Dear Rik, Karsten, and other experts-
based upon insights hopefully gained from the recent discussions of
re-fMRI-paradigms I am wondering about the following design:
2 stimuli types A & B with null stimuli 0, randomly presented at
modulated occurance probabilities, |SOA - TR| > 0 (exact jittering not
yet clear, I thought to set the difference equal to exactly the time bin
for a single slice, external triggering with modelling of "virtual time
bins" to account for the delay between consequtive volumes)
Now: I have two "basic" stimuli A (n= 111) & B (n=109) in addition to
the null stimulus 0 (n=180). However, in order to obtain some behavioral
response control I thought to instruct the volunteers to press a button
whenever they noted a change of the visual stimuli presented
subsequently, i.e. to press when ...0->A... / ...0->B... / ...A->B... &
...B->A... but NOT to press when ...0->0... / ..B->B... & ...A->A... is
noted, respectively. The rational was to model this discrimination task
and thus the motor response (trial C, n=195 with 66 simultaneously to A,
65 to B and 64 to 0, leaving n=116 "true null events") "dissociable"
from A & B. Looking at the design, the trails A, B & C are not totally
orthogonal but the values seems low enough (|cos(phi)|<0.28, i.e. A-B:
-0.22 / A-C: 0.23 / B-C: 0.28). My question:
1) In a three trial type design, is it possible to compute the
t-contrast of the effect of A & B vs. C? How would I specify such
contrast? 0.5 0.5 -1 or 1 1 -2? I have tried to compute the efficiency
for this using the formulas:
I] trace([0.5; 0.5; -1]'*inv(xX.X(:,1:3)'*xX.X(:,1:3))*[0.5; 0.5;
-1])^-1 and
II] trace([1; 1; -2]'*inv(xX.X(:,1:3)'*xX.X(:,1:3))*[1; 1; -2])^-1
yielding a much higher efficiency for I (528.6657) than for II
(132.1664). Are the formulas ok assuming I have just included the hrf
(no temporal derivatives, no interactions)? Is it correct to adjust
*xX.X(:,1:n)) to your matrix with n being the number of your columns?
Does your formula, Rik, pertain to epoch-related designs, too (in a way,
Afraim has addressed that question as well).
2) In my particular situation, the recognition of particulary A & B is
of course not absolutely independent from the recognition of ANY change.
Because the presentation of A or B can activate just the recognition (if
A had been preceded by A and B by B, respectively) or the recognition
AND discrimination (if A had been preceded by B or O and B by A or O,
respectively) and because of a rather short SOAs (2.4 s), I should
probably model nonlinear interactions by the Volterra kernel. Obviously,
this should account for interactions both within and between trials. The
interactions AxA, BxB, and CxC are not at all orthogonal to A (0.93), B
(0.93), and C (0.94), respectively. I guess that is inevitable but is it
then possible to estimate A, B, and C independent from AxA, BxB, and
CxC, respectively? Moreover, in the described design it seems to be of
concern that A & AxC (0.79), B & BxC (0.75), C & BxC (0.62) as well as C
& AxC (0.54) are not quite orthogonal. Will SPM be able to handle that,
does the design nevertheless make some sense or would you recommend to
pursue another definition of C (i.e., to press a button when either A or
B is being recognized - in that case, the motor response would NOT be
expected to appear in the differential effect 1 -1)? I know I am asking
for a lot of help but I most certainly appreciate your help... TIA-
andreas
|