Abstract
Joint models with random effects are proposed for the analysis of mixed overdispersed binomial and normal longitudinal data. A new parametric distribution, called the log Lindley-binomial distribution, is also introduced for analyzing overdispersed binomial data. The new distribution can be considered as an alternative to the classical beta-binomial distribution. Random effects are used to take into account the correlation between longitudinal responses of the same individual. The full likelihood approach is used to obtain maximum likelihood estimates of parameters of the log Lindley-binomial distribution and proposed models. Also, the generalized estimating equations approach, as an alternative nonlikelihood approach, is used to estimate models parameters. Some simulation studies are conducted to estimate parameters of the log Lindley-binomial distribution and the proposed models. These lead to the validity of the log Lindley-binomial distribution for analyzing related data. Finally, the proposed models are applied to analyze kidney function data of cancer patients to find the best-fitted model for analyzing the data.
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