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phi_1
2006 Aug 16
0
confusing about contrasts concept [long]
.../3 0
[3,] -1/12 -1/12 -1/12 1/4
(ginverse() will be available in S+4.0 and fractions(), now available in
the MASS2 library, simply displays numbers in fractional form so that
patterns are more obvious).
Thus the phi's are identified by requiring that they add to zero, and
*alpha_l = (phi_2 - phi_l )/2,
*alpha_2 = [phi_3 - (phi_l + phi_2)/2] / 3
&c. When the columns of C are not mutually orthogonal the story is not
quite so obvious, though. For example take a C matrix using contr.sdif
(available in the MASS2 library)
> contr.sdif(4)
[2-1] [3-2] [4-3]
1 -0.75 -0.5 -0.25
2 0.25 -0.5 -0...