ABtoAB {lazy.mat} | R Documentation |
Linear Constraints Matrices: from (A, d) and (B, c) to (AA,dd,EE,gg) and (BB,cc)
ABtoAB(A = 0, d = 0, E = 0, g = 0, B = 0, c = 0, eps = 1e-09, useginv = 1, useeigen = 1, print = 0)
A |
Form A constraints matrix A. |
d |
Form A constraints vector d. |
E |
Additional Form A constraints matrix E or 0. |
g |
Additional Form A constraints vector g or 0. |
B |
Form B constraints matrix B. |
c |
Form B constraints vector c. |
eps |
eps for zero. |
useginv |
= 0 to use matSwp function instead of ginv in MASS. |
useeigen |
= 0 to use QRGS with orth=0. |
print |
= 1 to print result |
This function converts a conbination of form A and form B
constraints to
quivalent form A and form B constraints.
To find a Form B expression of
beta = A %*% gamma + d with E %*% gamma = g,
where each row of E is in the row space of A,
we must proceed as follows:
First, using Form B to Aorm A conversion
where F = El and h = ginv(E' %*% E) %*% E' %*% g.
Second, write the original Form A restriction as
beta = A %*% (F %*% deta + h) + d
= AA %*% delta + dd,
where AA = A %*% F and dd = d + A %*% h.
Third, find Form B of the above, i.e.,
B = AAr and c = B %*% dd
where I(p) - AA %*% ginv(AA' %*% AA) %*% AA' = AAl %*% AAr
A list of new (A and d) and new (B and c).
Mayekawa, Shin-ichi. (1996)
Maximum likelihood estimation of the cell
probabilities under linear constraints.
Behaviormetrika, Vol.23, No.1, 111-128
Takane, Yoshio, Yanai, Haruo, and Mayekawa, Shin-ichi. (1991)
Relationships among several methods of linearly constrained correspondence
analysis. Psychometrika, Vol. 56, 667-684.