Good morning,

Thanks a lot for this forum, it helped me a lot and is really useful
I have a question because after making an analysis I realized that what I did is probably not statistically correct.

I have a longitudinal analysis (more or less 3 years between my 2 acquisitions T1 and T2). My idea was to compare the change of connectivity between my two acquisitions. However, my subjects have a large range of age so I wanted to add the age as covariate.

My design matrix is the identity matrix on column (size number of subject), a vector of 1 and -1 for the 2 time point and a vector of age:

example for 3 subjects (the 4 first columns: 3 comuns for the subjects one for the time)
1 0 0  1
0 1 0  1
0 0 1  1
1 0 0 -1
0 1 0 -1
0 0 1 -1
My problem and so my question is about the vector of age. Do I use only the age at T1 (so the vector would be [ageT1;ageT1])  because the information is redundant (more or less 3 years apart) or do I make a vector [ageT1;ageT2] considering that the 3 years is not exactly 3years. In the second case, I believe the model adequate should be a model mix linear, can we model it with NBS?

I hope I have been clear in my question/explanation.
Thanks a lot for your help!
Cecile

Hi Cecile,
I understand your question. 

It would not make sense to include [ageT1;ageT1] as an additional column. Indeed, this would result in the design matrix becoming rank deficient. To understand why, remember that each subject is already modeled with their own unique mean (random effect, separate column in the design matrix), which already accounts for age. 

It would also not make sense to include [ageT1;ageT2], if the gap between T1 and T2 is the same. It would however be ok if the gap differed between individuals, although that opens a whole new can of worms.

You might be interested in testing an interaction effect between age and acquisition time. For this, you could add an additional column formed from the element-wise multiplication of [ageT1;ageT1] and the -1/1 column for time. This would tell you whether the younger/older people show a bigger/small change between the two time points.I think that this is probably what you would be most interested in if you are studying age effects.

Another approach would be to use a full-blown mixed effects model, but this cannot be done in the NBS.

Andrew

Originally posted by Cecile Bordier: