I have 2 (20x10) data matrices,
Z2, which correspond to a 10-dimensional questionnaire acquired in two different days:
T2, on 20 subjects. I want to reduce dimensionality of the questionnaire, using PCA. I am interested in conducting a regression analysis:
Y ~ 1 + X1 + X2 + ... + Xn
where Y is the difference in brain activity between day1 and day2 (T1-T2),
n is the number of retained principal components, and predictors
X1...Xn represent the difference in the questionnaire scores between T1 and T2.
Does it make sense to run a PCA on the difference between the two questionnaires (
Z1-Z2)? Alternatively, which is the best approach in this case, if my primary interest is to reduce dimensionality before the regression analysis?
Useful info: 20 subjects filled a 10-dimensional questionnaire at time 1 (
T1) and time 2 (
T2). Brain activity was also measured at
T2. Dimensions of the questionnaire are not independent (there is correlation among them).
(In Can I do a PCA on repeated measures for data reduction? the solution was to use MFA, but, in my opinion, it makes no sense here, because I want the difference between questionnaire scores at T1-T2, and not a single score on repeated measures.)