Joint Models for Longitudinal Zero-Inflated Overdispersed Binomial and Normal Responses

In this paper, we propose joint random effects models for longitudinal mixed overdispersion binomial and normal responses where the overdispersion binomial response is inflated in zero point. Also, we propose a new parametric distribution forms called as the Zero-Inflated LogLindley-Binomial distribution for overdispersed binomial response with extra zeros. A LogLindley-Binomial distribution is obtained by compounding LogLindley and Binomial distributions. The random effect approach is used to investigate both of the correlation between responses. A Monte Carlo EM algorithm is utilized to obtain the parametric estimation of the models parameters. The models are illustrated by simulation study. Finally, these models are applied to air quality data, obtained from an observational study on Tehran where the correlated responses are the overdispersed binomial with extra zeros of particulate matter and normal response of AQI. The simultaneous effects of some covariates on both responses are also investigates.