The Equivalence of Parameter Estimates from Growth Curve Models and Seemingly Unrelated Regression Models

Seemingly unrelated regression models and growth curve models are examples of multivariate models that require special estimation techniques. Parameters in seemingly unrelated regression models can be estimated by using two-stage Aitken estimation based on unrestricted residuals; parameters in growth curve models can be estimated by using a Potthoff-Roy (1964) transformation based on an estimate of the dispersion. With proper choice of the seemingly unrelated regression model, the two multivariate models and corresponding parameter estimates are shown to be equivalent. Recognition of the equivalence simplifies the presentation of these more complicated multivariate models. The connection is also of interest for more flexible growth curve models.