Dear Jan and Volkmar,

Thank you for your quick replies! We have a couple of follow up questions 
we hope you or others could shed light on:

First of all, Jan, we should have indicated that your very informative 
tutorial on flexible factorial designs was actually the basis of our 
discussions.

>It is these subject constants that absorb much of the inter-subject 
>variability present in most imaging data, which in turns leads to more 
>sensitivity for the experimental effects (including group >differences).

>For these reasons, I would recommend for the flexible factorial design 
>with a subject factor (indep, equal variance) and include its main >effect 
>in the design matrix.

So if we understand it correctly: In your opinion a mixed design in which 
you are interested in Group or Group x Condition effects is best examined 
in a flexible factorial design with explicit subject regressors because it 
accounts for general intersubject variability. The full factorial does not 
give you this option of explicit subject regressors, which leaves the 
general intersubject variability in your residuals.

From now on we plan to use flexible factorial designs for mixed designs, 
but we expect that many colleagues across the world might still be happily 
using full factorial designs in such instances. Hence our remaining 
interest in the full factorial design. 

We reported that the sF1 factor, in which the full factorial automatically 
and implicitly specifies the subject factors, could be wrong. We noted that 
it modeled 26 subjects instead of 52 individual subjects (26 for each of 
the two groups). This would imply that when dependencies are estimated two 
images which actually come from two different subjects in two different 
groups, are assumed to be from one and the same subject. In this case, 
trying to specify mixed designs in as a full factorial design would not 
only be insensitive, but also wrong (based on wrongly assumed dependencies).

We therefore ran Volkmar’s batch and a couple of issues remain unclarified.

Volkmar wrote that
>In a full factorial design one would usually not model a subject >factor 
>at all. The assumption is, that subjects within each group are >random.

We agree. We didn’t mean to imply that we wanted or actually did include a 
subject factor explicitly in the Full Factorial.

>If I do the modelling as you describe (see attached batch), then I get
>(correctly) sF2 and sF3 modelled, and factors 1 and 4 set to all 1's.

Here we got lost. The batch you specified is not a mixed design, as 
condition is set to independent, instead of dependent (as we had it). This 
does, however, not affect the Files and Factors specification (though of 
course it does affect the results). We get 3 Factors (sF1, sF2, sF3), not 4 
as you say (or do you consider the “image” column as a separate factor?). 
sF2 and sF3 indeed indicate the levels of your group and condition factors 
and sF1 is the subject factor (which in your case is all 1’s because you 
only have one image). 

For our design we had 52 different subjects (26 for each group). Yet, this 
sF1 only runs from 1 to 26 (again the subject factor was NOT explicitly 
specified in the design, identical to your batch). After discussing this 
together we reached the conclusion that for the full factorial the <explore 
files and factors> option in spm5 simply gives you distorted info in that 
the sF1 is meaningless in the case of independent measures. We reached this 
conclusion because we get the same Files and Factors specification (with 
the same 3 factors and levels) also for a 2x2 design with both factors set 
to independent. Is this conclusion correct?

Therefore, in the light of a mixed design, can the full factorial be viewed 
a simply being more conservative than a flexible factorial, or as plain 
wrong? 

If our initial confusion about the full factorial was simply cosmetic 
(related to the <explore files and factors> option) then both options are 
in a sense correct. However, the tutorial of Glascher and Gitelman (2008) 
clearly indicates the superiority (in terms of sensitivity) of flexible 
factorial designs over full factorial designs for Group and Group x 
Condition effects. 

The question then is, which model is the right one? Is the full factorial 
too conservative in leaving the within-group between-subject variability in 
the residuals, or is the flexible model perhaps too liberal?

Thanks again for any input,

Matthijs, Laura, Lennart, Rick and René