## Approximate Standard Errors

Except for unweighted and diagonally weighted least-squares
estimation, approximate standard errors
can be computed as the diagonal elements of the matrix

The matrix **H** is the approximate Hessian matrix of *F* evaluated at
the final estimates, *c*=1 for the WLS estimation method,
*c*=2 for the GLS and ML method, and *N* is the sample size.
If a given correlation or covariance matrix is singular,
PROC CALIS offers two ways to compute a generalized inverse
of the information matrix and, therefore, two ways to compute
approximate standard errors of implicitly constrained
parameter estimates, *t* values,
and modification
indices.
Depending on the G4= specification, either a
Moore-Penrose inverse or a G2 inverse is computed.
The expensive Moore-Penrose inverse computes an estimate of the
null space using an eigenvalue decomposition. The cheaper G2
inverse is produced by sweeping the linearly independent rows and
columns and zeroing out the dependent ones.
The information matrix, the approximate covariance matrix of the
parameter estimates, and the approximate standard
errors
are not computed in the cases of unweighted or diagonally weighted
least-squares estimation.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.