Hi Heike,
> I’m trying to figure out how to run a repeated measurement ANOVA in SPM5
> (3 time points) for VBM analysis. I don’t know how to account for this in
> SPM5. Model a “time” factor in full factorial model and assume
> dependencies between the 3 factor levels (i.e. measurements)?
I think there are two different ways of doing this, but that there
might be a problem implementing one of them SPM5, which I'll talk
about below...
Classically, repeated measures ANOVA allows for individual subject
effects, with additional time effects. This is the extension of the
standard paired t-test. I think you can set this up by entering
subject and time as factors, into a flexible factorial model, where
you are not interested in the time-subject interactions.
The alternative, close to what you describe, uses a mixed model with
random subject effects, instead of fixed subject effects as above,
(giving certain dependencies between the levels). The covariance
matrix is constrained to have equal between-subject variance, and
equal within-subject covariance (compound symmetry). Then, if the
groups are balanced (all subjects measured on all three occasions) the
results are identical to the fixed subject effects case above. [The
advantage of this model over the above, is that if some subjects are
randomly missing some time points, the fixed-effects model must drop
these subjects from the analysis, while the mixed-effects one can take
advantage of this incomplete information.]
However, as far as I can tell from playing around with SPM, specifying
equal variances and dependent levels gives different within-subject
covariances between times 1 and 2, 1 and 3, and 2 and 3. This means
that SPM's results don't match those of the fixed effects model in the
balanced-data case when the fixed model is applicable.
http://www.cs.ucl.ac.uk/staff/gridgway/mixed/tripled_t.html
I think SPM's "equal var and dependencies" might still be a valid
model, but I'm not sure. Certainly the "unequal var and dependencies"
is valid; it's just an unstructured block-diagonal covariance matrix,
as I think one would get with e.g. SAS Proc Mixed's "repeated type=un"
statement.
There seems to be a slight problem to me though, in that the SPM5
options don't allow the standard random subject effects model
(equivalent to a block-diagonal covariance matrix with compound
symmetry, as I think e.g. SAS Proc Mixed's "repeated type=cs" or
"random subject=subj" would give).
Volkmar, do you think equal var but dependent levels should give
compound symmetry instead of the current model, or do you think this
could be offered as a different option (equal var with "equally
dependent levels" or similar)?
Best,
Ged.
P.S. Anyone who can remember my caveats in previous posts about me
"pretending to be a statistician" will note that I seem to be getting
worse... I do hope there's treatment ;-)
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