Analysis of mixed correlated overdispersed binomial and ordinal longitudinal responses: LogLindley-Binomial and ordinal random effects model.

We propose a new model called LogLindley-Binomial and ordinal joint model with random effects for analyzing mixed overdispersed binomial and ordinal longitudinal responses. A new distribution called the LogLindley-Binomial is presented, which is appropriate for the analysis of overdispersed binomial variables. A full likelihood-based approach is used to obtain maximum likelihood estimates. A comparison between LogLindley-Binomial and Beta-Binomial distributions are given by a simulation study. Also, to illustrate the utility of the proposed model, some simulation studies are conducted. In simulation studies, the performances of the LogLindley-Binomial distribution and the proposed model are well in some situations. Also, the new model's performance for analyzing a real dataset, extracted from the British Household Panel Survey, is studied. The proposed model performs well in comparison with another model for analyzing real data. Finally, the proposed distribution and the new model are found to be applicable for analyzing overdispersed binomial and mixed data.