Dear Christopher,
>
> I have data from a PET experiment of 10 subjects, 5 conditions per
> subject (some data missing). The images going into the analysis are
> themselves parametric maps of blood flow (instead of the more common
> scaled count rate images). I have reason to believe that the variances
> of the parameterized blood flow maps are spatially inhomogeneous. That
> is, areas of high residual variance (after parameterization) coincide
> with those of high blood flow. I suppose a more extreme case of the
> situation I describe would be that of, e.g., a dopamine receptor map.
>
> My problem is that I am very uncertain of the exact method SPM2
> uses to
> estimate standard deviations for inference in the type of PET setup
> described above. I want to make sure I am not pooling over brain
> tissue(Worsley et al., 1992). I think I've grasped the approach
> taken in FMRI
> to remove serial correlations (partly global hyperparameter
> estimation),but PET remains elusive. In "Human Brain Function"
> (2nd Ed), Chapter 37,
> p. 736, the authors write:
>
> "In PET data there is substantial evidence against an assumption of
> constant variance (homoscedasticity)..." ... "If homoscedasticity
> couldbe assumed, variance estimates could legitimately be pooled
> accross all
> voxels."
>
> Since I (want to) assume heteroscedasticity, what approach should
> I take
> when using SPM2?
PET is actually MUCH simpler. In PET (and SPM) it is all voxel-wise univariate, i.e. the estimates for the parameters (the weights of the regressors) and the hyper-parameters (i.e. the variance) for a given voxel are estimated using the data from that voxel alone.
In fMRI it is done slightly differently. There one estimates several "variance components", and since one estimates more (hyper-)parameters SPM pools SOME of these estimates across all voxels to ensure that the estimates are "numerically stable".
But, as I said, for PET it is much easier and you DO assume heteroscedasticity (at least across voxels) when you use SPM.
Good luck Jesper
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