ARMA Covariance Structures with Time Heteroscedasticity for Repeated Measures Experiments

Abstract

Rochon and Helms (1989) presented a model for analyzing repeated measures experiments. The general linear model was used to assess the influence of covariate information, and ARMA time series models were put forward to characterize the covariance matrix among the repeated measures. Practical experience has suggested, however, that the ARMA assumption of constant variances and autocovariances over time is too restrictive for many applications. For example, observations may be relatively stable toward the beginning of the study but become more variable toward the end. This article presents a modification to this structure, which provides for heteroscedasticity over time. Maximum likelihood (ML) estimation procedures are considered, and the estimators are found to enjoy optimal large sample properties. A scoring algorithm is described for iterating to a solution of the ML equations. The model is illustrated with data from a clinical trial investigating human erythropoietin for treating anemia in end-stage renal disease.

Key Words:

• Likelihood ratio test
• Linear models
• Longitudinal data
• Maximum likelihood estimation
• Scoring algorithm