Dear Stephen,

thank you so much for your detailed and clear reply, it was extremely
helpful.  With regards to your comments:

>The maps output by default by the group-ICA are standardised in the
>sense that the central fitted Gaussian (fitting the central noise) is
>standardised, taking with it the rest of the intensity distribution.
>Hence the maps are indeed "null" normalised.  

thanks for this information, it's very useful.

>However this isn't
>terribly important because the same spatial regressors are used
>against all subjects in stage one of the dual regression, so the
>relative amplitudes (etc) of the outputs from stage 1 (the timeseries)
>are unaffected by the scaling of the spatial regressors.

But isn't this true only if  "relative amplitudes" refers to a
between-subject comparison of the time series corresponding to a given
spatial mode? On the other hand,  if the comparison of interest is between
the time series corresponding to *different* spatial regressors (e.g., if
one is interested in comparing the amplitude or the spectrum of the time
signal fluctuations associated with different spatial modes), then wouldn't
a standardization of the spatial regressors make the interpretation of the
results clearer?


>The same is not true of the second stage, where each subject has a
>different (temporal) model, hence the question of normalisation at
>that stage is important.
>
>> Also, it seems to me that both the
>> standardization of the regressor maps and the GLM fitting would be
>> best
>> performed within a brain-only mask, to avoid  brain-nonbrain
>> differences in
>> intensity soaking up the bulk of the variance. Correct?
>
>I don't quite follow this question, as all stages are effectively
>using the same brain mask already.

I apologize, I was not very clear.  What I meant to ask was whether the
above logic was sound and whether "fsl_glm" actually used the mask for
cropping both regressors and input data before fitting.  I guess my
confusion stemmed from the difference in the use of the mask in the temporal
and the spatial regressions: in a temporal regression the mask only selects
a subset of the voxel space upon which the voxel-wise GLM is fitted, while
in the spatial regression scheme the only sensible way to use a mask is to
crop both input data and regressors before the fitting (and now I understand
that fsl_glm *must* work like this).  Sorry for the late realization...

>
>> 2) If one is interested in examining the spectra of the
>> reconstructed time
>> course, a common approach is to standardize the individual time
>> courses (to
>> have zero mean and unit st.dev.), so that the computed spectra will
>> all have
>> unit variance, before computing group means and between-group
>> statistics on
>> these PSD.  However, I have some concerns that in the specific case
>> of the
>> dual-regression method we may be throwing away useful information by
>> doing
>> so.  Since the reconstructed time courses from the spatial GLM
>> represent
>> individual "beta values", if we want to do a group-level analysis on
>> the
>> spectra, wouldn't we want to use the spectra from the timecourses
>> *as they
>> are* (that is, not-standardized)? Because if we standardize the time
>> courses
>> (i.e., equalize total energy across components and subjects), we
>> lose the
>> information about the relative importance (both within and between
>> subjects)
>> of those estimated individual time courses in explaining the group
>> ICA maps.
>> Does this make sense?
>
>That does indeed make sense, so yes you may well want to explicitly
>normalise or not normalise the variances, depending on what kinds of
>effects you want to look for.


>
>> 3) Before using reconstructed individual spatial maps and time
>> courses as
>> input to a group analyses, it would be better to scale them
>> according to the
>> intensity of original EPI images to remove this confounding between-
>> subject
>> variance. The simplest approach (a la SPM) would be to compute the
>> grand
>> mean of the original EPI data for each subject (mean over time and
>> voxels)
>> and transform the individual reconstructed spatial maps and time
>> courses as
>> percent change with respect to the subject's EPI grand mean.
>
>Indeed - and that's what FEAT and MELODIC preprocessing does as well.


>> Alternatively,
>> one could scale the timecourses with respect to the grand mean and the
>> spatial maps with respect to the EPI mean image (voxel-wise scaling),
>> although the first approach may be better for consistency. Is this
>> correct?
>
>The former (global 4D rescaling) is probably more 'robust', and is
>what we use by default, but the latter (a voxelwise normalisation,
>effectively turning any BOLD effects into voxelwise % signal change)
>may be necessary if comparing across subjects where (e.g.) there are
>localised confounds such as varying bias field (RF coil gain).


>> 4) If point 2) is correct, then I would think it would be better to
>> take the
>> *mean* of the individual (not normalized) spectra as a group
>> representative
>> instead of its rank-1 approximation (as was done e.g. in
>> Kiviniemi2009),
>> which if I understand it correctly discards information about total
>> energy.
>
>Maybe - again that would be up to you depending on the question.
>

The above comments really clarified these issues for me, many thanks once
again for your help

best,

    giuseppe