Hi Appu,
To do ANOVA with GLM, it is not so much a case of having different options
for fixed/random, as forming the right F ratios. The example at
http://www.fmrib.ox.ac.uk/fsl/feat5/detail.html#ANOVA3factors2levels
is correct for all fixed effects, and underneath this, there is a table
showing what ratios to use in other cases. You'll need to work out the
equivalent things for your particular ANOVA - good luck!
WRT correlations - forgetting ANOVA for the moment and concentrating on
the full covariance matrix in higher-level GLMs, which you rightly bring
up: in theory, one can pass up non-diagonal covariances from one level to
another, but this is overly-complicated to implement - hence, if you want
to model such correlations, then you need to do a 3-level analysis as
shown at
http://www.fmrib.ox.ac.uk/fsl/feat5/detail.html#MultiSessionMultiSubject
which then is a valid model for such things.
Hope this makes sense - thanks, Steve.
On Thu, 10 Jul 2003, Aprajita Mohanty wrote:
> Hi Steve,
>
> I have a few more questions about the following design that I e-mailed about. When
>
> we implement higher level stats in FEAT how is it specified which factor (between
> group and within group) will be treated as fixed or random. I did not see any
> option which will allow the user to specify for example that the within subject
> factor will be random and the between group factor should be fixed. Also, in the
> following example, each subject contributes three copes (pos, neg and neut) in the
>
> first level of analyses that serve as inputs for the higher level analyses. How
> does the higher level of analyses account for the dependency among these within
> subject measures?
>
> thanks
>
> Appu
>
> Stephen Smith wrote:
>
> > Dear Appu, nice! As far as I can see this design and contrast set looks
> > correct. Good luck :)
> >
> > Steve.
> >
> > On Thu, 26 Jun 2003, Appu Mohanty wrote:
> >
> > > Hi,
> > >
> > > We are interested in conducting a 1 between 1 within two-way ANOVA on our
> > > fMRI data. The between group factor has 5 levels corresponding to five
> > > groups and the within group factor has three levels corresponding to three
> > > experimental conditions (negative words, positive words, and neutral
> > > words). In our analyses we have 36 participants with 7 in group 1, 8 in
> > > group 2, 8 in group 3, 7 in group 4 and 6 in group 5. In the first level
> > > analyses we generate cope maps representing the negative, positive and
> > > neutral word conditions for each subject. We would like to use the copes as
> > > inputs to a higher-level analysis in such a way that we can implement the
> > > ANOVA, examining the main effect of emotion condition (positive, neutral or
> > > negative), the main effect of group (1-5), the interaction between the two
> > > main effects, and an omnibus test of the significance of the overall
> > > model. Our goal follows a traditional ANOVA design, in that we’re
> > > interested in finding those voxels/clusters whose activity significantly
> > > varies as a function of each of our factors (e.g. not just asking the
> > > question of whether one group or valence is significant).
> > >
> > > Our question: will the following model give use the ANOVA outputs looking
> > > for? Given that we have cope maps as inputs for each subject for each
> > > condition, here’s what the EV design matrix might look. Each row in the
> > > design matrix represents a single cope map (pos, neu and neg represent
> > > positive, neutral and negative word conditions respectively). For
> > > illustration, we’re pretending that there are only 3 subject per group.
> > >
> > > EV’s
> > > Input map grp 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
> > > pos_grp1_sub1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp1_sub2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp1_sub3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp2_sub1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp2_sub2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp2_sub3 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp3_sub1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp3_sub2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp3_sub3 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp4_sub1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp4_sub2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp4_sub3 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
> > > pos_grp5_sub1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
> > > pos_grp5_sub2 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
> > > pos_grp5_sub3 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
> > > neu_grp1_sub1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
> > > neu_grp1_sub2 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
> > > neu_grp1_sub3 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
> > > neu_grp2_sub1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
> > > neu_grp2_sub2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
> > > neu_grp2_sub3 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
> > > neu_grp3_sub1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
> > > neu_grp3_sub2 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
> > > neu_grp3_sub3 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
> > > neu_grp4_sub1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
> > > neu_grp4_sub2 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
> > > neu_grp4_sub3 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
> > > neu_grp5_sub1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
> > > neu_grp5_sub2 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
> > > neu_grp5_sub3 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
> > > neg_grp1_sub1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
> > > neg_grp1_sub2 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
> > > neg_grp1_sub3 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
> > > neg_grp2_sub1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
> > > neg_grp2_sub2 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
> > > neg_grp2_sub3 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
> > > neg_grp3_sub1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
> > > neg_grp3_sub2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
> > > neg_grp3_sub3 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
> > > neg_grp4_sub1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
> > > neg_grp4_sub2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
> > > neg_grp4_sub3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
> > > neg_grp5_sub1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
> > > neg_grp5_sub2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
> > > neg_grp5_sub3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
> > >
> > > And here is the contrast matrix and f-tests we’re thinking would give us
> > > the ANOVA outputs we’re interested in. The first four contrasts represent
> > > the main effect of group, the next two represent the main effect of
> > > valence, and the next 8 represent the interaction (this set of contrasts
> > > follows a cell-means model):
> > >
> > > 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 F1 F2 F3 F4
> > > C1 1 -1 0 0 0 1 -1 0 0 0 1 -1 0 0 0 on on off off
> > > C2 1 1 -2 0 0 1 1 -2 0 0 1 1 -2 0 0 on on off off
> > > C3 1 1 1 -3 0 1 1 1 -3 0 1 1 1 -3 0 on on off off
> > > C4 1 1 1 1 -4 1 1 1 1 -4 1 1 1 1 -4 on on off off
> > > C5 1 1 1 1 1 -1 -1 -1 -1 -1 0 0 0 0 0 on off on off
> > > C6 1 1 1 1 1 1 1 1 1 1 -2 -2 -2 -2 -2 on off on off
> > > C7 1 -1 0 0 0 -1 1 0 0 0 0 0 0 0 0 on off off on
> > > C8 1 1 -2 0 0 -1 -1 2 0 0 0 0 0 0 0 on off off on
> > > C9 1 1 1 -3 0 -1 -1 -1 3 0 0 0 0 0 0 on off off on
> > > C10 1 1 1 1 -4 -1 -1 -1 -1 4 0 0 0 0 0 on off off on
> > > C11 1 -1 0 0 0 1 -1 0 0 0 -2 2 0 0 0 on off off on
> > > C12 1 1 -2 0 0 1 1 -2 0 0 -2 -2 4 0 0 on off off on
> > > C13 1 1 1 -3 0 1 1 1 -3 0 -2 -2 -2 6 0 on off off on
> > > C14 1 1 1 1 -4 1 1 1 1 -4 -2 -2 -2 -2 8 on off off on
> > >
> > > So, my question: Will the four f-tests represent the omnibus test (F1), the
> > > main effect for group (F2), the main effect for emotion condition (F3), and
> > > the interaction (F4), given how the design and contrast matrices are set up?
> > > I can also send the fsf file as an attachment if it is more helpful.
> > >
> > > Thanks
> > >
> > > Appu
> > >
> >
> > Stephen M. Smith MA DPhil CEng MIEE
> > Associate Director, FMRIB and Analysis Research Coordinator
> >
> > Oxford University Centre for Functional MRI of the Brain
> > John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK
> > +44 (0) 1865 222726 (fax 222717)
> >
> > [log in to unmask] http://www.fmrib.ox.ac.uk/~steve
>
Stephen M. Smith MA DPhil CEng MIEE
Associate Director, FMRIB and Analysis Research Coordinator
Oxford University Centre for Functional MRI of the Brain
John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK
+44 (0) 1865 222726 (fax 222717)
[log in to unmask] http://www.fmrib.ox.ac.uk/~steve
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