A general coefficient of determination for covariance structure models under arbitrary GLS estimation

Previous results presented in Tanaka & Huba (1985) introduced a general Fit index for covariance structure models under generalized least squares (GLS) estimation which, in some cases, specialized to the fit indices presented in Jöreskog & Sörbom (1981). Here, it is shown that, for a wide class of models, the general form of this fit index can be expressed as a weighted coefficient of determination. This coefficient is given as the ratio of weighted trace functions of predicted and observed covariance matrix elements.