A mixed effects model for multivariate ordinal response data including correlated discrete failure times with ordinal responses.

The mixed effects model for binary responses due to Conaway (1990, A Random Effects Model for Binary Data) is extended to accommodate ordinal responses in general and discrete time survival data with ordinal responses in particular. Given a multinomial likelihood, cumulative complementary log-log link function, and log-gamma random effects distribution, the resulting marginal likelihood has a closed form. As a result, a Newton-Raphson estimation procedure is feasible without resorting to numerical, approximation-based, or Monte Carlo integration techniques. The parameters in the model have a proportional hazards interpretation in terms of multivariate discrete time data with ordinal responses. Using data from a psychological example, the proposed method is compared with other mixed effects approaches as well as population-averaged models.