Hello,
I had a question regarding estimability of the SPM99 two-sample t-test
basic model. First, I am assuming that SPM99 does the following in
estimating the model.
b = (X'X)^-1 * X' * Y
where b is the parameter estimate vector, X is the design matrix, and Y
is the vector of observed data.
t = c'b / sqrt(s^2 * c' * (X'X)^-1 * c)
where c is the contrast vector and s^2 is the variance estimate
Are these indeed the equations implemented in SPM99?
Now, my design matrix is given by the following (I have a group of 10
and a group of 1):
1 0 1
0 1 1
0 1 1
0 1 1
0 1 1 = X
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
0 1 1
From this, we have
1 0 1
0 10 10 = X'X
1 10 11
We can see that this matrix is rank-deficient. So, how does SPM
estimate b and t without computing (X'X)^-1?
Also, is the t-test implemented by SPM a one-sided test? In other
words, should a contrast of [1 -1 0]' give different results than a
contrast of [-1 1 0]'?
Thanks in advance for any comments.
Sunil
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