Dear Jonathan,
> How does SPM99 fit the AR(1) model to each voxel time series if you
> specify this option in the model set-up? Is this a global fit? Are both
> the AR coefficient and the innovations variance estimated globally or
> is one global and one local? I'd like to know the details and haven't
> been able to find them anywhere on the web site.
The AR coeficient is estimated at each voxel and then averaged over voxels:
In spm_spm:
%-Estimate intrinsic correlation structure AR(1) model
%-------------------------------------------------------
switch xX.xVi.Form
case 'AR(1)'
%---------------------------------------------------
fprintf('%s%30s',sprintf('\b')*ones(1,30),...
'...AR(1) estimation') %-#
for i = 1:length(xX.xVi.row)
y = spm_detrend(Y(xX.xVi.row{i},:));
q = 1:(size(y,1) - 1);
a = sum(y(q,:).*y(q + 1,:))./sum(y(q,:).*y(q,:));
A = A + [1; -mean(a)];
end
end
and
%-Compute (session specific) intrinsic autocorrelation Vi
%-----------------------------------------------------------------------
switch xX.xVi.Form
case 'AR(1)'
%---------------------------------------------------
p = length(A) - 1; % order AR(p)
A = A/A(1);
for i = 1:length(xX.xVi.row)
q = xX.xVi.row{i};
n = length(q);
Ki = inv(spdiags(ones(n,1)*A',-[0:p],n,n));
Ki = Ki.*(Ki > 1e-6);
Vi = Ki*Ki';
D = spdiags(sqrt(1./diag(Vi)),0,n,n);
Vi = D*Vi*D;
xX.xVi.Vi(q,q) = Vi;
end
end
xX.xVi.Param = A;
> Also, when using an F-test to test for the significance of a group of
> covariates (i.e. a main effect convolved with a basis of functions that
> span the space of possible HRF's) why is it that during the cluster
> detection the spatial extent threshold is automatically set to zero,
> whereas for t-test cluster detection you can choose the threshold?
The distributional approximations for spatial extent have only been
worked out for Z fields (i.e. t-fields with high d.f.). SPM enforces a
0 extent threshold for SPM{F} so that the height-based corrected p
values are valid.
I hope this helps - Karl
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