Modeling covariance structure in unbalanced longitudinal data

摘要

Modeling covariance structure is important for efficient estimation in longitudinaldata models. Modified Cholesky decomposition (Pourahmadi, 1999) is used as anunconstrained reparameterization of the covariance matrix. The resulting new parametershave transparent statistical interpretations and are easily modeled usingcovariates. However, this approach is not directly applicable when the longitudinaldata are unbalanced, because a Cholesky factorization for observed data that iscoherent across all subjects usually does not exist. We overcome this difficulty bytreating the problem as a missing data problem and employing a generalized EMalgorithm to compute the ML estimators. We study the covariance matrices in bothfixed-effects models and mixed-effects models for unbalanced longitudinal data. Weillustrate our method by reanalyzing Kenwards (1987) cattle data and conductingsimulation studies.