A Note on the Computer Generation of Mean and Covariance Expectations in Latent Growth Curve Analysis

Every "structural model" is defined by the set of covariance and mean expectations. These expectations are the source of parameter estimates, fit statistics, and substantive interpretation. The recent chapter by Cortina, Pant, and Smith-Darden ((this volume). In: F. Dansereau & F. J. Yammarino (Eds), Research in multi-level issues (vol. 4). Oxford, England: Elsevier) shows how a formal investigation of the data covariance matrix of longitudinal data can lead to an improved understanding of the estimates of covariance terms among linear growth models. The investigations presented by Cortina et al. (this volume) are reasonable and potentially informative for researchers using linear change growth models. However, it is quite common for behavioral researchers to consider more complex models, in which case a variety of more complex techniques for the calculation of expectations will be needed. In this chapter we demonstrate how available computer programs, such as Maple, can be used to automatically create algebraic expectations for the means and the covariances of every structural model. The examples presented here can be used for a latent growth model of any complexity, including linear and nonlinear processes, and any number of longitudinal measurements.