Jack,
>1. Does the F-test give you the best single linear combination of basis
>functions across all voxels
>or is it the best linear combination of basis functions for each single
voxel?
>In other words, for
>the F-test, is the HRF constrained to be identical across all voxels?
The HRF basis function fit is done separately for each single voxel.
However, an f-test isn't really about the "best" linear combination.
If anything, the best linear combination corresponds to the PEs. The
f-test tells you about how much variance is explained by the linear
combination in comparison to the noise variance.
>2. Is the parameter estimate for each individual basis function for the
single
>contrasts the same as
>the parameter estimates for the F-test? For example, if basis function
1, 2,
>and 3 account for
>10%, 20%. and 50% of a voxel's variance ( plus 20% residual) for each of
the
>individual contrasts, is
>this ratio the same for the F-test?
The PEs are the fit of the design matrix to the data_independently_ of
the t or f contrasts. These PEs (along with their covariances) are then
used to calculate t or f statistics using the t or f contrasts. Have a
look at Worsley's chapter in Steve's FMRI intro book, or similar text, for
an intro to f-tests.
>3. How can I get the three basis functions used by flobs? What I would like to
>do is take the
>parameter estimate for each function, determine the fraction of the total
>variance accounted for by
>each function (pe1/(pe1+pe2+pe3+residual)), then determine the HRF
>(HRF=fraction1*function1+fraction2*function2+fraction3*function3). This should
>give me
>something different from the peristimulus plots, i.e the peristimulus plots are
>the hemodynamic
>response for a given stimulus but not the hemodynamic response function that I
>want to convolve
>with my stimulus. Is this all valid reasoning?
Yes, it would give you something different to the peristimulus plots. It
gives you the deconvolved HRF under the assumption that things are linear
(which they will not be for a boxcar design, for example). The default
flobss basis functions are in ASCII format in the file
$FSLDIR/etc/default_flobs.flobs/hrfbasisfns.txt. Not sure why you think
you need the fractions, to get the HRF you just want
pe1*function1+pe2*function2+pe3*function3.
Cheers, Mark.
Mark Woolrich.
Oxford University Centre for Functional MRI of the Brain (FMRIB),
John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
Tel: (+44)1865-222782 Homepage: http://www.fmrib.ox.ac.uk/~woolrich
On Wed, 10 Nov 2004, Jack Grinband wrote:
> Hi All,
>
> On Sat, 1 May 2004 09:15:21 +0100, Stephen Smith <[log in to unmask]> wrote:
>
> >> Ah. So f-test results for the ps-plots, then. Great. Let me make sure I
> >> understand -- I can model using 5 gamma basis functions and do an
> >> f-test across all five, which gives me one map that is the best fit
> >> linear combination of all basis functions. (How do I know the weighting
> >> of each?)
> >
> >Yep, that's right. You can get a feel for the relative weightings by
> >looking to see how strongly each individual one fits in the partial model
> >fits on the right side of the web page. You can get the exact relative
> >values by extracting the relevant voxel values from the relevant pe?.hdr
> >image.
> >
> >Cheers, Steve.
>
> I'm still a bit confused by the meaning of the F-test.
>
> 1. Does the F-test give you the best single linear combination of basis functions across all voxels
> or is it the best linear combination of basis functions for each single voxel? In other words, for
> the F-test, is the HRF constrained to be identical across all voxels?
>
> 2. Is the parameter estimate for each individual basis function for the single contrasts the same as
> the parameter estimates for the F-test? For example, if basis function 1, 2, and 3 account for
> 10%, 20%. and 50% of a voxel's variance ( plus 20% residual) for each of the individual contrasts, is
> this ratio the same for the F-test?
>
> 3. How can I get the three basis functions used by flobs? What I would like to do is take the
> parameter estimate for each function, determine the fraction of the total variance accounted for by
> each function (pe1/(pe1+pe2+pe3+residual)), then determine the HRF
> (HRF=fraction1*function1+fraction2*function2+fraction3*function3). This should give me
> something different from the peristimulus plots, i.e the peristimulus plots are the hemodynamic
> response for a given stimulus but not the hemodynamic response function that I want to convolve
> with my stimulus. Is this all valid reasoning?
>
> many thanks,
>
> jack
>
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