Page 359 - Contributed Paper Session (CPS) - Volume 7

CPS2130 Abdul-Aziz A. Rahaman et al.

2.1 Residual Estimators
Three residual estimators, comprising regression, Bartlett’s and the
Anderson-Rubin methods, in SEM have been proposed in the past. This study
incorporates the EM method within the SEM framework and seeks to compare
it against the other known residual estimators.
2.1.1 Regression Method
The most popular choice to use for the weight matrix W is based on the
work of Thurstone (1935) who used the principles of least squares to derive
W. Consequently, this method is frequently referred to as the regression
method. Under this method, W is chosen such that

Where is the (m+n)×(m+n) population covariance matrix of Li such that

And is the inverse of the population covariance matrix of zi . Bollen and
Arminger (1991) and Sanchez et al. (2009) use this weight matrix in the
construction of their residual estimators.
2.2.2 Bartlett’s Method
Another popular choice to use for the weight matrix is referred to as
Bartlett's method due to Bartlett (1937) who derived the weight matrix using
the principles of weighted least squares. Under this method, W is chosen such
that

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