Dear Mathijs,

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.
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.
If you do model a subject factor in a full factorial design, then you
would indeed pair subject 1 in group 1 with subject 1 in group 2 etc. In
a full factorial design, you can not have a subject factor with 52
levels where levels 1:26 would only occur in group 1 while levels 27:56
only occur in group 2. In a full factorial design, all combinations of
all factor levels (i.e. cells) must be set.
Usually, you can just drop the subject factor. If you really need it,
you have to use a flexible factorial design instead.

Volkmar

Am Freitag, den 11.07.2008, 10:01 +0200 schrieb Matthijs Noordzij:
> Dear SPMers, 
> 
>  
> 
> In our centre we recently discussed the differences between the
> flexible and full factorial model in SPM5. We wondered what benefit
> might be gained from a flexible factorial design (over a full
> factorial one). The obvious advantage seems to be that the flexible
> factorial design gives more degrees of freedom in case only a few
> specific effects are considered. However, we also wondered whether the
> subject effect is modeled differently in the full and flexible
> factorial models. In our comparisons we came to some surprising
> results. This is what we tried and found:
> 
>  
> 
> We have a design with 2 factors of interest (GROUP and CONDITION),
> each with 2 levels. Each group has 26 subjects (52 different subjects
> in total). In the full factorial model, we entered GROUP as an
> independent factor (unequal variance), and CONDITION as a dependent
> factor (equal variance). In the flexible factorial design we modeled
> SUBJECT, as well as GROUP and CONDITION as above. W added the 2 x 2
> interaction as a contrast to the flexible factorial model. Then we
> compared the results from the two models. When looking at the main
> effect of CONDITION, we basically got (almost) identical results in
> the full factorial and flexible factorial models. This was as
> expected. However, when we compared the main effect of GROUP between
> the two models, it turned out that the flexible model was much more
> sensitive than the full factorial. This was surprising, because the
> subject effect is also (implicitly) modeled in the full factorial
> design. We then checked how the subject factor is modeled in the full
> factorial design. To our horror, we found that the factor subject
> (sF1) only ranged from 1 to 26 levels (instead of 52). We can only
> infer that subject nr. 1 from GROUP 1 and subject nr.1 from GROUP 2
> are modeled together as one subject. This is obviously not how it
> should be. This erroneous modeling of the subject factor might have
> lead to the inferior sensitivity of the full factorial model, with
> respect to the flexible model. 
> 
>  
> 
> Our questions are as follows:
> 
>      1. How is the subject factor modeled in the full factorial
>         design? When comparing two groups with different subjects, how
>         come that not all subjects (over groups) are modeled
>         separately? How can this be solved? 
>      2. How to deal with mixed designs within one model? Is it
>         possible at all to use the full factorial model correctly, or
>         should it be avoided at all times? If it should be avoided, is
>         the flexible factorial model the best solution? Or should we
>         use multiple regression analyses, or perform all
>         within-subjects contrasts at the first level? 
> 
>  
> 
> Related issues were raised in the below thread, but we feel that the
> above questions remain unsolved:
> 
>  
> 
> - questions on performing 2 x 2 within-subjects ANOVA in SPM5
> 
>  
> 
> http://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0801&L=SPM&P=R11681&I=-3
> 
>  
> 
> Any feedback would be highly appreciated.
> 
>  
> 
> Matthijs, Laura, Lennart, Rene & Rick
> 
>  
> 
>  
> 
> ----------------------------------------------------------------
> 
> Radboud University Nijmegen
> 
> F.C. Donders Centre for Cognitive Neuroimaging 
> P.O. Box 9101 
> 6500 HB Nijmegen 
> The Netherlands
> 
>  
> 
>  
> 
> 
-- 
Volkmar Glauche
-
Department of Neurology         [log in to unmask]
Universitaetsklinikum Freiburg  Phone   49(0)761-270-5331
Breisacher Str. 64              Fax     49(0)761-270-5416
79106 Freiburg                  http://fbi.uniklinik-freiburg.de/