The model-size effect on traditional and modified tests of covariance structures

According to Kenny and McCoach (2003), chi-square tests of structural equation models produce inflated Type I error rates when the degrees of freedom increase. So far, the amount of this bias in large models has not been quantified. In a Monte Carlo study of confirmatory factor models with a range of 48 to 960 degrees of freedom it was found that the traditional maximum likelihood ratio statistic, T-ML, overestimates nominal Type I error rates up to 70% under conditions of multivariate normality. Some alternative statistics for the correction of model-size effects were also investigated: the scaled Satorra-Bentler statistic, T-SC; the adjusted Satorra-Bender statistic, T-AD (Satorra & Bentler, 1988, 1994); corresponding Bartlett corrections, T-MLb, T-SCb, and T-ADb (Bartlett, 1950); and corresponding Swain corrections, T-MLs, T-SCs, and T-ADs (Swain, 1975). The empirical findings indicate that the model test statistic T-MLs should be applied when large structural equation models are analyzed and the observed variables have (approximately) a multivariate normal distribution.