Hi Torben,
The data reduction in the PCA is not accounted for in the dof
calculation - that would not make much sense as the reduction is data
driven and the F-test is calculated across time, not PCA loadings
space. As a thought experiment, imagine reducing the subspace to 1
(i.e. only retaining the largest Eigenvector, whatever that is in your
data) and then finding that a single regressor fits really well. Would
you be inclined to say that dof2 should be 1, so no matter what you're
not surprised at all? Conversely, if you find a nice fit between an IC
and a regressor for d=30, say, you could re-run with d=900, find the
same component and then see an increase in F that is very
significant.... that's clearly not right. You're right in thinking
that the PCA somewhat could be understood as a filter, but because
it's data driven the effect on the noise space is not easily
predictable. One could in theory calculate the F in the loadings
space, after projecting the GLM design into the same PCA subspace but
this would not get around the issue that e.g. if you retain only one
EIgenvector, even a F-value of 190 does not get you to p<0.05 with 2
and 1 dofs...
cheers
Christian
On 4 Jun 2008, at 15:28, Torben Ellegaard Lund wrote:
> Dear List (Christian in particular)
>
> Im am trying to sort the components from a MELODIC analysis based on
> a design.mat file. The original dataset consisted of 1000 volumes
> each containing 33 slices. MELODIC estimated the number of
> components after PCA reduction to be 677, so in interest of time I
> stopped the program and manually specified the number of components
> to 50. As far as I understand the algorithm, my data are now
> projected into this 50 dimensional subspace. The F-test on full
> model fit nicely show that the 2 regressors in my design.mat file do
> indeed have a significant contribution to some of the components,
> and that is basically what I would like to demonstrate. I assume the
> (uncorrected for # comp) refers to the the p-values not being
> corrected for the number of tests made. This is OK since I can
> multiply the p-values with the number of tested components to get
> Bonferroni corrected p-values. What worries me a bit is the way the
> degrees of freedom is calculated: dof1=2 is OK but dof2=997 seems to
> indicate that the reduction of the data from a 1000 dimensional
> space to a 50 dimensional space has not been taken into account,
> isn't this a problem? I am preparing for a talk on RSN at the HBM so
> I would really appreciate your comments on this.
>
> Best
> Torben
>
>
>
>
> Torben Ellegaard Lund
> Assistant Professor, PhD
> The Danish National Research Foundation's Center of Functionally
> Integrative Neuroscience (CFIN)
> Aarhus University
> Aarhus University Hospital
> Building 30
> Noerrebrogade
> 8000 Aarhus C
> Denmark
> Phone: +4589494380
> Fax: +4589494400
> http://www.cfin.au.dk
> [log in to unmask]
>
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