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Hi,

Your first model with a column of 1's for "group" is appropriate.  It is an extension of this model
http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/GLM#Two-Group_Difference_Adjusted_for_Covariate

There isn't much of a benefit in splitting the variance up over groups unless you have very, very large data sets (maybe more than 100 in each group).  This is just something I've observed, empirically.  Using all subjects in the variance estimate is better for the variance estimate.

Cheers,
Jeanette



On Fri, Aug 29, 2014 at 4:04 PM, Nathan Hutcheson <[log in to unmask]> wrote:
Hello,

I am performing an ANOVA with three groups and wish to control for the effect of age. How can I model my three groups  with separate variances in the "Group" column, while still being able to remove the effect of a covariate of no interest (Age)? I have demeaned age across the three groups. I can not use the below model (Wrong Model) because I will get an error message stating that "design matrix uses different groups (for different variances), but these do not contain "separable" EVS for the different groups ...". The solution I found of the FSL page (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/GLM#Single-Group_Average_with_Additional_Covariate) was to enter all 1's in the "Group" column so that the Age vector would not be across separate groups. However, I still wish to model separate variance for each group because I don't know if their variance is different.

Wrong Model
Group   GroupA   GroupB   GroupC   Age
1          1             0           0            .5
2          0             1           0           -.2
3          0             0           1            .1


What about doing this alternate model below (Alternate Model)? This variation is intended to test the interaction of age across groups but if I enter zeros in the "Contrasts & F-tests" (see below), shouldn't this look at group differences while removing the effect of age? Also, I have entered some contrasts at the end to investigate if there are any age interactions- because if their are that will confound my ability to look at A > C and B > C while controlling for age.


Alternate Model
Group   GroupA   GroupB   GroupC   AgeA   AgeB   AgeC
1          1             0           0            .5        0         0
2          0             1           0            0       -.2        0
3          0             0           1            0         0        .1


Contrasts & F-tests
Title                     EV1   Ev2   Ev3   EV4   EV5   Ev6
Group A > C         1      0       -1      0       0       0
Group B > C         0      1       -1      0       0       0
slope A>slope B    0      0       0       1      -1       0
slope B>slope C    0      0       0       0       1      -1