n Management Dynamics : Journal of the Southern African Institute for Management Scientists - Testing the invariance of second-order confirmatory factor analysis models that include means and intercepts

Volume 20, Issue 4
  • ISSN : 1019-567X



The methodology for invariance testing for a first-order confirmatory factor analysis is well documented in the literature. However, it is not the case for a second-order confirmatory factor analysis model. In addition, it is very often of interest to include means in the analyses, using means and covariance structure analysis (MACS) to investigate differences between groups in the structural part and between the means of latent variables. Most methodological papers on this topic are not very clear on how means should be treated in confirmatory factor analysis models. Also, the mathematical model that underlies a second-order model is not well documented. This study addresses all these issues, and uses empirical examples to provide the syntax for two software packages that are frequently used for invariance testing, namely LISREL 8.8 and AMOS 19. The study further sets out the procedure so that readers that are less familiar with matrix algebra can link the equations with the symbols used on the path diagram, and correspond these to the syntax provided in the appendices.

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