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Hi John, Assuming no-one replied, I'll have a quick attempt... > [...] > 3 groups, 2 time points for each subject. Mixed-model. > > Therefore I set one factor as ‘group’ with 3 levels. Set independence > to yes and variance to equal. > > The second factor as ‘time’ with 2 levels. Set independence to no and > variance to equal. > > The non-independence in the second factor is what I am having trouble > wrapping my mind around. I know this introduces a non-sphericity > correction. However, If I extract VOI data, I am not sure how the data > is being corrected. I am sure it is, but I am not sure how, or what > that exactly means. There is help in spm_spm.m about this, around line 86. Basically, in your case the dependence between times is modelled by allowing off-diagonal entries in the covariance matrix V. ReML is used to estimate V (from some of the voxels, as explained in spm_spm), and then a second pass estimates beta etc after whitening the data -- which means multiplying by W where W*W' = inv(V) -- because then W*Y has a scaled identity covariance matrix, i.e. has independent (white) errors. [The multiplication by W is done along with any fMRI time-series filtering in line 183 of spm_regions] > The xY.y data is not the original values from > the subject images, but some type of corrected value. However, I am > fairly certain that if there was no non-sphericity correction, the data > extracted would be the original data. If you select a contrast, then as well as being whitened as described above, y is also "adjusted". My understanding of this is that the uninteresting components are removed, where "uninteresting" is defined as orthogonal to the contrast you are testing. E.g. as I understand this, if you were interested in the main effect of time, ignoring the split of your data into three groups, then the adjusted data would have each group mean subtracted, so that only the time effect (and the residual error) would be present in y. > Also, I am also curious as to how SPM5 handles non-independence. For > example, if I have a group at two time points, I can declare > non-independence without the groups being equal. So there does not have > to be a matching of subjects like a paired t-test. So how is this being > handled? Well... I think this is a rather complicated issue, which I don't think is always that well explained... In particular, it is probably very badly explained whenever I try to do so ;-) The underlying mechanism is to allow certain variance components (e.g. off-diagonal covariance terms between time-points in your case), then to estimate these (with ReML), and to return Weighted Least Squares parameter estimates (etc) from using the covariance matrix. A complication is that different voxels should arguably be allowed to have different covariance matrices (i.e. ReML should be used for each voxel), since this would be analogous to allowing each voxel to have a different balance of time and subject effects in a conventional fixed-effects paired t-test, which is what happens. However, it would be very time-consuming to run ReML at each voxel, and I believe there is also a problem with the estimation of the variance components being itself quite variable. So in practice, what SPM does is to average the activated voxels (using a relatively low uncorrected threshold on an F-contrast for the effects of interest -- see spm_spm lines around 195, 466, 699 and 802) and to estimate a single set of variance components from this average. The result is then assumed to be accurate due to the large number of voxels averaged over, and a matrix is derived and used to whiten the data, as described in spm_spm around line 95. The actual covariance matrix at each voxel is given by the product of that voxel's ResMS and the single estimated covariance structure. There is more detail on this "factoring of the spatiotemporal covariance into non-stationary spatial variance and stationary temporal non-sphericity" in HBF2 ch.9: http://www.fil.ion.ucl.ac.uk/spm/doc/books/hbf2/pdfs/Ch9.pdf So I don't think SPM's modelling of dependence is quite what you'd expect, which means that if you do have within-subjects (e.g. paired) data, I think you still want to model (fixed) subject effects, as well as dependency, as discussed in this post: http://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0703&L=SPM&P=37802 rather than relying on purely random subject effects. I think this then means that you are stuck with the fixed-effects issue of having to throw away subjects if they have missing data for some levels of their within-subject factor. E.g. in a paired t-test scenario, unpaired observations are effectively dropped. Hopefully someone will correct me there (and elsewhere!) if wrong... I hope that helps, sorry if it's no clearer than the help in spm_spm.m! Best, Ged