Dear all and SPM:
Because of the confusion generated by random effects analyses, at
least in my own mind, I have taken the step of putting together a
summary of the SPM help-list emails about random effects. At least
this gets the information into one place. I have included most of the
relevant responses since March 1999.
You can access the page here:
http:/www.brain.nwu.edu/fmri/spm/ranfx.html
Darren
>Dear Jonatahan, Tom and Darren,
>
>at the risk of adding to the confusion, I thought I should have a go at
>this one as well.
>
>The point of the random effects analysis is to get a proper weighting
>between inter- and intrasubject error, such that intersubject differences
>in activation (effectively subject-by-condition interactions) enter the
>model in a proper way, and to ensure correct degrees of freedom for the
>type of inference that is attempted.
>
>The way to do this is to estimate the activation for each subject and each
>condition, i.e. calculate the beta*.img (which I assume are what you mean
>by cond*). When we have these we could in principle take these on to a
>second (RFx) level.
>
>This could be done through the "PET-models" OR the "Basic models". If you
>were to do it throgh the PET-models you should simply enter your beta*.img
>from the first level into a "Single subject, Conditions and Covariates"
>model and pretend these were 12conditions*15replications PET scans
>performed in the same subject. As is easily realised the residual error
>that is calculated in this way will now include subject-by-condition
>interactions (and is likely to be dominated by those).
>
>HOWEVER, this would assume the condition-by-subject interactions were
>identical for all conditions (to fulfill the ANOVA assumption of equal
>variance for all conditions). Now, I am no statistician but Andrew (Holmes)
>tells me that this is NOT a reasonable assumption, and results estimated
>this way are likely to give false positives (from the inflated degrees of
>freedom).
>
>Therefore, it is suggested that you create the contrasts you are interested
>in at the first stage (the fixed effects stage, through the results button
>as Darren pointed out). These contrasts may then be tested with a one
>sample t-test at the second level.
>
>I you perform your fixed effects analysis as one big multi-subject analysis
>the process of creating con* images isn't really that time consuming. As
>Darren pointed out you may create one contrast for all subjects at the same
>time using the "conjunction trick". Be cautioned though that if you try to
>do it for all contrasts at the same time they may not be orthogonal, so
>better avoid that.
>
>
> Good luck Jesper
>
>
> >Dear Tom and Jonathan and SPM:
> >
> >Following this thread I'm not sure the analysis needs to be that
> >complicated but I may have missed something along the way- the notes
> >are a bit out of sequence.
> >
> >I'm going to assume that you want to do RanFX analysis on fmri images
> >and that for the moment you have 2 conditions (active and rest) but
> >the analyses work the same for more conditions.
> >
> >My understanding is that you can start by creating a fixed effects
> >analysis for each subject or include all subjects together. SPM
> >finishes doing its initial business and you're prompted to look at
> >results through the results button.
> >
> >When it comes to creating contrasts- for each subject and each
> >condition create separate contrast images- So for 1 subject and 2
> >conditions that would be
> >[1 0] and [0 1]. SPM writes out the contrast images.
> >
> >Now take these contrast images for each condition across subjects and
> >enter that into your second level analyses using the designs you
> >suggest.
> >
> >I'm not sure what the cond* files are that you refer to. Are you
> >writing these out yourself? As far as I know spm produces con* files
> >only.
> >
> >I think this would shorten the number of steps by one, and actually
> >becomes very convenient, because what you can do is define all the
> >contrasts at once.
> >
> >([1 0 0 ...] [0 1 0 0..] then in the contrast manager select all of
> >them as if doing a conjunction. You're not interested in the
> >conjunction of course but this forces spm to write out all the
> >contrast images in one fell swoop, and if the contrasts are
> >orthogonal it won't add any additional contrasts. Now you have all
> >the con* images to do the second level analysis.
> >
> >Hopefully this is helpful.
> >
> >Darren
> >
> >
> >>Thomas Nichols wrote:
> >>
> >> > OK... we're on the same page; the dox you were referring to:
> >> >
> >> > % For instance,
> >> > % the "Multi-subj: cond x subj interaction & covariates" design can be
> >> > % used to write out an image of the activation for each subject. A
> >> > % simple t-test on these activation images then turns out to be
> >> > % equivalent to a mixed-effects analysis with random subject and
> >> > % subject by condition interaction effects, inferring for the
> >> > % population based on this sample of subjects (strictly speaking the
> >> > % design would have to be balanced, with equal numbers of scans per
> >> > % condition per subject, and also only two conditions per subject). For
> >> > % further details, see spm_RandFX.man.
> >> >
> >> > I understand this as such: Use the
> >> > 'Multi-subj: cond x subj interaction & covariates'
> >> > at the 'first level' to produce an intrasubject contrast for each
> >> > subject, for each contrast of interest. That is, each subject will
> >> > have a complete set of contrasts of interest. Then simply submit
> >> > each set of contrasts (consisting of nSubj images) to a one sample
> >> > t-test... et volia, you're done.
> >>
> >>This is what we did, but of course, there are 3 stages: (1) fMRI model for
> >>each subjects' data separately, to produce cond* file, (2) Multi-subj: cond
> >>x subj interaction & covariates to create con* files, (3) t-test on con*
> >>files.
> >>
> >> >
> >> >
> >> > *But*, as I see it, you don't need to do the
> >> > 'Multi-subj: cond x subj interaction & covariates'
> >> > because you
> >> > > fit separate fMRI model to each subject, which produced files
> >> > > cond_1.img through cond_12.img for each subject.
> >> >
> >> > Now, you don't have contrast images, you have condition images.
> >> > If you had followed the recommended path, you would have created
> >> > all the possible *intrasubject* contrast images within each of your
> >> > fMRI models.
> >> >
> >> > However, you should get the exact same result (check it once) just
> >> > by directly submitting your condition images to paired t tests.
> >> > The "official" path goes through the contrast images prevent
> >> > people from doing wacky things (SPM99 contrasts must be estimable).
> >> > But if you know what you're doing there's nothing wrong with
> >> > working with the condition images.
> >> >
> >> > To be specific: Say one contrast of interest is
> >> > -1 1 0 0 0 0 0 0 0 0 0 0
> >> > Then to get the RFX result for this run I'd do "Paired t-test" from
> >> > the "Basic Models" button, number of pairs is the number of subjects,
> >> > then you'd enter for each subject their cond_001.img and cond_002.img
> >> > images. Then you'll have to use the contrast manager to define
> >> > two contrasts, [-1 1] and [1 -1].
> >> >
> >> > Does this make sense (to all)?
> >>
> >>This seemed to work, but ONLY with the type of example you gave, where we
> >>are comparing two conditions. I found no way to use the Paired t-test to
> >>perform a contrast of the mean of 6 conditions with the mean of
>the other 6.
> >>
> >>I also tried doing the simple PET Multi-subject: conditions & covariates on
> >>the 15 subjects by 12 cond* files from stage 1 combined into two conditions
> >>(6 "scans" each). This gave results that seemed obviously wrong and had the
> >>df for the fixed effects model, which are MUCH greater than the correct df
> >>(14) for the RFX model.
> >>
> >>Jonathan
> >
> >Darren R. Gitelman, M.D.
> >-------------------------------------------------------------------------
> >Cognitive Neurology and Alzheimer's Disease Center
> >E-mail: [log in to unmask] WWW: http://www.brain.nwu.edu
> >Voice: (312) 908-9023 Fax: (312) 908-8789
> >Northwestern Univ., 320 E. Superior St., Searle 11-470, Chicago, IL 60611
> >-------------------------------------------------------------------------
> >
> >
>Jesper Andersson
>Wellcome Dept. of Cognitive Neurology
>12 Queen Square
>London WC1N 3BG
>phone: 44 171 833 7484
>fax: 44 171 813 1420
Darren R. Gitelman, M.D.
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Cognitive Neurology and Alzheimer's Disease Center
E-mail: [log in to unmask] WWW: http://www.brain.nwu.edu
Voice: (312) 908-9023 Fax: (312) 908-8789
Northwestern Univ., 320 E. Superior St., Searle 11-470, Chicago, IL 60611
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