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, TML, 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, TSC; the adjusted Satorra– Bentler statistic, TAD (Satorra & Bentler, 1988, 1994); corresponding Bartlett corrections, TMLb, TSCb, and TADb (Bartlett, 1950); and corresponding Swain corrections, TMLs , TSCs , and TADs (Swain, 1975). The empirical findings indicate that the model test statistic TMLs should be applied when large structural equation models are analyzed and the observed variables have (approximately) a multivariate normal distribution.