An Expert System for Integrating Multiple Fit Indices for Structural Equation Models

Determining the overall fit of a model is an important step in the application of structural equation modeling. Due to the sensitivity of the chi-square test of exact fit, one in unlikely to find a statistically plausible model. Therefore a whole set of descriptive measures have been developed to reflect, in practical terms, the degree to which a model fits the sample data. Unfortunately, a problem arises in terms of how to integrate those multiple fit measures, especially when they may be providing an inconsistent perspective (e.g., two indicating modest fit and two indicating poor fit). We surveyed leading researchers in structural equation modeling to learn their perceptions about the importance of twelve of the most common measures. Results indicate that Root Mean Error of Approximation and the Comparative Fit Index are considered the most important. We have developed an expert system that incorporates the relative importance weights provided by the experts, and, using fuzzy set mathematics within a rule based system, provides one assessment of model fit based upon the integration of twelve overall fit indices. The expert system is useful for a variety of purposes including: research, the application of integrating fit measures, and teaching about expert systems development and SEM fit measures.