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Re: st: MANCOVA versus Zellner's SUR


From   "Joseph Coveney" <jcoveney@bigplanet.com>
To   "Statalist" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: MANCOVA versus Zellner's SUR
Date   Sun, 4 Nov 2007 18:56:56 -0800

Phil Schumm wrote:

You don't indicate what the objective(s) of the analysis are
(including what other covariates might be relevant), but wouldn't
another option here be to compute the differences (pre to post) for
each measure, and then look at how the joint distribution of those
differences differs between the treatment groups?  For starters, a
simple test of the null hypothesis that the mean differences are the
same (using, say, Hotelling's T-squared test) would presumably be
informative.

--------------------------------------------------------------------------------

Thanks for your reply, Phil.  The objective of the study is to determine
whether there is a difference between treatments with respect to outcome as
measured by the response vector.

There is one other covariate, a categorical one with two levels, on which
randomization is stratified.  Values for that variable, too, are expected to
correlate, albeit weakly, with values of the response variables, hence, the
stratified randomization.  Both -manova- and -sureg- can readily accommodate
the stratification variable:

manova L1 R1 = trt L0 R0 Stratum, category(trt Stratum)
sureg (L1 = trt L0 Stratum) (R1 = trt R0 Stratum), isure small dfk

The model will not contain any interaction terms.  I didn't think that this
stratification covariate is relevent to the matter of using baseline values
of the two response variables as covariates, and so didn't mention it.

The option that you mention, pre-to-post differences in Hotelling's
T-squared test, is identical to the MANOVA at the bottom of my post (the
MANOVA model for which time-by-treatment interaction was mentioned).  It
suffers from a fairly large decrease in efficiency (statistical power)
vis--vis the corresponding MANCOVA and SUR models described earlier in the
post.

Joseph Coveney


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