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The CALIS Procedure |
Relationships among Estimation Criteria |
The five estimation functions, ,
,
,
, and
, belong to the following two groups:
The functions ,
, and
take into account all
elements of the symmetric residual matrix
. This means that the off-diagonal residuals contribute twice to
, as lower and as upper triangular elements.
The functions and
take into account only the
lower triangular elements of the symmetric residual matrix
. This means that the off-diagonal residuals contribute to
only once.
The function used in PROC CALIS differs from that used by the LISREL 7 program. Formula (1.25) of the LISREL 7 manual (Jöreskog and Sörbom 1988, p. 23) shows that LISREL groups the
function in the first group by taking into account all
elements of the symmetric residual matrix
.
Relationship between DWLS and WLS:
PROC CALIS: The and
estimation functions deliver the same results for the special case that the weight matrix
used by WLS estimation is a diagonal matrix.
LISREL 7: This is not the case.
Relationship between DWLS and ULS:
LISREL 7: The and
estimation functions deliver the same results for the special case that the diagonal weight matrix
used by DWLS estimation is an identity matrix (contains only 1s).
PROC CALIS: To obtain the same results with and
estimation, set the diagonal weight matrix
used in DWLS estimation to
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Because the reciprocal elements of the weight matrix are used in the goodness of fit function, the off-diagonal residuals are weighted by a factor of 2.
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Copyright © 2009 by SAS Institute Inc., Cary, NC, USA. All rights reserved.