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

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abstract 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.
   
type journal paper
   
keywords
   
language English
kind of paper journal article
date of appearance 1-9-2007
journal Structural Equation Modeling : A Multidisciplinary Journal
publisher Erlbaum (Mahwah, NJ)
ISSN 1070-5511
ISSN (online) 1532-8007
DOI 10.1080/10705510701301602
volume of journal 14
number of issue 3
page(s) 361-390
review double-blind review
   
citation Herzog, W., Boomsma, A., & Reinecke, S. (2007). The Model-Size Effect on Traditional and Modified Tests of Covariance Structures. Structural Equation Modeling : A Multidisciplinary Journal, 14(3), 361-390, DOI:10.1080/10705510701301602.