Maximum Likelihood Estimation in the Mover-Stayer Model

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Abstract
The discrete time mover-stayer model, a special mixture of two independent Markov chains, has been widely used in modeling the dynamics of social processes. The problem of maximum likelihood estimation of its parameters from the data, however, which consist of a sample of independent realizations of this process, has not been considered in the literature. I present a maximum likelihood procedure for the estimation of the parameters of the mover-stayer model and develop a recursive method of computation of maximum likelihood estimators that is very simple to implement. I also verify that obtained maximum likelihood estimators are strongly consistent. I show that the two estimators of the parameters of the mover-stayer model previously proposed in the literature are special cases of the maximum likelihood estimator derived in this article, that is, they coincide with the maximum likelihood estimator under special conditions. I thus explain the interconnection between existing estimators. I also present a numerical comparison of the three estimators. Finally, I illustrate the application of the maximum likelihood estimators to testing the hypothesis that the Markov chain describes the data against the hypothesis that the mover-stayer model describes the data.

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