hi eugene, we thanks you for this explanation.
I spent days reading several threads, in order to understand the covariate issue and its rule (orthogonalization, demeaning ), but I did not really catch that demeaning has no effect in zero-mean contrasts.
I indeed think that a web page addressing these issues is really necessary. Covariates management occurs in most (maybe all) studies, glm is very flexible and the official documentation do not cover all the main possibilities. This list is a wonderful pit of information but, at least for a beginner user like me, sometimes cryptic.
As a possible wishlist for your web page, I figured out several scenarios, would you please confirm my hypothesis or correct them.
1)
one group with 2 confounding variables (gender, age) I want to control for
Mean cov1 cov2
A 1 x +1
B 1 y +1
M 1 z +1
N 1 w -1
Mean controlling for age and gender [1 0 0]
Effect of gender controlling for age [0 1 0]
Effect of age controlling for gender [0 0 1]
If cov values are demeaned, its like they were orthog wrt mean, with respect to non-zero mean contrast like [1 0 0]. When I add a covariate and I orthogon it wrt mean, I just safely soak up extra variance and not affect the mean fitting?. as stated in
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0801&L=FSL&D=0&P=188382
I cannot find how to connect with what stated here;
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind06&L=FSL&D=0&P=1128606
>> The thing to remember is that if you orthogonalise variable A wrt variable B, it has no effect on the results for variable A. It only affects variable B. Counterintuitive, I know, but think about it this way. The GLM only uses the orthogonal part of the regressors to estimate the PEs. If you orthogonalise A wrt B. The orthogonal part of A (covariate) remains the same, but all of the joint space now moves into the orthogonal part of B (mean fitting). It is B that has really changed.
Actually I want to remove the effect of the covariate on mean fitting, the mean must change. So I should orthogon. what am I not understanding. What happens if I do not orthog or I do not demean?????
2)
like 1 but with a also covariate of interest (a RT) whom effect over the mean I want to investigate after having partialled out the 2 confounds
Mean cov1 cov2 cov3
A 1 x +1 x
B 1 y +1 y
M 1 z +1 z
N 1 w -1 k
Mean controlling for age/gender/RT [1 0 0 0]
Effect of gender controlling for age/RT [0 1 0 0]
Effect of age controlling for gender/RT [0 0 1 0]
Concerning RT:
I orthogon both age and gender wrt RT, so that RT might explain the max possible variance: [0 0 0 1] (controlling for age and gender)
(decipted from https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind04&L=FSL&D=0&P=424448)
Does this last contrast means: at which voxels my signal contain variance which can be explained by my RT after accounting for variance explained by my task EV , ?.
Or do I have to orthog also the mean wrt RT ? which is the latter meanings?
3)
I have two groups, unmatched for one or more covariates, eg. Age.
I want to know how would be group differences if they had similar ages (that is, I want to control group differences for age).
Grp mean1 mean2 Age gender
A 1 1 0 x +1
B 1 1 0 y +1
M 1 0 1 z +1
N 1 0 1 w -1
demeaning a covariate do not affect contrasts with zero sum. (like mean group differences), but just the regressor intercept.
If I demean I will just predict the level of signal when the covariate is at its mean level in the study ( What do I predict if I do not demean????).
You must demean over all subjects and not in the two groups separately, otherwise you will move some age-related variance to group differences one.
Gender values are not demeaned in order to represent the average response in the population rather than the average response in the sampled group,
which may have an imbalance in gender
And investigate group differences like this:
1>2 1 -1 0 0 (controlling for age and gender)
2>1 -1 1 0 0 (controlling for age and gender)
1 1 0 0 0
2 0 1 0 0
Voxel Corr with age 0 0 1 0 (controlling for gender)
4)
I would like to investigate if and how age correlates within each group (the age*group interaction)
Grp Gr1 Gr2 Age1 Age2
A 1 1 0 x 0
B 1 1 0 y 0
M 2 0 1 0 z
N 2 0 1 0 w
Using the same values as before (again demeaning around a global mean)
1>2 1 -1 0 0 (controlling for age)
Group diff in age corr 0 0 1 -1
Overall age corr 0 0 0.5 0.5
Gr1 age corr 0 0 1 0
Gr2 age corr 0 0 0 1
5)
I don’t want to control for age, I want to investigate the effect of age regardless of the task
I don’t know if the previous models (3: globally, 4: within each groups separately) already solve this questions.
There is in fact a further possibility. Orthogonalize the mean wrt the covariate.
I should obtain a “stricter” relation between areas activation and the covariate, regardless of the task.
For example, I have to 1st level conditions that have different mean RT. I want to know which area may explain this RT difference. How do I proceed?
Thanks in advance
Alberto
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