Computational aspects of likelihood-based estimation of first-order antedependence models

Computational aspects of the problem of estimating the parameters of first-order antedependence models for the covariance structure of longitudinal data are considered. These models may be useful when serial correlation exists among measurements within subjects but is nonstationary. For those situations in which measurement times are common across subjects, the maximum likelihood estimators of unstructured first-order antedependent model parameters can be given explicitly. When measurement times are not identical across subjects or when the first-order antedependence model is more structured, however, the likelihood-based estimation of model parameters must be accomplished numerically and would thus appear to require extensive computations-In this article we show how this computational burden can be substantially reduced. The usefulness of the results is illustrated by analyses of longitudinal data from a 100-km race and from a study on cochlear implants.