Good morning!

I am writing to you to check if my design matrix/ test makes sense and is right.

So I have a group of subject which are tested at 3 time points (M1,M2,M3). Each time we have mri acquisition and we are making some cognitive test (one of them is the MMSE).

I would like to see if some of the change in my connectivity is related to the change of my MMSE over time.
So my idea was to compute the difference of connectivity between my first time point and my second time point as well as between my first time point and my third time point (so M1-M2 and M1-M3) and try to covariate with the difference of MMSE (but keep the information of the individual subject using the block exchange).

So my design matrix:

1 2 1  0  0
1 3 0  1  0
1 1 0  0  1
1 6 1  0  0
1 2 0  1  0
1 3 0  0  1
with the second column the difference between my MMSE (first 3 lines the M1-M2 and the last 3lines M1-M3), and the 3 last columns the subjects.
So my contrast is 0 1 0 0 0.

Am I allowed to use the covariate with block exchange or  would it be better to drop the columns of subjects?
I hope I am clear in my explaination.

Thanks a lot for the help!
Cecile

Hi Cecile,

This appears to be a reasonable design. However, note that that you will need to remove the first column of 1's because you are modelling the within-subject mean. You will receive a rank deficient error if you include a columns of 1's.

Adding a covariate (or multiple covariates) is fine.

Note that one of the potential disadvantages of this design is that you could also consider the differences M1-M2 and M2-M3, and thus M2 becomes your reference point. I am pretty sure that this will yield different results than if you use M1-M2 and M1-M3, where M1 is your reference. The choice of reference might be considered arbitrary. 

If you use a t-test, you should probably try two constrasts: [ 0 1 0 0 ....] and [0 -1 0 0 ...]

Anyway, I think that this is a reasonable design. Perhaps others may have alternative opinions on this design?

Andrew
PS I sent you and email a few week ago explaining a solution the previous issue with negative test statistic values. I hope you received the comment. 

Originally posted by Cecile Bordier:

Fantastic!!!
Thanks a lot!

Cc

Ps: Yes I saw your message... I left a reply on the conversation yesterday to explain to people who could be interested my mistake (the ttest instead of ftest). I re-ran it and now my fvalue are very near zero but positive. Thanks a lot for your patience!