A Limited-Information Estimator for LISREL Models With or Without Heteroscedastic Errors
The estimation of structural equation models (SEMs) is marked by two traits. One is the use of full-information estimators such as maximum likelihood (ML) or generalized least squares (GLS). The other is that the derivations of these estimators assumes that the variances of the disturbances or errors in each equation are constant across observations, that is, they are ho moscedastic. This chapter has two primary purposes. First, I present an alternative two-stage least squares (2SLS) estimator and its asymptotic standard errors for the coefficients of LISREL1 models developed in Bollen (1995, in press) under the assumption of homoscedastic errors. Second, I apply results from econometrics and sociometrics to expand the model to allow for heteroscedasticity of the disturbance term. This is done by providing heteroscedastic-consistent standard errors and developing alternative estimators that allow known or unknown forms of heteroscedasticity.