Dear Philippe,
At 15:24 28/10/99 +0100, Philippe Peigneux wrote:
| Could you please comment further on how to enter images in the
| second level analysis ? We are here in trouble since your message to
| Stephen (At 10:45 28/10/99 +0100), where you said :
|
| > It's contrast images from a first level (individual subject say)
| > analysis that can be re-entered into SPM to effect an analysis at a
| > higher level (across subjects say). In SPM99 these are names
| > con_????.img.
| >
| >.....................
| >
| > Contrast images are used because they are guaranteed to be
| > estimable whatever the design. In general the parameter images
| > (beta_????.img) are not estimable: The "parameter estimability" bar
| > on SPM printouts tells you which parameters are uniquely estimable
| > for this model. A contrast with a single "1" picking out these
| > estimable parameters would be a valid contrast, and the contrast
| > image would be the same as the parameter image.
|
| When I ran a RFX analysis in SPM96, according to the helpfile, I
| create adjusted mean images for each subject and each condition,
| using for example "MultiSubj: Condition means (AnCova by subject)",
| assuming that (in spm_adjmean_ui.m) "Once the weights have been
| worked out for each adjusted mean image, computation proceeds by
| passing appropriate weights and image filenames to spm_mean, which
| writes out the appropriate parameter image .... as the input
| images.". Then, I entered these adjusted images in the second level
| analysis, compare par pairs only, and so on ...
This is fine, provided you only enter a single pair of adjusted mean
condition images, and provided that the contrast with +1 for one condition
and -1 for the other condition is a valid contrast.
The adjusted condition images you get from the SPM96 AdjMean/fMRI are the
parameter estimates for a very simple model using box-cars, optionally
convolved with a synthetic haemodynamic response function, and optionally
including global intensity normalisation. Although these adjusted mean
condition images themselves may not be uniquely estimated, the difference
between any two usually is (for the limited models of the AdjMean/fMRI
module). I.e. The difference between two of these adjusted mean condition
images is the same as a contrast image for a contrast with weights of the
form [...+1...-1...] which would contrast the two conditions.
By putting the pairs of adjusted mean condition images into SPM96's
PETstats "Multi-Subject: Conditions only" design (with no global
normalisation), you're just doing a paired t-test: This SPM model used this
way is equivalent to doing a t-test on the inter-condition intra-subject
differences. I.e., The SPM96 way is implicitly putting [...+1...-1...] type
contrasts into the second level analysis, by virtue of using a paired
t-test on the adjusted mean condition images, which are just parameter
estimate images.
The reason for this convoluted scenario was that SPM96 had difficulty
dealing with negative data, since the "grey matter threshold" couldn't be
used to limit the analysis to the intracerebral voxels where there was
data.
| In SPM99, it seems that two possibilities exist : either use the
| "AdjMean" option in the same way as in SPM96, or use in the
| statistics section the PET model : "Multi-subjects : condition by
| subject interactions and covariates", given that in both cases I
| ensure subject-separability using the within group options for
| centering, scaling and Ancova.
|
| So, the point here is that I obtain adjusted images for subj1Xcond1,
| subj1Xcond2, etc .... in the first case, and with the second method
| I obtain corresponding beta_????.img but *not* con_????.img. Until
| now I was thinking that to enter those beta_????.img in the 2nd
| level of the analysis was the right way, because I believed that
| these are equivalent to the adjusted images obtained with the fisrt
| method.
For exactly the same model the difference between pairs of adjusted mean
condition images from AdjMean/fMRI will be the same as the contrast image
for a contrast comparing the two conditions in SPM99, provided that
contrast is estimable. (SPM99 won't let you use inestimable contrasts.)
(The AdjMean/fMRI images will differ from the corresponding SPM99 parameter
images by the addition of a mean effect image, included so that a "grey
matter threshold" still has some structure to work on.)
The advantage of using SPM99's fMRI models and extracting contrast images
is that you have all the flexibility of SPM99 modelling, and estimability
is guaranteed.
| However, you say here that beta_????.img are not uniquely estimable,
| hence I check my two designs and discover that in both cases
| (statistics or adjmean) these are indeed not.
The issue is whether a contrast comparing a pair of conditions is
estimable. If so, then the "old style" random effects analyses you have
been doing are OK.
| Now the problem is
| that I cannot really figure out how to handle con_????.img . I
| cannot create one for for each subject in each condition, because
| these are the product of the comparison between two conditions, and
| if it is the case, how to compare comparisons ? I'm sure I missed a
| point here, but I cannot see where.
I'm assuming you know how to make the con_????.img images: These are
created when assessing a contrast for the first time in the SPM results
section.
You should only take a single contrast per subject forward to a second
level analysis. Taking more assumes that the repeat contrasts within
subject are independent: implicitly implying that the variance is
"spherical". It is fairly rare that repeated measures data is spherical, so
it's safest to just put in one contrast per subject. The degrees of freedom
should be just less than the number of subjects for valid random effects
comparisons.
Your last question about comparing comparisons would suggest that you were
previously taking (say) adjusted condition images from four conditions into
the second level analysis, and then comparing them with a contrast like {+1
-1 -1 +1] to look for an interaction. This should be effected by applying
the contrast comparing pairwise differences at the first level, and then
taking only the corresponding contrast images (1 per subject) through to a
second level t-test (single group, population inference) or two-sample
t-test (two groups, population inference).
A last caveat is that the first level models (individual subject models)
should be identical, so that the intra-subject (scan to scan residual)
component of variance is equally represented in each subjects contrast
image. However, it is likely that inter-subject variance is much bigger
than intra-subject component, such that the models need only be similar in
terms of scan numbers and general design.
Hope this clarifies things for you!
-andrew
+- Dr Andrew Holmes [log in to unmask]
| ___ __ __ Wellcome Department of Cognitive Neurology |
| ( _)( )( ) Functional Imaging Laboratory, Stats & |
| ) _) )( )(__ 12 Queen Square, Systems |
| (_) (__)(____) London. WC1N 3BG. England, UK |
+------------------------------------- http://www.fil.ion.ucl.ac.uk/ -+
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