Abstract
A predictive continuous time model is developed for continuous panel data to assess the effect of timeโvarying covariates on the general direction of the movement of a continuous response that fluctuates over time. This is accomplished by reparameterizing the infinitesimal mean of an OrnsteinโUhlenbeck processes in terms of its equilibrium mean and a drift parameter, which assesses the rate that the process reverts to its equilibrium mean. The equilibrium mean is modeled as a linear predictor of covariates. This model can be viewed as a continuous time firstโorder autoregressive regression model with timeโvarying lag effects of covariates and the response, which is more appropriate for unequally spaced panel data than its discrete time analog. Both maximum likelihood and quasiโlikelihood approaches are considered for estimating the model parameters and their performances are compared through simulation studies. The simpler quasiโlikelihood approach is suggested because it yields an estimator that is of high efficiency relative to the maximum likelihood estimator and it yields a variance estimator that is robust to the diffusion assumption of the model. To illustrate the proposed model, an application to diastolic blood pressure data from a followโup study on cardiovascular diseases is presented. Missing observations are handled naturally with this model.