The Model-Size Effect on Traditional and Modified Tests of Covariance Structures

• Published in: Structural equation modeling Vol. 14; no. 3; pp. 361 - 390
• Main Authors: Herzog, Walter, Boomsma, Anne, Reinecke, Sven
• Format: Journal Article
• Language: English
• Published: Hove Taylor & Francis Group 31.07.2007; Lawrence Erlbaum; Psychology Press
• Subjects: Bayesian Statistics; Effect Size; Improvement Programs; Maximum Likelihood Statistics; Media Adaptation; Monte Carlo Methods; Monte Carlo simulation; Multivariate analysis; Program Validation; Statistical Bias; Statistical methods; Structural Equation Models
• ISSN: 1070-5511; 1532-8007
• DOI: 10.1080/10705510701301602

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-Bentler 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.