ABSTRACT
Suppose that the mean structure and an antedependent covariance structure for a set of longitudinal data have been tentatively identified, possibly using the informal methods described in the previous chapter. The next step of the data analysis will naturally be to estimate the tentative model’s parameters. In this chapter, we consider the estimation of the parameters of this model by likelihood-based methods, under the assumption that the joint distribution of responses on each subject is multivariate normal. Under appropriate regularity conditions, maximum likelihood estimates have several good properties, including consistency, asymptotic efficiency, and asymptotic normality. Some alternative estimation methods for antedependence models are described briefly in Chapter 9. In the first section of this chapter, we formulate a general normal linear model with antedependent covariance structure for the longitudinal responses, {Ys1, . . . , Ysns : s = 1, . . . , N}, within the sampling framework described at the beginning of Chapter 4. This model serves as the basis for estimation in this chapter, as well as for other inference procedures in subsequent chapters. Following that, we describe in detail two likelihood-based estimation procedures, maximum likelihood and residual maximum likelihood (REML), for the parameters of this general model. We then specialize these procedures to several practically important special cases of unstructured antedependence models, for which it is possible to either express the estimators in closed form or otherwise obtain them more efficiently than in the general case. Finally, we specialize the procedures to structured antedependence models.
