A fit index for covariance structure models under arbitrary GLS estimation

A general fit index for covariance structure models is obtained for all estimators that can be considered under generalized least squares (GLS) approaches including asymptotically efficient, robust, and resistant methods of estimation. This fit index is expressed as a function of the ratio of two trace functions. Normal theory ordinary least squares (OLS) and maximum likelihood (ML) fit indices previously given by Jöreskog and Sörbom can be derived from this framework. Fit indices for normal theory and generic GLS approaches including robust/resistant estimation methods are also obtained.