Mover-stayer Model Research Articles

A Method for Analyzing Backward Recurrence Time Data on Residential Mobility

Data on duration of current residence are used to estimate models of duration-dependent residential mobility rates. "We use the theory of backward recurrence times in renewal processes to infer the hazard rate of residential mobility from the density of the duration of current residence. We demonstrate that the inferences made using the asymptotic solution of the density of the backward recurrence times will be severely biased if the renewal process has not reached stability. We present an unbiased finite time solution and estimate univariate and multivariate models of residential mobility rates using 1980 U.S. census data on duration of current residence. These models include mover-stayer models represented by mixture densities. The multivariate analysis shows that the most important covariates of residential mobility are age, homeownership, race, and presence of school-aged children."

The Mover-Stayer Model

Recent developments in nonparametric marginal likelihood have generated a very general, but readily operationalized, method of overcoming the nuisance parameter problem in stochastic models. Theoretical, empirical, and simulation analyses show that the nonparametric approach seriously undermines the modeling advantages traditionally associated with the mover-stayer model. Moreover, the goodness-of-fit success often achieved by the mover-stayer model is shown to have a plausible explanation not requiring a true mover/stayer dichotomy in the population.

Testing the Adequacy of Markov Chain and Mover-Stayer Models as Representations of Credit Behavior

We summarize methodology for testing the compatibility of discrete time stochastic processes—stationary and nonstationary Markov chains and an extension, the mover-stayer model—with longitudinal data from an unknown empirical process. We apply this methodology to determine the suitability of these models to represent the payment behavior of a sample of retail revolving credit accounts. We are led to reject stationary and also nonstationary Markov chain models for our data and for our state space definition in favor of the mover-stayer model. The mover-stayer model, in contrast to Markov chains, incorporates a simple form of population heterogeneity. Stationary Markov chains have been used extensively in finance literature to model payment behavior of credit accounts. Our empirical study suggests, however, that stationary Markov chains may not appropriately model payment behavior. It also indicates that incorporating heterogeneity in modeling payment behavior may be more important than incorporing nonstationarity.

Maximum Likelihood Estimation in the Mover-Stayer Model

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.

Maximum Likelihood Estimation in the Mover-Stayer Model

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.

Parameter Estimation for Mover-Stayer Models

Mover-stayer models provide an important tool for analyzing changes in attitudinal and psychological states over time. Two general methods are presented for estimating the parameters of the mover-stayer model that are asymptotically efficient and straightforward to calculate using available computer programs. These methods provide procedures for estimating parameters for various modifications of the first-order mover-stayer model. Data from a study of depression among adults are used to illustrate how methods for estimating parameters of the mover-stayer model under various hypotheses can be employed to test the validity of the assumptions of the mover-stayer model.

STATIONARY DISCRETE AUTOREGRESSIVE‐MOVING AVERAGE TIME SERIES GENERATED BY MIXTURES

Abstract. Two simple stationary processes of discrete random variables with arbitrarily chosen first‐order marginal distributions, DARMA (p, N+ 1) and NDARMA (p, N), are given. The correlation structure of these processes mimics that of the usual linear ARMA (p, q) processes. The relationship of these processes to mover‐stayer models, and to models for discrete time series given separately by Lindqvist and Pegram is discussed. Ad hoc nonparametric estimators for the parameters in the DARMA (p, N+ 1) and NDARMA (p, N) are given. A simulation study shows them to be as good as maximum likelihood estimators for the first‐order autoregressive case, and to be much simpler to compute than the maximum likelihood estimators.

A note on individual choice models of migration

In this paper individual probabilistic choice models are developed for the decision to migrate and the choice among alternative destinations. The models are developed to investigate how characteristics of decision makers and of alternative destinations affect choice. Several migration models in the literature (e.g., mover-stayer models) are shown to be special cases, their behavioral assumptions are made explicit, and a framework for testing these assumptions is provided.

Some Methodological Problems in Explaining Social Mobility

Orcutt, Guy H., M. Greenberger, J. Korbel, and A. Rivlin 1961 Microanalysis of Socioeconomic Systems: Simulation Study. New York: Harper and Bros. Palmer, G. 1954 Labor Mobility in Six Cities. New York: Social Science Research Council. Prais, S. J. 1955 Measuring social mobility. Journal of the Royal Statistical Society 118 (Series A):55-66. Rogers, Andrei 1966 A Markovian analysis of migration differentials. Proceedings, American Statistical Association, Social Science Section 1966. Spilerman, Seymour 1971 The causes of racial disturbances: Tests of an explanation. American Sociological Review 36:427-442. 1972 Extensions of the mover-stayer model. American Journal of Sociology 78. November. Stinchcombe, A. 1968 Constructing Social Theories. New York: Harcourt, Brace and World. Taeuber, Karl E., L. Chiazze, Jr., and W. Haenszel 1968 Migration in the United Washington: Government Printing Office. Taeuber, K. E. and A. E. Taeuber 1965 Negroes in Cities. Chicago: Aldine. Tarver, Jaries D. and William R. Gurley 1965 A stochastic analysis of geographic mobility and population projections of the census divisions in the United States. Demography 2:134-139. Thiel, Henri 1970 On the estimation of relationships involving qualitative variables. American Journal of Sociology 76:103-154.

Stayers and Movers

A new model for inheritance in intergenerational mobility is developed and related to mover-stayer models of intragenerational mobility. Application is made to data for the United States, Britain, and Denmark. Predictions are required to match observed proportions of men remaining in their origin strata and also the observed distribution of men among destination strata.

Statistical Methods for the Mover-Stayer Model

Abstract The mover-stayer model, a generalization of the Markov chain model, assumes that there are two types of individuals in the population under consideration: (a) the “stayer,” who with probability one remains in the same category during the entire period of study; (b) the “mover,” whose changes in category over time can be described by a Markov chain with constant transition probability matrix. The transition probability matrix for movers, and the proportion of stayers among the individuals in each category at, say, the initial point in time, are unknown parameters. Various estimators of these parameters are presented herein, and the accuracy of these estimators is compared. We show, for example, that the estimators of these parameters used by Blumen, Kogan, and McCarthy [3] are not consistent estimators, while the estimators recommended herein are. In addition, tests of several hypotheses concerning the mover-stayer model are presented herein. The methods developed in this paper can be applied to the study of various phenomena where panel data are available.

Statistical Methods for the Mover-Stayer Model

Abstract The mover-stayer model, a generalization of the Markov chain model, assumes that there are two types of individuals in the population under consideration: (a) the “stayer,” who with probability one remains in the same category during the entire period of study; (b) the “mover,” whose changes in category over time can be described by a Markov chain with constant transition probability matrix. The transition probability matrix for movers, and the proportion of stayers among the individuals in each category at, say, the initial point in time, are unknown parameters. Various estimators of these parameters are presented herein, and the accuracy of these estimators is compared. We show, for example, that the estimators of these parameters used by Blumen, Kogan, and McCarthy [3] are not consistent estimators, while the estimators recommended herein are. In addition, tests of several hypotheses concerning the mover-stayer model are presented herein. The methods developed in this paper can be applied to the study of various phenomena where panel data are available.