ABtoAB {lazy.mat}R Documentation

Linear Constraints Matrices: from (A, d) and (B, c) to (AA,dd,EE,gg) and (BB,cc)

Description

Linear Constraints Matrices: from (A, d) and (B, c) to (AA,dd,EE,gg) and (BB,cc)

Usage

ABtoAB(A = 0, d = 0, E = 0, g = 0, B = 0, c = 0, eps = 1e-09,
  useginv = 1, useeigen = 1, print = 0)

Arguments

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

Details

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

Value

A list of new (A and d) and new (B and c).

References

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.


[Package lazy.mat version 0.1.3 Index]