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Mixture models for capture-recapture count data

Author

Listed:
  • Dankmar Böhning

    (University Medicine Berlin)

  • Ekkehart Dietz

    (University Medicine Berlin)

  • Ronny Kuhnert

    (University Medicine Berlin)

  • Dieter Schön

    (Robert-Koch-Institut Berlin)

Abstract

The contribution investigates the problem of estimating the size of a population, also known as the missing cases problem. Suppose a registration system is targeting to identify all cases having a certain characteristic such as a specific disease (cancer, heart disease, ...), disease related condition (HIV, heroin use, ...) or a specific behavior (driving a car without license). Every case in such a registration system has a certain notification history in that it might have been identified several times (at least once) which can be understood as a particular capture-recapture situation. Typically, cases are left out which have never been listed at any occasion, and it is this frequency one wants to estimate. In this paper modelling is concentrating on the counting distribution, e.g. the distribution of the variable that counts how often a given case has been identified by the registration system. Besides very simple models like the binomial or Poisson distribution, finite (nonparametric) mixtures of these are considered providing rather flexible modelling tools. Estimation is done using maximum likelihood by means of the EM algorithm. A case study on heroin users in Bangkok in the year 2001 is completing the contribution.

Suggested Citation

  • Dankmar Böhning & Ekkehart Dietz & Ronny Kuhnert & Dieter Schön, 2005. "Mixture models for capture-recapture count data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(1), pages 29-43, February.
    • Handle: RePEc:spr:stmapp:v:14:y:2005:i:1:d:10.1007_bf02511573
    DOI: 10.1007/BF02511573
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    References listed on IDEAS

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    1. Shirley Pledger, 2000. "Unified Maximum Likelihood Estimates for Closed Capture–Recapture Models Using Mixtures," Biometrics, The International Biometric Society, vol. 56(2), pages 434-442, June.
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    5. Miloslavsky, Maja & van der Laan, Mark J., 2003. "Fitting of mixtures with unspecified number of components using cross validation distance estimate," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 413-428, January.
    6. Robert M. Dorazio & J. Andrew Royle, 2003. "Mixture Models for Estimating the Size of a Closed Population When Capture Rates Vary among Individuals," Biometrics, The International Biometric Society, vol. 59(2), pages 351-364, June.
    7. Peter G.M. Van Der Heijden & Maarten Cruyff & Hans C. Van Houwelingen, 2003. "Estimating the Size of a Criminal Population from Police Records Using the Truncated Poisson Regression Model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(3), pages 289-304, August.
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    Cited by:

    1. Yang Liu & Rong Kuang & Guanfu Liu, 2024. "Penalized likelihood inference for the finite mixture of Poisson distributions from capture-recapture data," Statistical Papers, Springer, vol. 65(5), pages 2751-2773, July.

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