Dear Eric:
Thank you for the clarification. So my understanding is that the "true"
inter-subject variance can never be less than the intrasubject variance;
however, "estimates" of the variances may work out to show smaller RFX than FFX
variance for particular subject(s). This can occur because of SNR issues or
problems with estimates of the autocorrelations or other reasons you mentioned.
Thanks,
darren
Quoting Eric Zarahn <[log in to unmask]>:
> Dear David and Darren,
>
> If one defines intersubject variance as the variance associated with the the
> pdf of true within-subject parameters (call this sigma^2) plus the variance
> associated with the pdf of the estimator of the parameter within a subject
> (i.e.., the intra-subject variance), then it is impossible for the
> intersubject variance to be less than the intrasubject variance (however it
> is possible for the estimated intersubject variance to be less than the
> estimated intrasubject variance).
>
> Also, if sigma^2 is many times smaller than the intra-subject variance, then
> the signal:noise for an N = 7 RFX estimator is sqrt(7) = 2.6 times greater
> than an N = 1 FFX estimator. Taking this into account, there are effect
> sizes such it is not unlikely to get a p value < .001 in the RFX analysis and
> a p value > .01 in the N = 1 FFX analysis.
>
> An additional point is that the autocorrelation structure of the random
> variables is assumed in the FFX analyses, while independence seems
> self-evidently assured in the RFX analysis. Thus, it is not unreasonable to
> entertain the possibility that one is overestimating (or underestimating) the
> FFX variance depending on the temporal structure of the paradigm, the
> extrinsically applied temporal filtering, and the assumed intrinsic
> autocorrelation stucture. This could lead to incorrectly inflated (or
> deflated) p values at the FFX level. This is not a concern per se at the RFX
> level.
>
> Eric
>
> ----- Original Message -----
> From: "Kareken, David A." <[log in to unmask]>
> To: <[log in to unmask]>
> Sent: Sunday, June 19, 2005 12:49 PM
> Subject: Re: [SPM] Random vs Fixed Effects discrepancy in fMRI
>
>
> > Hi Darren,
> > Not only does your suggestion make good sense, it indeed turns out to
> > be the case. The ResMS.img shows nice focal "black holes" of very low
> > variance/SD in these areas (SD ~1.3).
> >
> > Thanks for the lead.
> >
> > -David
> >
> > > -----Original Message-----
> > > From: [log in to unmask]
> > > [mailto:[log in to unmask]]
> > > Sent: Saturday, June 18, 2005 3:42 PM
> > > To: Kareken, David A.
> > > Cc: [log in to unmask]
> > > Subject: Re: [SPM] Random vs Fixed Effects discrepancy in fMRI
> > >
> > >
> > > Hi David:
> > >
> > > This sounds like a case in which, for unclear reasons, the
> > > intersubject variance is less than intrasubject variance.
> > > Thus despite possibly small parameter effects they are
> > > consistent across subjects. I suggest looking at the variance
> > > images in the random effects data (ResMS.img files). Using
> > > imcalc with a function of sqrt(i1) will give you standard
> > > deviation. Also look at these images for some fixed effects
> > > data. Plot the "time series" (actually subject
> > > series) for some voxels using the RanFX analysis in the area
> > > of activation. Presumably you'll see consistent effect sizes
> > > across subjects.
> > >
> > > Darren
> > >
> > > Quoting "Kareken, David A." <[log in to unmask]>:
> > >
> > > > Hi all,
> > > >
> > > > I wonder if someone has insights into the following discrepancy
> > > > between a random (RFX) and fixed effect (FFX) result in fMRI. The
> > > > essential problem is that there is a much stronger RANDOM effects
> > > > result in selected areas in which not one single subject shows
> > > > activation in their single-subject, fixed effect analysis.
> > > There is
> > > > huge "activation" spanning the lateral ventricles, and an uncinate
> > > > focus (all < 0.001), but NONE of the single subject FFX
> > > analyses show
> > > > anything like this at < 0.01.
> > > >
> > > > I would certainly expect much stronger FFX signals than RFX
> > > signals,
> > > > but have never seen the opposite-- and wouldn't expect any.
> > > >
> > > > Some quick details are:
> > > > n= 7 subects (yes, I know, quite small, but not a final sample).
> > > > Blocked design. FFX analyses with corrections for serial
> > > correlation.
> > > > The FFX results are a somewhat complicated interaction consisting of
> > > > conditions
> > > >
> > > > 1/1 1/2 1/1 1/2 2/1 2/2 2/1 2/2
> > > >
> > > > where the number to left of the ''/" is a drug condition (drug v
> > > > placebo) and the number to the right of '/' is a task (1 or 2).
> > > >
> > > > The contrast images analyzed consist of the drug x task
> > > interaction: 1
> > > > -1 -1 1 -1 1 1 -1.
> > > >
> > > > Thanks for any help,
> > > > David K
> > > >
> > > > David A. Kareken, Ph.D., ABPP/ABCN
> > > > Board Certified Neuropsychologist
> > > > Associate Professor & Director of Neuropsychology
> > > > Department of Neurology (RI-1773)
> > > > Indiana University School of Medicine
> > > > Indianapolis, IN 46202
> > > > Tel: 317 274-7327
> > > > Fax: 317 274-1337
> > > >
> > > >
> > > >
> > >
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