Can fit Indices be used to evaluate structural equation models?

Abstract

In recent years, many different fit indices have been formulated as an alternative for the standard likelihood ratio test (LRT) of Structural Equation Models (SEM). These fit indices were developed to solve specific problems associated with the LRT namely, sensitivity to sample size; the problem that no SEM will ever be an exact representation of reality; and the problem of deviation from the assumptions of the standard test. There is, however, oneproblem related to using the LRT that has been largely ignored by the developers of fit indices and this is the LRT’s varying sensitivity to the different characteristics of a model and different types of error. Because of this problem, it is impossible to use the LRT to test the fit of models with a fixed critical value. Since most new fit indices are functions of the fitting function or the test statistic itself, it was expected that the fit indices would have the same sensitivity problems as the LRT statistic. In the present paper, we confirm this by means of a Monte Carlo experiment. We also show that fit indices do not provide a simple instrument to test the fit of models. We conclude that the current practice of evaluating the fit of a model on the basis of the value of fit index and a general specified threshold is not justified.