Unequally spaced longitudinal data with AR(1) serial correlation

This paper discusses longitudinal data analysis when each subject is observed at different unequally spaced time points. Observations within subjects are assumed to be either uncorrelated or to have a continuous-time first-order autoregressive structure, possibly with observation error. The random coefficients are assumed to have an arbitrary between-subject covariance matrix. Covariates can be included in the fixed effects part of the model. Exact maximum likelihood estimates of the unknown parameters are computed using the Kalman filter to evaluate the likelihood, which is then maximized with a nonlinear optimization program. An example is presented where a large number of subjects are each observed at a small number of observation times. Hypothesis tests for selecting the best model are carried out using Wald's test on contrasts or likelihood ratio tests based on fitting full and restricted models.