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Longitudinal  study  plays  an  important  role  in  the  epidemiological,  clinical, and  social  science studies. In these kinds of studies, every individual is observed frequently during a period of time. The statistical analysis of longitudinal presents special opportunities  and challenges. The repeated outcomes for one individual tend to be correlated among themselves also one of the problems that we face in longitudinal studies is the missing data. These two issues are taken into account in this article. By using the logit link function, designed for longitudinal data, we introduce a mixed model, and then present the evaluation of variance components by Bayesian methods. The applied method exploits the non-conjugate priors. The conjugate priors, however, are easier to deal with. Finally, an application of the model in a clinical experiment is presented.