above are solely
those of the author. Any relationship between my own
views and those of the University of Texas and/or The
Computation Center at the University of Texas are
due merely to regression to the mean.
____________________________________________________
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