Evaluating Small Sample Approaches for Model Test Statistics in Structural Equation Modeling

Through Monte Carlo simulation, small sample methods for evaluating overall data-model fit in structural equation modeling were explored. Type I error behavior and power were examined using maximum likelihood (ML), Satorra-Bentler scaled and adjusted (SB; Satorra & Bentler, 1988, 1994), residual-based (Browne, 1984), and asymptotically distribution free (ADF; Browne, 1982, 1984) test statistics. To accommodate small sample sizes the ML and SB statistics were adjusted using a k-factor correction (Bartlett, 1950); the residual-based and ADF statistics were corrected using modified x² and F statistics (Yuan & Bentler, 1998, 1999). Design characteristics include model type and complexity, ratio of sample size to number of estimated parameters, and distributional form. The k-factor-corrected SB scaled test statistic was especially stable at small sample sizes with both normal and nonnormal data. Methodologists are encouraged to investigate its behavior under a wider variety of models and distributional forms.