On Mon, 2 Aug 1999, Thomas Nichols wrote:
> Greetings Karl,
>
> I would like to clarify your reponse...
>
> > Dear Andreas
> >
> > > we have exactly the same problem using SPM99b as Richard, but our study
> > > is event-related with events whose onset differs from scan run to scan
> > > run (in our case we have seven subjects with seven runs of 240 scans
> > > each), so the workaround that Cathy suggests will not work for us. Is
> > > there any other way to deal with that problem? Any help would be
> > > greatly appreciated.
> >
> > If the 'workaround' refers to a second level analysis then you should
> > be OK. The design matrices for each first (session) level analysis do
> > not have to be identical, they only have to model the same 'causes' of
> > the data (even if the causes or events are different in number or
> > timing).
>
> While the design matrices may differ, the variance (image) of each
> contrast (image) should be the same.
>
> As an extreme case consider the following second level analysis consisting
> of 10 subjects. The first 5 subjects have a first level analysis consisting
> of just 30 seconds of data imaging a single trial/event; the other 5 subjects
> each have 20 minutes of data with 40 events. The response estimates
> (contrasts) from the second 5 subjects will be much less variable than
> first 5 subjects, simply because there is more data (more df). The
> differing variances violate the homogeneous variance assumption of
> the second level model.
>
> This issue can be summarized as
>
> The random effects analysis obtained by analyzing
> contrast images assumes a balanced design.
>
> (which Andrew noted in his RFX poster). If the design is very
> unbalanced then weighted regression or other approaches are necessary.
>
> -Tom
>
>
> -- Thomas Nichols -------------------- Department of Statistics
> http://www.stat.cmu.edu/~nicholst Carnegie Mellon University
> [log in to unmask] 5000 Forbes Avenue
> -------------------------------------- Pittsburgh, PA 15213
>
>
>
I am a little confused by this. Doesn't a random effects model assume
that the variance is dominated by across subject variance to the point
that the within-subject variance is negligible? This suggests that
the question isn't whether the design matrix is balanced in an absolute
sense, but whether it is balanced enough to satisfy the assumptions
required by a random-effects model.
John
--------------------------------------------------------------
John Ollinger
Washington University
Neuro-imaging Laboratory
Campus Box 8225
St. Louis, MO 63110
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|