Assessment of Fit in Overidentified Models with Latent Variables

In recent years a number of measures have been suggested for the assessment of fit of overidentified models with latent variables (i.e., covariance structure models). This article discusses the logic of the fit problem, reviews the analytical intentions of six of these measures, with emphasis on their dependence on sample size, and compares the operational behavior of these measures in three-model situations: in a confirmatory factor model based on small N, and in two covariance structure models, one based on a slightly larger N and the other based on a large N. Given that these models and data are “typical,” results suggest that certain measures are both more stable across sample sizes and more sensitive to important variation in fit across substantively plausible models. The article concludes by suggesting a three-component approach to fitting: use of multiple measures, strategical overfitting, and comparison of parameter estimates in borderline versus more clearly sufficient models in terms of fit.