Analysis of longitudinal data unbalanced over time

Summary.  The paper considers modelling, estimating and diagnostically verifying the response process generating longitudinal data, with emphasis on association between repeated meas-ures from unbalanced longitudinal designs. Our model is based on separate specifications of the moments for the mean, standard deviation and correlation, with different components possibly sharing common parameters. We propose a general class of correlation structures that comprise random effects, measurement errors and a serially correlated process. These three elements are combined via flexible time-varying weights, whereas the serial correlation can depend flexibly on the mean time and lag. When the measurement schedule is independent of the response process, our estimation procedure yields consistent and asymptotically normal estimates for the mean parameters even when the standard deviation and correlation are misspecified, and for the standard deviation parameters even when the correlation is misspecified. A generic diagnostic method is developed for verifying the models for the mean, standard deviation and, in particular, the correlation, which is applicable even when the data are severely unbalanced. The methodology is illustrated by an analysis of data from a longitudinal study that was designed to characterize pulmonary growth in girls.