38 Management Dynamics Volume 20 No 4, 2011 ABSTRACT _____________________________________________ 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. The issue of the need to test for measurement equivalence in confirmatory research, especially when measurement instruments with clearly defined sub-dimensions are used, is a matter that has become an increasingly important topic in leading international journals. However, in South Africa, although researchers often make use of instruments developed elsewhere and apply them across different cultural groups or other subgroupings, these studies rarely evaluate the measurement invariance of the instruments. This situation may lead to invalid findings, which may limit the usefulness of our studies to international scholars. In addition, during data collection, some bias may have been introduced for reasons that are beyond the control of the researcher. An example of this type of bias could be acquiescence bias or extreme response styles, which may be an artefact of the cultural tendencies of one or more groups being studied in the target population. Method bias could also be introduced, for example, when different methods of data collection have been used. Whenever there is reason to be concerned about the presence of bias, it is necessary for the researcher to test for measurement equivalence to establish whether it would be valid to proceed with further analyses. The methodology for invariance testing for first-order confirmatory factor analysis models (1CFA) within a structural equation modelling (SEM) framework is clearly set out in the statistical and applied literature. The application of the technique and its value in cross-cultural studies is well established, and more recently, the methodology is also applied in South African studies. Second-order confirmatory factor analysis models are appealing (2CFA) when several first-order factors are present in the model. The robustness of 2CFA models, given that they are plausible higher-level explanations of the covariances between the first-order factors, are very useful for empirical testing of theory. Although the methodology and software for fitting 2CFA models are available, the method is not often used in situations where it could be beneficial. Except for a methodological paper by Chen, Sousa and West (2005), invariance testing of 2CFA models is also very seldomly applied, probably because the methodology is not always clearly described. The mathematical exposition of the 2CFA model has also not been well-documented, and the treatment of means and intercepts in invariance testing is also often very vaguely treated in the literature. This study seeks to address all these issues. INTRODUCTION Testing the invariance of second-order confirmatory factor analysis models that include means and intercepts Arien Strasheim University of Pretoria