Date:         Fri, 22 Feb 2002 06:46:54 GMT
Reply-To:     Jeremy Fox <jerfox@STANFORD.EDU>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         Jeremy Fox <jerfox@STANFORD.EDU>
Subject:      Re: proc GLM?

Dale McLerran <stringplayer_2@yahoo.com> wrote:

: As Olaf Kruse has stated, you can fit the OLS model without problem,
: but if you wish to interpret p-values or generate confidence intervals
: (flip sides of the same coin), then you have to assume normality.

Well, not if you believe in asymptotic theory, but I will cede you
your point.

: There are several problems here.  First, the tests are undoubtedly
: NOT independent of each other.

Obviously.

:  If they are not independent, then
: a summary statement that 15 out of 90 tests were significant at p<.05
: has no meaning.

It means for each of those tests individually there is less than 1 in
20 chance that the null hypothesis is true.

: For an ordered response coded (1,2,3,4), you may have a tough time
: fitting an appropriate joint model.  What is your joint model and
: how do you fit it?  (I can think of a couple of different methods,
: but want to assess what you would do.)

I would fit a seemingly unrelated regression (SUR) model where all of
the dependent variables are the 90 different responses. This is just
estimated by stacking the 90 equations and running GLS.

Now the problem becomes is that there is a very surprising
mathematical result that if all the regressors in each equation are
the same, then SUR is equivalent (I think numerically!) to equation by
equation OLS. This leads me to believe that accounting for dependence
across equations is not helpful in a linear regression setting where
the covariates are going to be the same in each equation.

The original poster just seems to have two covariates, time and
treatment. Running proc glm 90 times (one for each response) seems
good to me. This would account for any differences in the mean
response for each category that is consistent across time and
treatment groups.

--
------------------------
Jeremy T. Fox
jerfox@stanford.edu