Monte Carlo Evaluations of Goodness of Fit Indices for Structural Equation Models

This article reviews proposed goodness-of-fit indices for structural equation models and the Monte Carlo studies that have empirically assessed their distributional properties. The cumulative contributions of the studies are summarized, and the variables under which the indices are studied are noted. A primary finding is that many of the indices used until the late 1980s, including Jöreskog and Sörbom's (1981) GFI and Bentler and Bonett's (1980) NFI, indicated better fit when sample size increased. More recently developed indices based on the chi-square noncentrality parameter are discussed and the relevant Monte Carlo studies reviewed. Although a more complete understanding of their properties and suitability requires further research, the recommended fit indices are the McDonald (1989) noncentrality index, the Bentler (1990)-McDonald and Marsh (1990) RNI (or the bounded counterpart CFI), and Bollen's (1989) DELTA2.