IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v69y2017i3d10.1007_s10463-016-0561-1.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-016-0561-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10463-016-0561-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Chang Xuan Mao, 2008. "On the Nonidentifiability of Population Sizes," Biometrics, The International Biometric Society, vol. 64(3), pages 977-979, 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alessio Farcomeni, 2015. "Latent class recapture models with flexible behavioural response," Statistica, Department of Statistics, University of Bologna, vol. 75(1), pages 5-17.
    2. Richard Arnold & Yu Hayakawa & Paul Yip, 2010. "Capture–Recapture Estimation Using Finite Mixtures of Arbitrary Dimension," Biometrics, The International Biometric Society, vol. 66(2), pages 644-655, June.
    3. 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.
    4. 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.
    5. William A. Link, 2006. "The author replied as follows:," Biometrics, The International Biometric Society, vol. 62(3), pages 936-939, September.
    6. Danilo Fegatelli & Luca Tardella, 2013. "Improved inference on capture recapture models with behavioural effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(1), pages 45-66, March.
    7. B. J. T. Morgan & M. S. Ridout, 2008. "A new mixture model for capture heterogeneity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 433-446, September.
    8. 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.
    9. Jakub Stoklosa & Wen-Han Hwang & Sheng-Hai Wu & Richard Huggins, 2011. "Heterogeneous Capture–Recapture Models with Covariates: A Partial Likelihood Approach for Closed Populations," Biometrics, The International Biometric Society, vol. 67(4), pages 1659-1665, December.
    10. Fodé Tounkara & Louis‐Paul Rivest, 2015. "Mixture regression models for closed population capture–recapture data," Biometrics, The International Biometric Society, vol. 71(3), pages 721-730, September.
    11. Chang Xuan Mao & Nan Yang & Jinhua Zhong, 2013. "On Population Size Estimators in the Poisson Mixture Model," Biometrics, The International Biometric Society, vol. 69(3), pages 758-765, September.
    12. Chang Xuan Mao & Jun Li, 2009. "Comparing Species Assemblages Via Species Accumulation Curves," Biometrics, The International Biometric Society, vol. 65(4), pages 1063-1067, December.
    13. Shirley Pledger & Kenneth H. Pollock & James L. Norris, 2010. "Open Capture–Recapture Models with Heterogeneity: II. Jolly–Seber Model," Biometrics, The International Biometric Society, vol. 66(3), pages 883-890, September.
    14. Chang Xuan Mao, 2008. "On the Nonidentifiability of Population Sizes," Biometrics, The International Biometric Society, vol. 64(3), pages 977-979, September.
    15. R. King & S. P. Brooks, 2008. "On the Bayesian Estimation of a Closed Population Size in the Presence of Heterogeneity and Model Uncertainty," Biometrics, The International Biometric Society, vol. 64(3), pages 816-824, September.
    16. Hannah Worthington & Rachel S. McCrea & Ruth King & Richard A. Griffiths, 2019. "Estimation of Population Size When Capture Probability Depends on Individual States," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(1), pages 154-172, March.
    17. Hajo Holzmann & Axel Munk, 2008. "The authors replied as follows:," Biometrics, The International Biometric Society, vol. 64(3), pages 979-981, September.
    18. 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.
    19. repec:jss:jstsof:19:i05 is not listed on IDEAS
    20. J. Andrew Royle, 2009. "Analysis of Capture–Recapture Models with Individual Covariates Using Data Augmentation," Biometrics, The International Biometric Society, vol. 65(1), pages 267-274, March.
    21. Zhang, Hongmei & Ghosh, Kaushik & Ghosh, Pulak, 2012. "Sampling designs via a multivariate hypergeometric-Dirichlet process model for a multi-species assemblage with unknown heterogeneity," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2562-2573.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:aistmt:v:69:y:2017:i:3:d:10.1007_s10463-016-0561-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.