There are several reasons why the results won't be identical but the
most important one is likely the different (implicit) assumption
about the covariance of the 4 repeated measures.
The MANOVA approach assumes an unstructured covariance matrix, i.e.
the covariances among the 4 measurements have no structure with each
measurement having its own variance and each covariance separately
estimated.
If you use the REML approach with subject as a random factor, you are
forcing compound symmetry on the covariance matrix, i.e. all
variances down the diagonal are equal and all covariances are also
forced equal.
In SAS, but not in JMP, you can use proc mixed to fit repeated
measures in various ways. In SAS, the repeated statement = manova
approach and you can specify different covariance structures and get
it to match the random(suject) approach.
There is a long detailed explanation in the SAS for Mixed Models book
by Littell et al .
I am familiar with two ways of analyzing repeated measures effects
in jmp. One of them uses a vertically-organized file structure, with
multiple lines per subject, and uses subject as a random factor. The
other uses a horizontally-organized file structure, with MANOVA.
(Fit Model: MANOVA Personality: Choose Response: Coompound;
interaction effects) The former approach makes sense to me and I can
get it to work. However, I have the same dataset organized both
ways, and I cannot get the MANOVA approach to reproduce the results
I obtain in the random effects approach. Maybe it's not supposed to?
And I don't know MANOVA, so maybe I'm not looking in the right way.
If anyone is sufficiently interested and knowledgeable, I'd
appreciate your input. I'm attaching the two datasets in case you
want to check 'em out.
In the horizontal file, the four variables, prefleft, prefright,
nonleft, nonright represent the repeated measures. The two
within-subjects variables are laterality (left versus right) and
preference (pref versus nonpref). So laterality is the faster moving
variable. Orientation is a between-subjects factor. As an example of
a result I would like to find in the MANOVA, in the random effects
analysis (with all main effects and interactions), I get a
significant interaction for Prefnon*Orientation, F(1,59)=10.8,
P=.0017.
Attachment converted: Macintosh HD:amygdalahorizontal.jmp (SGPD/SGP
) (0025C01A)
Attachment converted: Macintosh HD:amygdalavertical.jmp (SGPD/SGP ) (0025C01B)
Michael Bailey
jm-bailey@northwestern.edu
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