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Estimating population sizes with the Rasch model

Author

Listed:
  • Chang Xuan Mao

    (Shanghai University of Finance and Economics)

  • Cuiying Yang

    (Shanghai University of Finance and Economics)

  • Yitong Yang

    (Shanghai University of Finance and Economics)

  • Wei Zhuang

    (Shanghai University of Finance and Economics)

Abstract

The Rasch model has been used to estimate the unknown size of a population from multi-list data. It can take both the list effectiveness and individual heterogeneity into account. Estimating the population size is shown to be equivalent to estimating the odds that an individual is unseen. The odds parameter is nonidentifiable. We propose a sequence of estimable lower bounds, including the greatest one, for the odds parameter. We show that a lower bound can be calculated by linear programming. Estimating a lower bound of the odds leads to an estimator for a lower bound of the population size. A simulation experiment is performed and three real examples are studied.

Suggested Citation

  • Chang Xuan Mao & Cuiying Yang & Yitong Yang & Wei Zhuang, 2017. "Estimating population sizes with the Rasch model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 705-716, June.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:3:d:10.1007_s10463-016-0561-1
    DOI: 10.1007/s10463-016-0561-1
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    References listed on IDEAS

    as
    1. Mao, Chang Xuan, 2006. "Inference on the Number of Species Through Geometric Lower Bounds," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1663-1670, December.
    2. Rivest Louis-Paul, 2011. "A Lower Bound Model for Multiple Record Systems Estimation with Heterogeneous Catchability," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-21, May.
    3. Huggins, Richard, 2001. "A note on the difficulties associated with the analysis of capture-recapture experiments with heterogeneous capture probabilities," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 147-152, September.
    4. William A. Link, 2003. "Nonidentifiability of Population Size from Capture-Recapture Data with Heterogeneous Detection Probabilities," Biometrics, The International Biometric Society, vol. 59(4), pages 1123-1130, December.
    5. Chang Xuan Mao & Na You, 2009. "On Comparison of Mixture Models for Closed Population Capture–Recapture Studies," Biometrics, The International Biometric Society, vol. 65(2), pages 547-553, June.
    6. Louis-Paul Rivest & Sophie Baillargeon, 2007. "Applications and Extensions of Chao's Moment Estimator for the Size of a Closed Population," Biometrics, The International Biometric Society, vol. 63(4), pages 999-1006, December.
    7. Hajo Holzmann & Axel Munk & Walter Zucchini, 2006. "On Identifiability in Capture–Recapture Models," Biometrics, The International Biometric Society, vol. 62(3), pages 934-936, September.
    8. Chang Xuan Mao, 2008. "On the Nonidentifiability of Population Sizes," Biometrics, The International Biometric Society, vol. 64(3), pages 977-979, September.
    9. Brent A. Coull & Alan Agresti, 1999. "The Use of Mixed Logit Models to Reflect Heterogeneity in Capture-Recapture Studies," Biometrics, The International Biometric Society, vol. 55(1), pages 294-301, March.
    10. Francesco Bartolucci & Antonio Forcina, 2001. "Analysis of Capture-Recapture Data with a Rasch-Type Model Allowing for Conditional Dependence and Multidimensionality," Biometrics, The International Biometric Society, vol. 57(3), pages 714-719, September.
    11. Xuan Mao, Chang, 2007. "Estimating population sizes for capture-recapture sampling with binomial mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5211-5219, July.
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