The Influence of Model Features on Goodness-of-Fit Indices: Choosing Indices to Evaluate Your Model
Two studies were conducted to examine the performance of eight goodness-of-fit indices (i.e., the chi-square statistic, Comparative fit index, Critical N; Goodness-of-fit index, Normed fit index, Nonnormed fit index, Root mean square error of approximation, and Relative noncentrality index) used in structural equation applications. Study 1 consisted of (a) an empirical review in four journals (1986-1996) to determine the "typical" application, (b) a "recreation" of the goodness-of-fit indices from the published research, (c) a multiple regression analysis of the "recreated" indices to determine if values were predicted based on model and sample features, and (d) the development of a representative sample for model selection in Study 2. Study 1 identified 366 articles, and recreated indices for 187 of those articles. The regression analysis demonstrated that several indices were predicted by sample size and the hypothesized model's degrees of freedom. Study 2 consisted of (a) three Monte Carlo simulations differing in model complexity which assessed the performance of the indices under conditions of sample size, number of indicators, and model misspecifications, and (b) an evaluation of recommended and alternative cutoff values for the indices. In Study 2, simulated results replicated effects for sample size and number of indicators and extended findings to single indicator models. In agreement with prior research, indices were successful at detecting omitted misspecifications, but unsuccessful at detecting inclusion misspecifications. Most indices favored simple over complex models. Previously recommended values of indices were often inappropriate, but alternative values were suggested to reduce the frequency of accepted models with omission errors. When evaluating model fit with indices, researchers should consider the effects of sample and model features to avoid drawing erroneous conclusions.
Goodness-of-fit, Indices, Model features, Structural equation, Industrial and Organizational Psychology
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