Fit Indexes, Lagrange Multipliers, Constraint Changes and Incomplete Data in Structural Models

Certain aspects of model modification and evaluation are discussed, with an emphasis on some points of view that expand upon or may differ from Kaplan (1990). The usefulness of BentlerBonett indexes is reiterated. When degree of misspecification can be measured by the size of the noncentrality parameter of a xSUP2 distribution, the comparative fit index provides a useful general index of model adequacy that does not require knowledge of sourees of misspecification. The dependence of the Lagrange Multiplier XSUP2 statistic on both the estimated multiplier parameter and estimated constraint or parameter change is discussed. A sensitivity theorem that shows the effects of unit change in constraints on model fit is developed for model modification in structural models. Recent incomplete data methods, such as those developed by Kaplan and his collaborators, are extended to be applicable in a wider range of situations.