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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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%