Testing Multivariable Covariance Structure and Means Hypotheses via Structural Equation Modeling

A didactic collection of multivariate covariance and mean structure hypotheses is presented, which can be tested using structural equation modeling. The hypotheses reflect specific structures of the manifest covariance matrix or means, which are often of interest in social, behavioral, or educational research or represent assumptions of widely applied multivariate analysis methods. This large-sample method (a) is generally applicable with normal and nonnormal data (particularly with very large samples in the latter case), (b) can be considered complementing corresponding likelihood ratio tests in the nonnormality case with very large samples, and (c) is straightforwardly implemented in widely circulated structural modeling programs such as LISREL, EQS, AMOS, RAMONA, and SEPATH. The approach is illustrated using data from a two-group cognitive intervention study.