You have to be aware of the role of observational designs in this  
issue. I suppose the two groups you are analyzing are like patients  
and controls, i.e. that the assignment to the two groups was not  
randomized.

In this case, 'covariates'  for which you can adjust are those that  
took their value before the group status (patient or control) was  
determined. Otherwise, the 'covariate' could be itself an effect of  
the group status. In fact, in the statistical literature on  
observational studies, 'covariates' are defined in this way; your  
global gray matter is not a legitimate covariate. You do not know if  
the differences in global gray are themselves an effect of being a  
patient or not. For an easy introduction and discussion, see the  
relevant chapter in the book by Gelman & Hill, Cambridge University  
Press.

If you include global gray as a covariate, you adjust your data  
potentially throwing away a real effect of group. If you do not, the  
large differences in global gray may swamp your voxel-by-voxel  
statistic, if they are not a real effect of group. Splitting the  
covariate into two does not help here, it just adjusts better (by  
adding an additional df).

My preference would be for reporting both analyses. If anyone can  
quote any reference on orthogonalizing the global gray before adding  
it as a covariate, I would be interested to read it.

Best wishes,
Roberto Viviani
Dept. of Psychiatry, University of Ulm, Germany

Quoting "Stephen J. Fromm" <[log in to unmask]>:

> On Wed, 23 Dec 2009 11:36:44 +0000, Harma Meffert
> <[log in to unmask]> wrote:
>
>> Dear SPM-ers
>>
>> I would very much appreciate your opinion on the following matter. I am
>> analyzing T1 images of two groups using VBM. Often global gray matter is
>> used as a nuisance covariate but I cannot do that because my groups differ
>> significantly on this covariate, as also commented on in a few other posts
>> and in the paper by Miller and Chapman (2001).
>>
>> However, it is very common in VBN to use a global measure as a nuisance
>> covariate to ?take out? or ?control for? the effect of global differences in
>> gray matter. So maybe another way to approach this would be to create two
>> covariates for global gray matter. One for the controls and one for the
>> patient group. Each would contain zeros for the other group and their scores
>> would be mean corrected. In that way you do ?correct? for global differences
>> in gray matter, but now I would do it per group. However, I am not sure this
>> is sound either, because it would change the groups in different ways.
>
> I believe the formal terminology would be that you're now modeling a "group-
> by-covariate interaction."
>
> I think your hesitancy ("not sure this is sound either") is well-founded.  I
> assume you're interested in group differences.  I think modeling a group-by-
> covariate interaction makes it difficult/impossible to consider a   
> _well-defined_
> group difference.
>
> Consider the case of no covariate.  Put simply, the group difference (this is
> voxel-by-voxel, of course) is the difference of the means of the groups.
> Graphically, each group is represented by a (vertical) scattering of  
>  data; the
> difference is the difference in the height of the centers of each scatter,
> where "center" is given by mean.
>
> Now suppose you do a simple ANCOVA, against the recommendation of Miller
> and Chapman.  Graphically, you now have a plot in two dimensions; the
> horizontal axis represents the covariate.  The data are no longer vertical
> scatters.  The best fit for each group will be a line; because there's only a
> single covariate, the lines are parallel.  So you can still   
> meaningfully define a
> difference between the groups; it's the vertical distance between the lines.
> The meaning is the predicted difference between the groups, assuming an
> individual in each group with the same global gray matter.  Because the lines
> are parallel, it doesn't matter what the global gray matter is---the  
>  distance is
> the same.
>
> If you now model a group-by-covariate interaction, the lines are no longer
> parallel.  There's no single vertical distance between the lines,   
> and there's no
> natural, canonical way to define a difference between the groups.  You _can_
> define a difference that depends on global gray matter, but there's no single
> choice of global gray matter.  One might suggest picking e.g. the average
> global over all subjects (both groups), but there's nothing inherently
> natural/canonical about that.
>
> Best,
>
> S
>
>
>>
>> Does anyone have an opinion on this matter?
>>
>> Harma Meffert
>> NeuroImaging Center Groningen
>