Journal
STRUCTURAL EQUATION MODELING-A MULTIDISCIPLINARY JOURNAL
Volume 19, Issue 1, Pages 86-98Publisher
PSYCHOLOGY PRESS
DOI: 10.1080/10705511.2012.634724
Keywords
confirmatory factor analysis; fit assessment; model size; sample size; structural equation modeling
Funding
- Baden-Wurttemberg Stiftung
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The size of a model has been shown to critically affect the goodness of approximation of the model fit statistic T to the asymptotic chi-square distribution in finite samples. It is not clear, however, whether this model size effect is a function of the number of manifest variables, the number of free parameters, or both. It is demonstrated by means of 2 Monte Carlo computer simulation studies that neither the number of free parameters to be estimated nor the model degrees of freedom systematically affect the T statistic when the number of manifest variables is held constant. Increasing the number of manifest variables, however, is associated with a severe bias. These results imply that model fit drastically depends on the size of the covariance matrix and that future studies involving goodness-of-fit statistics should always consider the number of manifest variables, but can safely neglect the influence of particular model specifications.
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