On Adding a Mean Structure to a Covariance Structure Model

Abstract

The vast majority of structural equation models contains no mean structure, that is, the population means are estimated at the sample means and then eliminated from modeling consideration. Generalized least squares methods are proposed to estimate potential mean structure parameters and to evaluate whether the given model can be successfully augmented with a mean structure. A simulation evaluates the performance of some alternative tests. A method that takes variability due to the estimation of covariance structure parameters into account in the mean structure estimator, as well as in the weight matrix of the generalized least squares function, performs best. In small samples, the F test and Yuan-Bentler adjusted chi-square test perform best. For example, if there is interest in modeling whether arithmetic skills or vocabulary levels are increasing across time, as one would expect in school, an analysis of means is an essential modeling component.