ABSTRACT
We noted in the previous chapter that the unstructured antedependence (AD) covariance model is more parsimonious than the general multivariate model (provided that the order of the AD model is less than n − 1) while also being more flexible than stationary autoregressive models, and that consequently an unstructured AD model may be useful for longitudinal data exhibiting heterogeneous variances and nonstationary serial correlation. For many longitudinal data sets, however, an AD covariance model that is more parsimonious than an unstructured AD model, but possibly not as parsimonious as a stationary autoregressive model, may be even more useful. For example, if variances increase over time, as is common in growth studies, or if measurements equidistant in time become more highly correlated as the study progresses, then a model that incorporates these structural forms of nonstationarity is likely to be more useful. In this chapter we consider such models, which we call structured antedependence (SAD) models.
