Dear Badreddine,

> I have PET scans using a BEHAVIORAL PARADIGM
> 2 conditions
> scan s1 & s2 and respectively
> behavioral scores b1 & b2.
> 
> I wanted to regress the differences between s1 & s2 against b2. Since
> b1 is 0 (or almost 0) for all subjects, I used only b2 as a covariate
> of INTEREST in a similar design as of 5 Aug 1997. An Ancova model was
> used because this model was found to be appropriate for our studies.  I
> obtained interesting correlations but in a small cluster in an expected
> anatomical location (adjacent to the area of absolute change s1>s2.
> 
> Since there was a (neurobiological) possibility that 1) score b2
> (during s2) OR 2) diff (s1 - s2) could depend on the GLOBAL count s1
> (Gs1), I used exactly the same design as of Aug 1997 but in ADDITION I
> added GLOBAL_s1 as a CONFOUNDING covariate (after mean centering it and
> entering consecutively [0 G1subject1 0 G1subject2 .............
> G1subjectN]
> 
> The correlation are significantly better (with higher Z values and
> significant increase in size) when the CONFOUNDING covariate is added
> than when it is not added.
> 
> My questions are then purely statistical (but any comment is
> appreciated).  1) is this design still valid (by adding a confounding
> covariate the way I did)

I see no reason why not.  You are effectively allowing for condition
specific global regressors or, equivalently, modeling global x
condition interactions.  We tried this for a while with fMRI data, as a
model that went some way to accommodating geometric (as opposed to
additive) global effects,

> 2)Is there any redundancy in it (since Ancova
> used Gs1 and Gs2 to obtain adjusted values for s1 and s2, and I am
> again using Gs1 as a counfounding covariate).

It is not redundant - you are now effectively modeling global x
condition interactions in addition to the main effect of global
activity.

> 3) Is the confounding covariate (centeredGs1) added to the model as
> written below
> 
> WITH CONFOUNDING covariate
> binding s1 = s1 condition effect + subject effect + error;
> binding s2 = s2 condition effect +(centered b2)*regression slope + 
> (centeredGs1)  *regression slope + subject effect + error;
> Difference is
> Delta s2-s1= (CONDs2-CONDs1) + (centered b2)*regression slope + 
> (centeredGs1)  *regression slope + error
> 
> Previously WITHOUT CONFOUNDING covariate
> binding s1 = s1 condition effect + subject effect + error;
> binding s2 = s2 condition effect +(centered b2)*regression slope + 
> subject effect + error;
> Difference is
> Delta s2-s1= (CONDs2-CONDs1) + (centered b2)*regression slope + error

Yes but in all the above expressions there is also a 'common global
effect' which, because of the way you have entered the second global
confound, is the global effect estimated over s1 scans.

I hope this helps - Karl


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