Hi
just to avoid any confusion: the number of regressor that need to be
added when there are repeated measures varies and depends on the
number of repeats!
cheers
christian
On 27 Jul 2007, at 14:38, Christian Beckmann wrote:
> Hi,
>
> I'm afraid we won't be able to look at additional examples until
> we're finished with the next release but I can give you a quick
> 'ANOVA->GLM cookbook':
>
> (i) when setting up the GLM design matrix in my mind there is no
> difference between what are factors and what are levels: in an
> ANOVA the different combinations are cells in the ANOVA table while
> in the GLM equivalent design they turn into EVs with blocks of 1s -
> the only questions are how many of these EVs you end up having and
> what to do with the mean. Every ANOVA cell you need modelling will
> become a single EV to be included in your GLM. That is, a 3x2 ANOVA
> gives you 8 regressors if you don't have repeated measures and 9
> regressors if you do. For a 2x3 anova there then are 6/7 regressors.
>
> (ii) the contrasts are relatively easy to calculate using the logic
> I described in our previous email exchange
>
> (iii) As steve said the complexity comes in when you try to create
> the relevant F statistics: the GLM F's are always relative to the
> residual noise variance - if you want them relative to the amount
> of variance explained by one or a set of GLM EVs (or equivalently
> relative to the sum-of-squares explained by a factor/level) you
> simply form the quotients of the two, that is, if F_AR is the
> default GLM estimated F-test on a part of your design A against the
> overall residual sum-of-squares (and similarly for F_BR) then F_AR/
> F_BR calculates the amount of variance that A explains relative to
> B, i.e. gives you rfx of factorial anovas, see the notes after the
> 2x2 and 3x2 examples at http://www.fmrib.ox.ac.uk/fsl/feat5/index.html
>
> If you need more help please feel free to email again once FSL 4.0
> is out
> hope this helps
> Christian
>
> On 27 Jul 2007, at 00:32, Sophie Anisa wrote:
>
>> On 7/26/07, Steve Smith <[log in to unmask]> wrote: Hi Sophie,
>> yes you're probably right that 2x3 isn't quite the same as
>> 3x2, although presumably the difference really only comes down to
>> which set of options you want to describe different factors and
>> levels as fixed or random (see for example the table at the bottom of
>> http://www.fmrib.ox.ac.uk/fsl/feat5/
>> detail.html#ANOVA3factors2levels ).
>>
>> Hello Steve
>>
>> And thank you for replying to my question. I am sorry however, but
>> I must disagree with you! As I understand it a 2 factor by 3 level
>> design
>> (2x3) is *very* different from a 3 factor by 2 level design (3x2).
>> The former
>> involves 6 unique conditions, the latter 8 (2x2x2). Hence, no simple
>> rearrangement or relabelling from fixed to random can map 6 to 8
>> dimensions. More particularly, for a FEAT setup, the latter can be
>> modelled by binary classications in the structure of the FEAT design
>> matrix, making it easy to do intra-level comparisons. The former
>> cannot,
>> as it is it necessary to do separate events for each level.
>>
>> I'm afraid that the number of possibilities for ANOVA designs is
>> endless so we can't provide examples for all of them!
>>
>> Of course I must sympathise with your positition! But I am so very
>> stuck at the moment as I just cannot get my head around this. I just
>> do not see how to make the design matrix for such a higher order
>> model.
>> I guess from the later post of at least one other person
>> (Kristofer Kinsey)
>> I am not alone!
>>
>> So rather than asking for all possible examples, please please please
>> could you provide ONE example of a higher order ANOVA where there
>> is more than 1 factor (e.g. 2) and these factors are at more than
>> 2 levels
>> (e.g. 3)? I think the simplest example of this is the 2x3 design
>> (and yes
>> I know this is what I originally asked for but feel free to give a
>> better
>> example if it is more helpful)...
>>
>> merci
>>
>> Sophie
>
> ____
> Christian F. Beckmann
> University Research Lecturer
> Oxford University Centre for Functional MRI of the Brain (FMRIB)
> John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
> [log in to unmask] http://www.fmrib.ox.ac.uk/~beckmann
> tel: +44 1865 222551 fax: +44 1865 222717
____
Christian F. Beckmann
University Research Lecturer
Oxford University Centre for Functional MRI of the Brain (FMRIB)
John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
[log in to unmask] http://www.fmrib.ox.ac.uk/~beckmann
tel: +44 1865 222551 fax: +44 1865 222717
|