Hi,
I have a group of 14 subjects with a single task at 3 different
different levels of difficulty. I did a fixed level analysis for the
task at each difficulty level.
I would like to do a RFX analysis and examine if there is a linear
increase (decrease) with difficulty level. I can think of 2 approaches
to model the variance with difficulty level and I am undecided about the
best way to proceed.
Would it be correct to define the model as (shown with 2 subjects for
simplicity)
EV1 EV2 EV3 EV4
subj1, level1 1 0 0 1
subj1, level2 0 1 0 2
subj1, level3 0 0 1 3
subj2, level1 1 0 0 1
subj2,level2 0 1 0 2
subj2,level3 0 0 1 3
.....
where the contrasts for linear increases in activation would be [0 0 0
1] and decreases would be [0 0 0 -1].
EV1 would model the average variance across subjects for level 1, EV2
would model the average variance across subjects for level 2, and
similarly for EV3 and level 3. EV4 would model the linear increase in
variance (if any) due to task difficulty.
The second approach would be
EV1 EV2 EV3
subj1, level1 1 0 1
subj1, level2 1 0 2
subj1, level3 1 0 3
subj2, level1 0 1 1
subj2,level2 0 1 2
subj2,level3 0 1 3
so that EV1 would be the average variance across the 3 levels of
difficulty for subj1, EV2 would be the average variacne across the 3
levels of difficulty for subj2. EV3 would model the linear increase in
variance with difficulty level. Thus in this model, there would be one
EV for each subject to model the average variance across the tasks.
It seems to me that the second approach would be the better one. I have
tried this model and I get a message that the design matrix is rank
deficient. If this would be the better model, is there a better way to
define the model so that I do not have a rank deficient matrix ?
TIA
Best, Arun
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