Hello all,
I have a question concerning the set up for a 2 x 2 design.
First I am going to assume that the beta values are estimated
using
beta=pinv(X)*Y
instead of
beta=(XT*X)-1*X*Y
If I have a 2x2 design which of course has four cells I can model this
with four columns one for each cell. Now since regression always uses a
column of ones to model the constant I can have two situations:
1)If I convolve with the hrf I have independent columns so there
is no problem with the inversion; except that the columns are almost NOT
uniquely specified.
2)If I do not convolve with the hrf I no longer have independent
columns because the columns of my design sum across rows to equal ones.
Therefore the columns are not uniquely specified and the (XT*X)-1 would
not work.
I know that the psuedoinverse takes care of such inversion
problems but would it just be better to create a design that CAN be
inverted, so that (XT*X)-1 would work?
For example only specify three of the cells as seperate columns
and perform all tests in the context of the three columns.
If the design is:
A B
C D (this is supposed to represent a 2x2 design)
Only specify B,C,D and the interaction is D-B-C
the two main effects are C+D-B and B+D-C
So if anyone has any input on this topic it is greatly
appreciated,
thank you,
Jason.
Jason R. Steffener, RTSV
Department of Psychiatry, University Hospital, UMDNJ
Office: (973) 972-1604
Updated Webpage!!
http://www.umdnj.edu/~steffejr
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