A transition binary logistic model with random coefficients is proposed to model the unemployment statues of household members in two seasons of spring and summer. Data correspond to the labor force survey performed by Statistical Center of Iran in 2006. This model is introduced to take into account two kinds of correlation in the data one due to the longitudinal nature of the study, that will be considered using a transition model, and the other due to the assumed correlation between responses of members of the same household which is taken into account byintroducing random coefficients into the model. Due to the use of special sampling method in this survey (rotation sampling), some kinds of non-monotone missing pattern occur that are considered in the proposed model using the breakdown of the joint distribution of the response variables. A Bayesian approach is used to estimate model parameters via the Gibbs sampling method and data augmentation. Results of using this model are compared with those of three other transitional models. The most applicable model which gains more interpretability and precision due to consideration of all aspects of the collected data is found. Also some sensitivity analysis are performed to assess asymmetric departures from the logistic link function and robustness of the posterior estimation of the transition parameter to the perturbations of the prior parameters.