Modeling the Covariance
Garrett M. Fitzmaurice, Nan M. Laird, James H. Ware · Wiley series in probability and statistics · 2011
This chapter discusses the various covariance pattern models for longitudinal data. It first considers some of the implications of the correlation among longitudinal data, before looking at approaches for modeling the covariance or correlation among repeated measures. The chief advantage of an "unstructured" co-variance is that no assumptions are made about the variances and covariances. The various models discussed here are compound symmetry model, Toeplitz model, autoregressive model, banded patterns, exponential model, and hybrid models, which are a combination of autoregressive and the compound symmetry models. As the choices of models for the covariance and for the mean are interdependent, it is important to follow a modeling strategy that will result in a sensible choice of models for both aspects of the data. The chapter illustrates the main ideas by considering covariance pattern models for data from a trial examining the effectiveness of two different exercise therapy regimens.