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# st: MANCOVA versus Zellner's SUR

 From "Joseph Coveney" To "Statalist" Subject st: MANCOVA versus Zellner's SUR Date Sun, 4 Nov 2007 14:39:52 -0800

```Two response variables are each measured at baseline and again after
treatment in a study with random allocation to treatment groups.  I would
like to use the baseline measurements as covariates in a multivariate
analysis.  Does anyone have a recommendation as to whether -manova-
or -sureg- would be more appropriate here?

Using -left- and -right- as the response variables and -treatment- as the
indicator variable for treatment group, the commands would be analogous to

manova left_after right_after = treatment left_before right_before, ///
category(treatment)

and

sureg (left_after = treatment left_before) ///
(right_after = treatment right_before), isure small dfk
test treatment // treatment is 0/1, i.e., only two groups

(with correction of the denominator degrees of freedom reported with -test-
after -sureg-).

The two baseline measurements are certainly not orthogonal predictors, and
are not even on the same scale (they're actually more like apples and
oranges than left and right).  So, it bothers me somehow that, with
MANCOVA, -left_after- is regressed on -right_before- and vice versa.  Should
I be concerned?  SUR does appear to take care of that (I don't know about
the linear algebra under the hood, however).  But SUR doesn't seem quite so
efficient as MANCOVA in simulations.  Is there a reason to choose one over
the other on the basis of expected intraclass correlation coefficients, that
is, if the correlation of left and right exceeds that of before and after?

In addition, I have a concern about putting the two baseline measurements on
the right-hand side at all; each is nothing but a response variable measured
before treatment, and so is measured with error in the same magnitude as the
respective after-treatment response variable.  But putting them on the
left-hand side and testing for time-by-treatment interaction is not very
efficient.

matrix define M = (-1, 1, 0, 0 \ 0, 0, -1, 1)
matrix define C = (0, -1, 1)
manova left_before left_after right_before right_after = treatment
manovatest , test(C) ytransform(M)

Is there a multivariate instrumental variables approach that I could use?

Joseph Coveney

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