> Hi experts,
> I am trying to grasp differences in statistical design of VBM analyses. Consider these two cases:
> 1. First, we have two groups with diagnoses A (control) and B (disease 1) that we want to compare in a VBM analysis. The design matrix would be
> [1 1 0
> 1 0 1]
> and to check for regions where intensity in A is higher than in B we use the contrast [0 1 -1].
yes - except in SPM the constant is at the end of the design matrix
X = [1 0 1 ; 0 1 1];
and thus your contrast [1 -1 0] shows A>B
> 2. In this case, we add two (diseased) groups, now having with 4 groups with different diagnoses A (control) B C D (different diseases) and a design matrix
> [1 1 0 0 0
> 1 0 1 0 0
> 1 0 0 1 0
> 1 0 0 0 1]
> To find for regions where intensity(A) is higher than intensity(B) we use a contrast [0 1 -1 0 0].
yes (but again remember that the constant should be shifted to the right
> As far as I understand, the main difference between 1 and 2 would be the estimation of the intercept (different now that C and D were added) and the template used (if I use a study specific template, which I probably should?).
> So, here is my question: If I want to compare subjects from different groups, should I make lots of investigations of type 1 above, or just one investigation with different contrasts like 2 above?
In this kind of design it doesn't really matter as long as you test
pair-wise like eg A vs another group -- now if you have multiple
subgroups of patients, it is more elegant to use model 2 (and more
numerically more efficient/stable)
Here is a little demo
A = [9 10 11];
B = [19 20 21];
C =[29 30 31];
Y = [A ; B ; C];
if you model A, B, C altogether ie X = [kron(eye(3), ones(3,1)) ones(9,1)];
the constant is 15 and A=-5 B=5 C = 15
so for A vs B you have a difference of 10 and A vs C a difference of 20
now running twice model 1 X = [kron(eye(2), ones(3,1)) ones(6,1)], would
for Y = [A ; B]; the constant is 10 and A=0 B=10
so for A vs B you have a difference of 10
for Y = [A ; C]; the constant is 13.33 and A=-3.33 B=16.66
so for A vs C you have a difference of ~20 (not in that case it is
numerically less accurate)
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