TRAN1 is a hybrid Survo module for investigations
in transformation analysis related to factor analysis.
Assuming that A and B are factor matrices of p variables
and r factors,
TRAN1 A,B,L0
makes a transformation analysis from factor matrix A to B
by minimizing ||A*L-B||^2 with respect to L with certain
restrictions.
The optimal L is saved as a matrix file L1.M and it is
found iteratively from an initial matrix L0.
In most cases L1.M obtained by
/TRAN-SYMMETR A,B
is a good choice for L0.
Restrictions are given by specification RESTRICTION with
following alternatives:
RESTRICTION=0 no restrictions which leads to original
least squares solution.
Faster alternative: /TRAN-LEASTSQR A,B
RESTRICTION=1 (default) diag[inv(L'L)]=I,
RESTRICTION=2 ||E(A,B)||=||E(B,A)|| where
E(A,B)=A*L-B and E(B,A)=B*inv(L)-A,
RESTRICTION=3 1 and 2 simultaneously,
RESTRICTION=4 diag[E(A,B)*E(A,B)']=diag[E(B,A)*E(B,A)']
which seems to lead to the symmetric
solution with an orthogonal L.
Faster alternative: /TRAN-SYMMETR A,B
The solution is found iteratively by the polytope algo-
rithm of Nelder and Mead by minimizing
f(L)=||A*L-B||^2 + penalty*restriction
The penalty coefficient is given by PENALTY. Default is
PENALTY=10000.
1 = More information on additional multivariate operations
M = More information on multivariate analysis
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