The Analysis of Longitudinal Ordinal Response Data in Continuous Time
Abstract A simple Markov model is developed for assessing the predictive effect of time-dependent covariates on an intermittently observed ordinal response in continuous time. This is accomplished by reparameterizing an ergodic intensity matrix in terms of its equilibrium distribution and a parametrically independent component that assesses the rate of movement between ordinal categories. The effect of covariates on the equilibrium distribution can then be modeled using any link appropriate for ordinal data. A robust maximum likelihood estimator based on this model that is consistent and asymptotically normal is constructed. Practical data analysis issues are discussed, and a simple diagnostic tool for assessing model adequacy is developed. The utility of these methods is demonstrated with several analyses of visual acuity data, including a comparison analysis based on generalized estimating equation (GEE) methods.