STRUCTURED ANTEDEPENDENCE MODELS FOR LONGITUDINAL DATA
 
                           Dale Zimmerman
                         University of Iowa 
 
         Antedependence (AD) models are a useful, though not widely known,
    class of models for the covariance structure of longitudinal data.
    Like stationary autoregressive models, AD models allow for serial
    correlation within subjects, but they are more general in the sense
    that they do not stipulate that the variance is constant over time
    nor that correlations between measurements equidistant in time are
    equal.  Thus, AD models provide a more parsimonious approach to
    the analysis of nonstationary data than the completely unstructured
    classical multivariate approach.
         For some nonstationary longitudinal data, however, a highly 
    structured AD model may be more useful than an unstructured AD
    model.  For example, if the 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 talk I review AD models in
    general and then I introduce some structured AD models.
    Properties of the models and estimation of model parameters by 
    maximum likelihood are considered.  A new graphical diagnostic,
    the PRISM, is introduced, which can help in determining the most
    appropriate order and type of AD model.