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ulsresids() is used by macro ulsfactor() to do ULS factor extraction by
a nonlinear least squares method.

Keywords: factor analysis
ulsresid(theta,0,vector(r),m) returns the residual matrix r - rhat as a
vector of length p^2, where r is a REAL p by p correlation or variance-
covariance matrix.  m > 0 is an integer specifying the number of
factors to extract.

rhat = dmat(psi) + V, where V is the best rank m approximation to r -
dmat(psi) in the least squares sense.

ulsresids() is used by macro ulsfactor() to do unweighted least squares
(ULS) factor extraction.

When __USELOGSULS, a LOGICAL scalar defined by ulsfactor(), has value
False, argument theta is interpreted as psi, the length(p) REAL vector
of uniquenesses.  When __USELOGSULS is True, theta is interpreted as
log(psi).  ulsresids() saves a copy of psi in variable _PSIULS.

Gary Oehlert 2003-01-15