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Subject:

Re: Dear Dr. Penny, without con*.img, how to do 2nd level analysis?

From:

Will Penny <[log in to unmask]>

Reply-To:

Will Penny <[log in to unmask]>

Date:

Mon, 17 May 2010 11:59:50 +0100

Content-Type:

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Dear Donna,

francis8 wrote:
> Dear Dr. Penny,
> Thank you so much for the help!
> Sorry for several further questions:
>  
> 1) For getting con*.img, I MUST define T contrast instead of F contrast, 
> even if the model specification uses informed basis function. Right?
>  

Yes !

> 2) For a contrast [1 0 0], a con*.img = a beta*.img. (I ever tested it 
> with one subject and found it is right, but I am not completely sure.) 
> Right? So, in this situation, 2nd level analysis using con is equivalent 
> to that using beta. Right?

Yes !

>  
> 3) For a contrast [1 -1], a con*.img = a beta*.img SIMPLY MINUS another 
> beta*.img. Right? 

Yes.

So, the following two analysis methods should be
> equivalent: a) getting the con in the 1st level and then use it in the 
> 2nd level. b) using two betas instead of one con in the 2nd level 
> analysis; and define the contrast [1 -1] in the 2nd level. Right?

Almost. The degrees of freedom in the test will be different - you have 
twice as many scans and an extra parameter. So for (a) DF=N-1, (b) 
DF=2N-2.  Also the estimated error variances will be different. These 
two factors will make a minor difference to the result.

>  
> 4) For several sessions, the con*.img is just the simple sum of the 
> beta*.imgs. (I ever tested it with one subject and found it is right, 
> but I am not completely sure.) Right? So, the following two analysis 
> methods should be equivalent: a) getting the con in the 1st level and 
> then use it in the 2nd level. b) using several betas instead of one con 
> in the 2nd level analysis; and define the contrast [1 0 0 1 0 0 1 0 0 ] 
> in the 2nd level. Right?
>  
> 

Yes - but see answer to last question


> 5) Generally speaking, a con*.img always = weighted sum of related 
> betas, where the weights are EXACTLY a b c... in the corresponding 
> contrast [a b c ...]. Right? 

Yes !

So, the following two analysis methods
> should be equivalent: a) getting the cons in the 1st level and then 
> use them in the 2nd level. b) using betas instead of cons in the 2nd 
> level analysis; and define the contrasts in the 2nd level. Right?
> 
> 6) What does the following two contrasts EXACTLY mean? They are EXACTLY 
> equivalent?
> 
> 1 0 0; 0 1 0; 0 0 1 OR
> 

If you put these in an F-test then it will test for all linear 
combinations of the first 3 variables.

> 1 0 0
> 
> 0 1 0
> 
> 0 0 1
> 

If you tried these 3 t/F's serially then is tests for each variable 
separately.

> 7) I tried a sencond level analysis in the following way:
> 
> I defined a full factorial of 3 (sessions) * 2 (main concerns) * 3 
> (basis functions), and so got 18 cells. For each cell I then input  each 
> subject's correponding beta*.img. I then defind contrast as should in 
> 1st level.
> 

If I were you I'd just take the canonicals to the 2nd level. Given you 
have two 'main concerns', then for each subject make a differential 
contrast: 1 -1 on the canonicals. This gives a single con image per 
subject.

If your 'Sessions' are the different fMRI sessions or runs for the same 
subject then I would average over them ie. do a 1 -1 .... 1 -1 .... 1 -1
for each subject. This then still gives you a single con per subject to 
take to the second level.

Your second level design is then just a simple t-test.

You can then compare the above approach with taking two effects to the 
second level per subject ie the canonical and the temporal deriv (with 
the latter defined using exactly the same 1 -1 ... 1 -1 ... 1 -1 
contrasts but now loaded onto the temp derive columns). Then use a two 
sample t-test at the second level and a [1 0; 0 1] contrast at the 
second level. See the face group data analysis chapter in the SPM manual 
for more on this.



> Is the above analysis right? SPM8 takes these factors as  within subject 
> or between subject? If between, then how can the manual define 3 basis 
> functions in this way? If within, then how to define a between subject 
> factor?
> 
> INSTEAD OF using the button "Specify 2nd level", I used button "Batch" - 
> "SPM" - "Stats" - "Factorial design specification" (so as to add other 
> convenient modules). Are these two methods equivalent?
> 

Yes.

> I cannot understnad the resulted design matrix of "positive effect of 
> ..." ( I can undertand those of "main effect of..." and "interaction 
> of...) Could you recommend some material which can help me understand it?
> 
> If I use a total test of informed bfs, then it MUST be a F-test. Right? 
> In fMRI area, is it common to publish no-direction F-test? Or only 
> with-direction T-test is common? I am worrying that if I adopt a T-test, 
> there will not be enough activated voxels.

You can mask these results with a t-test on the canonical so as to 
restrict your inferences to positive (or negative responses).

Best,

Will.

> 
> Thanks a lot again!
> 
> Looking forward to you reply!
> 
> Best wishes,
> 
> Donna
> 
> 
> 2010-05-14"Will Penny" <[log in to unmask]> д
>>Dear Donna,
>>
>>francis8 wrote:
>>> Dear Dr. Penny,
>>> 
>>> Could you help me with the following questions about group analysis,
>>> which I cannot solve even after spending two days in searching and
>>> reading relevant webpages (including SPM emaillist archives and your
>>> ppt on it.)
>>> 
>>> I did 1st level F-test with informed basis functions on each
>>> subject's multi-sessions (each session has the same design matrix
>>> columns). My interested variables are two parametric ones. So, in
>>> each sesssion, the contrast has only one 1 like 1 0 0...; for
>>> informed bf, the contrast is like [1 0 0...; 0 1 0...; 0 0 1...]
>>> (RIGHT?). 
>>
>>Yes, that's correct.
>>
>>Now I move to 2nd level analysis and encounter the
>>> following questions. My SPM edition is SPM8.
>>> 
>>> i) The first level analysis produced image files prefixing with beta,
>>> ess and spmF (but not con as in the example in the manual.) 
>>So, which
>>> kind of image files should I select for the 2nd level analysis?
>>
>>You will need to enter three separate contrasts for each effect you are 
>>interested in [1 0 0], [0 1 0], then [0 0 1].
>>
>>If you have two effects, then this will give you 6 con images per 
>>subject to take to the 2nd level.
>>
>>  (A
>>> related question: for a contrast 1 -1, the con*.image is just a
>>> beta*.image - another one? or it also takes variance for each beta
>>> into account?)
>>
>>No, for 1 - 1 it is a difference of bete images. It does'nt take the 
>>variance into account.
>>
>>> 
>>> ii) If the beta should be used, then a further question: I have
>>> several sessions, and so have several beta images for each regressor
>>> per subject. Since the relationship of beta images within one subject
>>> (between sessions) should be different from that of between subjects,
>>> it seems unreasonable to simply pool these sessions as subjects. So,
>>> what is the reasonable solution?
>>> 
>>
>>You should average within subject ie take your 3 sessions for each 
>>subject and average them eg. if you have 3 sessions and 6 con images per 
>>session then average over sessions to produce 6 con images.
>>
>>Hope this helps.
>>
>>Let me know if you have a problem.
>>
>>Best, Will.
>>
>>> a) firstly average the corresponding images across sessions within
>>> each subject and then only input the average images for the group
>>> analysis? Is this reasonable if not best? (note: session effect is
>>> not what I care about.) b) take sessions as an independent varibale?
>>> In this case, how should I define the contrast (for the 2nd level
>>> analysis) for informed basis functions? As I know, the original form
>>> should be eye (n); but now what should it be? c) any other better
>>> solutions?
>>> 
>>> Looking forward to your help.
>>> 
>>> Many thanks and best wishes,
>>> 
>>> Donna Francis
>>> 
>>
>>-- 
>>William D. Penny
>>Wellcome Trust Centre for Neuroimaging
>>University College London
>>12 Queen Square
>>London WC1N 3BG
>>
>>Tel: 020 7833 7475
>>FAX: 020 7813 1420
>>Email: [log in to unmask]
>>URL: http://www.fil.ion.ucl.ac.uk/~wpenny/
>>

-- 
William D. Penny
Wellcome Trust Centre for Neuroimaging
University College London
12 Queen Square
London WC1N 3BG

Tel: 020 7833 7475
FAX: 020 7813 1420
Email: [log in to unmask]
URL: http://www.fil.ion.ucl.ac.uk/~wpenny/

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