Structured Antedependence Models for Longitudinal Data

Abstract

Antedependence (AD) models can be a useful class of models for the covariance struçture of continuous longitudinal data. Like stationary autoregressive (AR) models, AD models allow for serial correlation within subjects but are more general in the sense that they do not stipulate that the variance is constant nor that correlations between measurements equidistant in time are equal. Thus, AD models are more parsimonious class of models for nonstationary data than the completely unstructured model of the classical multivariate approach.

For some nonstationary longitudinal data, 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 (due, e.g., to a “learning” effect), then a model that incorporates these structural forms of nonstationarity is likely to be more useful. We introduce and illustrate the utility of some structured AD models. Properties of these models and estimation of model parameters by maximum likelihood are considered. An example is given in which a structured AD model is superior to both a stationary AR model and an unstructured AD model.

^†Núñez-Antón’ work supported by Dirección General de Enseñanza Superior del Ministerio Educaión y Cultura under research grant PB95-0346.