Robustness of normal theory statistics in structural equation models

A condition is given by which optimal normal theory methods, such as the maximum likelihood methods, are robust against violation of the normality assumption in a general linear structural equation model. Specifically, the estimators and the goodness of fit test are robust. The estimator is efficient within some defined class, and its standard errors can be obtained by a correction formula applied to the inverse of the information matrix. Some special models, like the factor analysis model and path models, are discussed in more detail. A method for evaluating the robustness condition is given.

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