Hi Steve,
A few more questions.
Stephen Smith wrote:
> 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
|