Abstract
Mixtures of distributions are a common modelling tool for durations of social phenomena, especially when the population is believed to be heterogeneous. We discuss heterogeneity patterns which can be captured by various mixing distributions in continuous and discrete time. Particular attention is given to recidivism data which Kaplan modeled by beta-mixtures of geometric distributions. We also investigate the dynamics of heterogeneity, measured via the variance of the mixing distribution, over the duration. It is shown that not all mixture models display decreasing heterogeneity over time.
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References
Barlow, R.E. and F. Proschan (1975) Statistical Theory of Reliability and Life Testing: Probability Models, Holt, Rinehart and Winston.
Bartholomew, D.J. (1959) Note on the Measurement and Prediction of Labor Turnover, J. Roy. Stat. Soc., A112, pp. 232–239.
Bartholomew, D.J. (1982) Stochastic Models for Social Processes (3rd edition), John Wiley & Sons.
Gerchak, Y. (1983) Durations in Social States: Concepts of Inertia and Related Comparisons in Stochastic Models, Sociological Methodology 1983–4, S. Leinhardt (ed.), Jossey-Bass.
Ginsberg, R.B. (1973) Stochastic Models of Residential and Geographic mobility for Heterogeneous Populations. Envir. Planning, 5, pp. 113–124.
Gupta, R.C. (1980) On the Mean Residual Life Function of a Mixture in Reliability Studies, Comm. Stat., A9, pp. 1365–1369.
Harris, C.M., A.R. Kaylan and M.D. Maltz (1981) Recent Advances in the Statistics of Recidivism Measurement in Models in Quantitative Criminology, J.A. Fox (ed.), Academic Press.
Kaplan, E.H. (1981) Discrete Statistical Models for Recidivism Data. Dept. of Urban Studies and Planning, M.I.T.
Maltz, M.D. and R. McCleary (1977) The Mathematics of Behavioral Change, Eval. Quarterly, 1, pp. 421–438.
March, J.C. and J.G. March (1977) Almost Random Careers: The Wisconsin School Superintendency 1940–1972, Adm. Science Quarterly, 22, pp. 377–409.
Morrison, D.G. and D.C. Schmittlein (1980) Jobs, Strikes and Wars: Probability Models for Duration, Org. Beh. Hum. Per., 25, pp. 224–251.
Silcock, H. (1954) The Phenomenon of Labour Turnover, J.R. Stat. Soc., A117, pp. 429–440.
Spilerman, S. (1972) Extensions of the Mover-Stayer Model, Amer. J. Sociol., 78, pp. 599–626.
Winkler, R.L. and W.L. Hayes (1975), Statistics (2nd edition), Holt, Reinhardt and Winston.
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Gerchak, Y., Kubat, P. Patterns and dynamics of population heterogeneity in mixtures models. Qual Quant 20, 285–291 (1986). https://doi.org/10.1007/BF00227433
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DOI: https://doi.org/10.1007/BF00227433