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Longitudinal studies with binary or ordinal responses are widely encounteredin various disciplines, where the primary focus is on the temporal evolution ofthe probability of each response category. Traditional approaches build fromthe generalized mixed effects modeling framework. Even amplified withnonparametric priors placed on the fixed or random effects, such models arerestrictive due to the implied assumptions on the marginal expectation andcovariance structure of the responses. We tackle the problem from a functionaldata analysis perspective, treating the observations for each subject asrealizations from subject-specific stochastic processes at the measured times.We develop the methodology focusing initially on binary responses, for which weassume the stochastic processes have Binomial marginal distributions.Leveraging the logits representation, we model the discrete space processesthrough sequences of continuous space processes. We utilize a hierarchicalframework to model the mean and covariance kernel of the continuous spaceprocesses nonparametrically and simultaneously through a Gaussian process priorand an Inverse-Wishart process prior, respectively. The prior structure resultsin flexible inference for the evolution and correlation of binary responses,while allowing for borrowing of strength across all subjects. The modelingapproach can be naturally extended to ordinal responses. Here, thecontinuation-ratio logits factorization of the multinomial distribution is keyfor efficient modeling and inference, including a practical way of dealing withunbalanced longitudinal data. The methodology is illustrated with syntheticdata examples and an analysis of college students' mental health status data.

Flexible Bayesian Modeling for Longitudinal Binary and Ordinal Responses