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Unobserved Heterogeneity in Multiple-Spell Multiple-States Duration Models

  • Govert Bijwaard


    (Netherlands Interdisciplinary Demographic Institute (NIDI))

In survival analysis a large literature using frailty models, or models with unobserved heterogeneity, exist. In the growing literate on multiple spell multiple states duration models, or multistate models, modeling this issue is only at its infant phase. Ignoring unobserved heteogeneity can, however, produce incorrect results. This paper presents how unobserved heterogeneity can be incorporated into multistate models, with an emphasis on semi-Markov multistate models with a mixed proportional hazard structure. First, the aspects of frailty modeling in univariate (proportional hazard, Cox) duration models are addressed and some important models with unobserved heterogeneity are discussed. Second, the domain is extended to modeling of parallel/clustered multivariate duration data with unobserved heterogeneity. The implications of choosing shared or correlated unobserved heterogeneity is highlighted. The relevant differences with recurrent events data is covered next. They include the choice of the time scale and risk set which both have important implications for the way unobserved heterogeneity influence the model. Multistate duration models can have both parallel and recurrent events. Incorporating unobserved heterogeneity in multistate models, therefore, brings all the previously addressed issues together. Although some estimation procedures are covered the emphasis is on conceptual issues. The importance of including unobserved heterogeneity in multistate duration models is illustrated with data on labour market and migration dynamics of recent immigrants to The Netherlands.

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Paper provided by Norface Research Programme on Migration, Department of Economics, University College London in its series Norface Discussion Paper Series with number 2012033.

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Date of creation: Nov 2012
Date of revision:
Handle: RePEc:nor:wpaper:2012033
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  1. Courgeau, Daniel & Lelievre, Eva, 1993. "Event History Analysis in Demography," OUP Catalogue, Oxford University Press, number 9780198287384, July.
  2. van den Berg, Gerard J., 1997. "Association measures for durations in bivariate hazard rate models," Journal of Econometrics, Elsevier, vol. 79(2), pages 221-245, August.
  3. Van den Berg, Gerard J., 2000. "Duration Models: Specification, Identification, and Multiple Durations," MPRA Paper 9446, University Library of Munich, Germany.
  4. Bijwaard, Govert E. & Franses, Philip Hans & Paap, Richard, 2006. "Modeling Purchases as Repeated Events," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 487-502, October.
  5. Geert Ridder & Tiemen Woutersen, 2001. "The Singularity of the Efficiency Bound of the Mixed Proportional Hazard Model," UWO Department of Economics Working Papers 20019, University of Western Ontario, Department of Economics.
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  14. Luc Duchateau & Paul Janssen & Iva Kezic & Catherine Fortpied, 2003. "Evolution of recurrent asthma event rate over time in frailty models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(3), pages 355-363.
  15. Gerda Claeskens & Rosemary Nguti & Paul Janssen, 2008. "One-sided tests in shared frailty models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 17(1), pages 69-82, May.
  16. Christopher J. Flinn & James J. Heckman, 1982. "Are Unemployment and Out of the Labor Force Behaviorally Distinct Labor Force States?," NBER Working Papers 0979, National Bureau of Economic Research, Inc.
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