Dear Rik,
> This question is about validity of cluster-level inference in random
> effects analyses of fMRI data.
>
> In a previous message it was stated that height-based inference should
> generally be more powerful than cluster-based inference when degrees of
> freedom are low (<16) and smoothness relatively high (>8mm3). In my 2nd
> level analysis d.f. was 8 (we plan to add about 3 more subjects) and
> final smoothness estimate was 13 13 19. Random effects was chosen given
> the total number of images to be processed.
>
> Cluster level inference yielded a number of activations far above the
> correction threshold while at voxel-level inference only a single focus
> survived the threshold. Interestingly, all activations obtained using
> cluster level inference were consistent with our a priori knowledge
> about what this task should activate.
>
> I understand there may potentially be theoretical problems using a
> cluster-level inference in this context (cfr previous email by G
> Aguirre (16 june 99)). Do these problems render the cluster-level
> inference statistically invalid?
There are tow issues here:
1) Validity of spatial extent (cluster-level) inference for SPM{T}
with low d.f.
You are quite right that the distributional approximations for these
are only true (asymptotically) for high d.f. This is because the
equations are based on Gaussian fields with a multinormal distribution
(i.e. SPM{Z}). T values with high d.f. conform to this. I am afraid I
do not know how robust these inferences are for very low d.f. (e.g.
8). One way to find out would be to perfom analyses on null data (or
use contrasts with no expected effects) and estimate the false positive
rate. For SPM{T} with 32 d.f. or higher there should be no problem and
I would not expect severe problems with d.f. of 16 or more.
2) Are cluster-level inferences more sensitive?
The original power analysis suggested that if smoothness is large
relative to underlying signal then voxel-based tests are more
powerful. This may be the case for highly smoothed second-level
analyses. However, the model assumed, for the alterante hypothesis,
was a continuously distributed activation field, not a small number of
focal activations. Sensitivity under the latter remains an open
question and it may be that your results are both valid (if not exact)
and more sensitive with the cluster-based tests.
I hope this helps - Karl
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