A Bayesian Approach to Estimate Parameters of a Random Coefficient Transition Binary Logistic Model with Non-monotone Missing Pattern and some Sensitivity Analyses

‎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.‎