Beta - Binomial and Ordinal Joint Model with Random Effects for Analyzing Mixed Longitudinal Responses

The analysis of discrete mixed responses is an important statistical issue in various sciences. Ordinal and overdispersed binomial variables are discrete. Overdispersed binomial data are a sum of correlated Bernoulli experiments with equal success probabilities. In this paper, a joint model with random effects is proposed for analyzing mixed overdispersed binomial and ordinal longitudinal responses. In this model, we assume an overdispersed binomial response variable follows Beta-Binomial distribution and use a latent variable approach for modeling the ordinal response variable. Also, the model parameters are estimated via the Maximum Likelihood method, and the estimates are evaluated with a simulation study via the Monte Carlo method. Finally, an application of the proposed model to real data is introduced.