Modeling covariance structure in unbalanced longitudinal data

Modeling covariance structure is important for efficient estimation in longitudinal data models. Modified Cholesky decomposition (Pourahmadi, 1999) is used as an unconstrained reparameterization of the covariance matrix. The resulting new parameters have transparent statistical interpretations and are easily modeled using covariates. However, this approach is not directly applicable when the longitudinal data are unbalanced, because a Cholesky factorization for observed data that is coherent across all subjects usually does not exist. We overcome this difficulty by treating the problem as a missing data problem and employing a generalized EM algorithm to compute the ML estimators. We study the covariance matrices in both fixed-effects models and mixed-effects models for unbalanced longitudinal data. We illustrate our method by reanalyzing Kenwards (1987) cattle data and conducting simulation studies.