Dear SPMers,
Could you please help me and my collegue to understand what the predicted
and adjusted responses plotted by SPM are?
We DID read Rik's very useful post from 29/10/2003 "Re: fitted response?"
[many times].
From spm_graph.m we understood the following:
assuming
Y=x1*beta1 + x[2..n]*beta[2..n] + epsilon
where x1 is a regressor(s) for condition(s), x[2..n] are all the remaining
regressors (i.e. confounds)
then, do we understand correctly, that w.r.t. a contrast 'C1' spanning x1
predicted response = P = x1*beta1 + epsilon
adjusted response = A = x[2..n]*beta[2..n] + epsilon
(this means we understand X1o(see fragment of code below) to be x[2..n])
This goes well with spm_graph.m (see fragment at the end of this email).
But the logic to call A 'adjusted' is not obvious because there are only
confounds there.
Well. (Another "but" in the opposite direction) But this goes well if we
consider that SPM uses this terminology when it automatically creates the
contrast "effects of interest" - which includes all confounds.
Dear SPM gurus, experts and amateurs, could you please make this more clear
for us?
Your help is very much appreciated.
Helmut & Roman
Here is a fragment of spm_graph.m which plots those responses:
% predicted or adjusted response
%------------------------------------------------------------------
str = 'predicted or adjusted response?';
if spm_input(str,'!+1','b',{'predicted','adjusted'},[1 0]);
% fitted (predicted) data (Y = X1*beta)
%--------------------------------------------------------------
Y = SPM.xX.X*SPM.xCon(Ic).c*pinv(SPM.xCon(Ic).c)*beta;
else
% fitted (corrected) data (Y = X1o*beta)
%--------------------------------------------------------------
Y = spm_FcUtil('Yc',SPM.xCon(Ic),SPM.xX.xKXs,beta);
end
% adjusted data
%------------------------------------------------------------------
y = Y + R;
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