Martin

>I have one more question regarding the between groups analysis.
>
>As a reminder, I have two groups (15 and 13 subjects each) and 
>have made 
>contrast images for each subject as follows, based on the 
>three parameter 
>estimates for three basis functions (HRF + derivatives):
>
>con1: 1 0 0 -1 0 0      (1st beta A > B)
>con2: 0 1 0 0 -1 0      (2nd beta A>B)
>con3: 0 0 1 0 0 -1      (3rd beta A>B)
>
>Now I want to compare groups I and II, so I put the contrast 
>images into 
>one way ANOVA without constant:
>
>group 1:        con1    group I
>group 2:        con2    group I
>group 3:        con3    group I
>group 4:        con1    group II
>group 5:        con2    group II
>group 6:        con3    group III
>
>I say [yes] to non-sphericity correction.
>
>Then is asks: replications are over? AND THIS THE PROBLEM.
>
>The replications should be over subjects but my first group 
>has 15 subjects 
>and the second one only 13.
>
>So I put in "repl(15)" but then the pre-whitened design matrix 
>looks weird. 
>The color changes for the first three columns (group I) but 
>not for the 
>next three columns (group II). So I think the error covariance 
>matrix is 
>not correct and furthermore is not the inhomogeneity of 
>variance is not 
>modelled the same way for the two groups.
>
>Because ultimately, I want to compare groups I and II for all three 
>parameters (F-test):
>1 0 0 -1 0 0
>0 1 0 0 -1 0
>0 0 1 0 0 -1

Aha! My fault: remember, we are trying to trick SPM to handle 
within+between subject designs, but the SPM GUI cannot handle 
"correlated errors" when there are unequal numbers of replications 
per "group" (which makes sense, because if "group" really were 
a repeated measure - ie could induce correlated errors - it would 
have the same number of replications per level!).

Try the attached "batch_mixed_anova.m" script. It should give
you the kind of design you want, ie with the correct modelling of
correlated errors for the within-subject factors (condition/basis
function), but not for the between-subject factor (group).

Again, I hope this messy GUI will be updated in SPM5!

Rik

--------------------------------------------------------
DR RICHARD HENSON 
MRC Cognition & Brain Sciences Unit 
15 Chaucer Road, Cambridge, 
CB2 2EF England 
 
EMAIL: [log in to unmask] 
URL: http://www.mrc-cbu.cam.ac.uk/~rik.henson 
 
TEL +44 (0)1223 355 294 x522 
FAX +44 (0)1223 359 062 
MOB +44 (0)794 1377 345 
--------------------------------------------------------


>At 09:44 AM 6/23/2005 +0100, Rik Henson wrote:
>>>Martin wrote:
>>>I have two groups: controls and schizophrenics. I used the 
>canonical hrf +
>>>the two derivatives in my model. I created the following 
>contrasts for the
>>>difference between A and B for each subject from each group:
>>>[1 0 0 -1 0 0] canonical HRF A-B
>>>[0 1 0 0 -1 0] temporal derivative A-B
>>>[0 0 1 0 0 -1] dispersion derivative A-B
>>>I was then able to examine the overall effect for _each 
>group_ separately
>>>using a one-way ANOVA (without constant term), modelling the 
>three contrast
>>>images as three groups using the F-contrast:
>>>[1 0 0
>>>   0 1 0
>>>   0 0 1]
>>
>>>Antonia wrote:
>>>I think this step is a mistake (one I was making until 
>yesterday!). This 
>>>ANOVA means that you are looking for areas where the HRF, temp
>>>and disp differ from each other, not where they differ from zero.  So
>>>if you had a giant effect with positive values for all 3 contrasts,
>>>you wouldn't find it in this analysis.  Can anyone confirm 
>and suggest
>>>the proper analysis, because I don't know what it is?
>>
>>No, Martin is correct. If the contrast images are already
>>differences between conditions, then the F-contrast [1 0 0; 0 
>1 0; 0 0 1] 
>>is CORRECT for testing any
>>differences between the conditions in the shape of
>>the HRF (at least those shape differences that can be captured by the 
>>three basis functions).
>>
>>You are correct that an F-contrast that tested for
>>differences between the basis functions would NOT
>>be appropriate. However, such an F-contrast would be
>>some rotation of [1 -0.5 -0.5; -0.5 1 -0.5; -0.5 -0.5 1]
>>instead.
>>
>>And this is why it is important NOT to include a constant
>>term in the ANOVA. If you do include one, you will
>>find that you cannot evaluate the F-contrast [1 0 0; 0 1 0; 0 0 1],
>>because the design matrix is now rank deficient and the
>>contrast weights will need to sum to 1. You will also see
>>that the default "effects of interest" contrast looks like [1 
>-0.5 -0.5; 
>>-0.5 1 -0.5; -0.5 -0.5 1], and so is not
>>appropriate. You would need to redo without a constant.
>>
>>Finally, note that you should use "full" nonsphericity correction
>>(ie non-identically distributed and non-independent (correlated
>>errors)), because the (contrasts of) basis functions come from
>>the same subjects, and have quite difference scalings, so both
>>the variance and covariance of errors are likely to be nonspherical.
>>
>>
>>>Martin wrote:
>>>What if I want to compare the two groups now? Do I do a 
>one-way ANOVA where
>>>I enter six groups - one for each contrast for each group 
>and then do an
>>>F-contrast like:
>>>[1 0 0 -1 0 0
>>>   0 1 0 0 -1 0
>>>   0 0 1 0 0 -1]
>>>to get the overall effect?
>>
>>Yes. (If the contrast images were already differences between
>>two conditions, then this would actually test the "Group X Condition
>>interaction". To test the "main effect of Group", perform another
>>ANOVA, but this time with the contrast images being the average
>>(sum) of the two conditions, for each basis function).
>>
>>There is a slight problem here that this ANOVA really consists of
>>one within-subject factor (basis function) and one between-subject
>>factor (group), yet the SPM2 GUI does not allow you to specify a
>>error covariance basis set (for nonsphericity correction) with only
>>some (but not all) of the off-diagonal terms included. You can do this
>>by hand in matlab (in a batch script), or you can wait until 
>(hopefully) 
>>the whole "second-level" stats GUI options in SPM5 are 
>over-hauled (about 
>>time!).
>>But for now, I doubt there would be much harm in allowing "full"
>>nonsphericity correction anyway, and hopefully ReML will estimate
>>covariance terms close to zero for the between-subject covariances.
>>
>>
>>>Can I do an equivalent of the t-test above, such as:
>>>[1 0 0 -1 0 0] to find A>B group 1>2?
>>
>>Yes.
>>
>>Rik
>>
>>
>>----------------------------------------
>>Dr Richard Henson
>>MRC Cognition & Brain Sciences Unit
>>15 Chaucer Road
>>Cambridge
>>CB2 2EF, UK
>>
>>Tel: +44 (0)1223 355 294 x522
>>Fax: +44 (0)1223 359 062
>>
>>http://www.mrc-cbu.cam.ac.uk/~rik.henson
>>----------------------------------------
>