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Subject:

Re: AnCoVa Design

From:

Jesper Andersson <[log in to unmask]>

Reply-To:

[log in to unmask]

Date:

Wed, 20 Dec 2000 10:17:11 +0100

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text/plain (76 lines)

Dear Wei,


> My problem:
>
> I was doing analysis on a group of 8 subjects who had a scan (SPECT)
> each before and after treatment. I used "Population mean effect: 2
> conditions 1 scan/cond (paired t-test)". I guess this is the right
> model. But according to the discussion outlined in the lecture notes
> Chapeter 3 by Holmes and Friston, this model suffers from the problem of
> so-called "weighted" regression. I was then trying to use AnCOVa and see
> what would happen.  And I found that I could only use "compare
> population: 1 scan/subject (AnCOVA)" but not "multi-subj: conditions and
> covariates".
> What I tried to use:
> Multi-subjects conditions and covariates: I put 2 condtions, no
> covariate, no nuisance but in the end the report said: 2 condition, + 0
> covariate, + 8 block, + 8 nuisance: 18 total, having 16 degrees of
> freedom leaving 0 degrees of freedom from 16 images. Since there is no
> degree of freedom left and SPM couldn't carry on.

>
> I have noticed that Alex Gamma had 2 scans for each condition which is
> different from my case: 1 scan for each condition. Therefore, Alex could
> carry on with this design, but not me.  Therefore, my question is:  Is
> it correct to say that I cannot use this design (multi-subject:
> conditions and covariates) since I have only one scan for each
> condition? Besides the paired t-test and compare population mean
> (AnCoVa), anything else I could use? I found that I am getting different
> results from paired t-test and compare
> population mean (AnCoVa) (I used Ancova for the global normalization).
> If these 2 models are both OK, which results should I trust more? Back
> to the # of nuisance: I input the nuisance as 0, how come it came out as
> 8? (since there were 8 subjects and each one of them having a different
> residual? Is the error N(0, sigma) called nuisance here? And 8 subjects
> having 8 different this type of error? {N(0, sigma_k) k=1,2...,8}. If my
> last question is correct, then if I use "comparing population mean 2
> effects: 1 scan / condition" how come I only got one nuisance? Are all
> the subjects effectly taken as a single subject in this computational
> model?

The 8 nuisance regressors are columns of global activity for each subject (and zeros for the rows wich do not pertain to that subject). For example the first nuisance variable should be a column with the upper two values representing the global activity in the tow scans of the first subject, and zero elsewhere.
When using AnCova for global normalisation in multisubject studies SPM will (as of SPM99) always use what used to be called "AnCova by subject" in SPM jargon. Basically that means that it models a subject specific relation between local and global activity. The disadvantage, as you have well noticed, is that it consumes degrees of freedom, the advantage
is that the model is separable in subjects. The latter means that the variance explained by the globals in a specific subject does not depend on the other subjects in the group.
I see a couple of options for you

1. You could use "Multisubject: Conditions and Covariates" with proportional scaling for global normalisation. Current wisdom (I think) says that if you believe that the main source of global variation is differences in injected activity you should use proportional scaling, and if you believe it comes from "true" global regulation you should use AnCova.
Having said that, for practical purposes the two methods mostly generate very similar results. By the way, this will in your case generate an identical model to the "Population mean effect ...", I think.

2. You could "tweak" things to generate your own (good?) old fashioned AnCova design. You would then  start matlab, start SPM and then type in the matlab window

P = spm_vol(spm_get(Inf,'*.img'));
for i=1:length(P) my_global(i) = spm_global(P(i)); end

The first line will allow you to pick the scans in your study. You will have make sure you select the scans in the same order as you later select them when building the model. The second line will calculate a vector called "my_global" containing the global activity for each scan.

Having done that you select "Multisubject: Conditions and Covariates", select "No global normalisation" and enter 1 when asked for number of nuisance variables. When asked for the vector of values you just enter my_global. You dont want any interaction, and it doesnt matter if you select centering around "global mean" or "subject mean".

>
> One more thing, Alex, I have also noticed that you used an average of 2
> replications of each condition, which means that you used only one scan
> for each condition.It sounded that your design was the same as mine: one
> SPECT scan for each condition, no covariates, no nuisance etc. using
> AnCova for the
> global normalization and therefore, you would have zero degree of
> freedom
> left. How did you carry out the computation then? In my case, SPM
> refused to go on, which makes sense?
>

I'll leave this to Alex.

Good luck Jesper

>

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