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glsresids() is used by macro glsfactor() to do GLS factor extraction by
a nonlinear least squares method.

Keywords: factor analysis
glsresid(theta,0,vector(r),m) returns a length p^2 "residual vector"
computed from but not identical with dmat(p,1) - solve(r) %*% rhat,
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.

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

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

glsresids() is used by macro glsfactor() which does generalized least
squares (GLS) factor extraction.

Gary Oehlert 2003-01-15