Inproceedings: an article in a conference proceedings.
How should the fit of structural equation models be judged? Insights from Monte Carlo simulations.
Title of the conference
Academy of Management Proceedings
Academy of Management, Anaheim, U.S.A.
At small sample sizes or when the model is complex, the chi-square test of model fit is known to over-reject correctly specified structural equation models. To counter these limitations, corrections to the chi-square test (i.e., rescalings) have been proposed (Swain, 1975; Yuan, Tian, & Yanagihara, 2013). In addition, several goodness-of-fit indexes (GoF), like the CFI (Bentler, 1990a) and RMSEA (Browne & Cudeck, 1992) have been developed and are popular decisions heuristics. We studied the usefulness of these measures by examining their Type I and Type II error rates. Using Monte Carlo simulations, we manipulated sample size, model complexity, measurement model quality, and degree of model endogeneity resulting in 560 conditions, simulated 2,500 times each. Results show that the chi-square test rescalings obtained appropriate Type I error rates (i.e., they rejected about 5% of true models); however, compared to the chi-square test, they lacked power to detect wrong models at small samples resulting in high Type II error rates. GoF indexes generally performed poorly, particularly in detecting wrong models, indicating that they cannot be trusted to judge model fit. We found too that using a rescaled chi-square test in combination with modification indices achieved acceptable Type I and Type II error rates.
Chi-Square test, Goodness-of-fit indexes, Monte Carlo simulations
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