IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v77y2021i3p1050-1060.html
   My bibliography  Save this article

Maximum likelihood abundance estimation from capture‐recapture data when covariates are missing at random

Author

Listed:
  • Yang Liu
  • Yukun Liu
  • Pengfei Li
  • Lin Zhu

Abstract

In capture‐recapture experiments, individual covariates may be subject to missingness, especially when the number of captures is small. When the covariate information is missing at random, the inverse probability weighting method and the multiple imputation method are widely used to obtain point estimators of the abundance. These estimators are then used to construct Wald‐type confidence intervals. However, such intervals may have seriously inaccurate coverage probabilities. In this paper, we propose a maximum empirical likelihood (EL) estimation approach for the abundance in the presence of missing covariates. We show that the maximum EL estimator is asymptotically normal, and that the EL ratio statistic for the abundance has a chi‐square limiting distribution with one degree of freedom. Simulations indicate that the proposed estimator has a smaller mean square error than existing estimators, and the proposed EL ratio confidence interval usually has more accurate coverage probabilities than the existing Wald‐type confidence intervals. We illustrate the proposed method by analyzing data collected in Hong Kong for the yellow‐bellied prinia, a bird species.

Suggested Citation

  • Yang Liu & Yukun Liu & Pengfei Li & Lin Zhu, 2021. "Maximum likelihood abundance estimation from capture‐recapture data when covariates are missing at random," Biometrics, The International Biometric Society, vol. 77(3), pages 1050-1060, September.
    • Handle: RePEc:bla:biomet:v:77:y:2021:i:3:p:1050-1060
    DOI: 10.1111/biom.13334
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13334
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13334?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
    ---><---

    References listed on IDEAS

    as
    1. Yan Wang & Paul S. F. Yip, 2003. "A Semiparametric Model for Recapture Experiments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(4), pages 667-676, December.
    2. Paul S. F. Yip & Hua-Zhen Lin & Liqun Xi, 2005. "A Semiparametric Method for Estimating Population Size for Capture–Recapture Experiments with Random Covariates in Continuous Time," Biometrics, The International Biometric Society, vol. 61(4), pages 1085-1092, December.
    3. 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.
    4. Paul S. F. Yip & Yan Wang, 2002. "A Unified Parametric Regression Model for Recapture Studies with Random Removals in Continuous Time," Biometrics, The International Biometric Society, vol. 58(1), pages 192-199, March.
    5. Wen-Han Hwang & Steve Y. H. Huang, 2003. "Estimation in Capture-Recapture Models When Covariates Are Subject to Measurement Errors," Biometrics, The International Biometric Society, vol. 59(4), pages 1113-1122, December.
    6. Richard Huggins & Wen‐Han Hwang, 2011. "A Review of the Use of Conditional Likelihood in Capture‐Recapture Experiments," International Statistical Review, International Statistical Institute, vol. 79(3), pages 385-400, December.
    7. Shen‐Ming Lee & Wen‐Han Hwang & Jean de Dieu Tapsoba, 2016. "Estimation in closed capture–recapture models when covariates are missing at random," Biometrics, The International Biometric Society, vol. 72(4), pages 1294-1304, December.
    8. Yang Liu & Yukun Liu & Pengfei Li & Jing Qin, 2018. "Full likelihood inference for abundance from continuous time capture–recapture data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(5), pages 995-1014, November.
    9. D. Y. Lin & P. S. F. Yip, 1999. "Parametric regression models for continuous time removal and recapture studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 401-411, April.
    10. Yukun Liu & Pengfei Li & Jing Qin, 2017. "Maximum empirical likelihood estimation for abundance in a closed population from capture-recapture data," Biometrika, Biometrika Trust, vol. 104(3), pages 527-543.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yulu Ji & Yang Liu, 2024. "A Penalized Empirical Likelihood Approach for Estimating Population Sizes under the Negative Binomial Regression Model," Mathematics, MDPI, vol. 12(17), pages 1-23, August.

    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. Wen-Han Hwang & Jakub Stoklosa & Ching-Yun Wang, 2022. "Population Size Estimation Using Zero-Truncated Poisson Regression with Measurement Error," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 303-320, June.
    2. Paul S. F. Yip & Hua-Zhen Lin & Liqun Xi, 2005. "A Semiparametric Method for Estimating Population Size for Capture–Recapture Experiments with Random Covariates in Continuous Time," Biometrics, The International Biometric Society, vol. 61(4), pages 1085-1092, December.
    3. Linda Altieri & Alessio Farcomeni & Danilo Alunni Fegatelli, 2023. "Continuous time‐interaction processes for population size estimation, with an application to drug dealing in Italy," Biometrics, The International Biometric Society, vol. 79(2), pages 1254-1267, June.
    4. Stoklosa, Jakub & Huang, Yih-Huei & Furlan, Elise & Hwang, Wen-Han, 2016. "On quadratic logistic regression models when predictor variables are subject to measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 109-121.
    5. Yulu Ji & Yang Liu, 2024. "A Penalized Empirical Likelihood Approach for Estimating Population Sizes under the Negative Binomial Regression Model," Mathematics, MDPI, vol. 12(17), pages 1-23, August.
    6. Liu, Yang & Zhang, Xiuzhen & Li, Mengke & Liu, Guanfu & Zhu, Lin, 2019. "Abundance estimation based on optimal estimating function with missing covariates in capture–recapture studies," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 15-20.
    7. Yang Liu & Yukun Liu & Yan Fan & Han Geng, 2018. "Likelihood ratio confidence interval for the abundance under binomial detectability models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 549-568, July.
    8. Riki Herliansyah & Ruth King & Stuart King, 2022. "Laplace Approximations for Capture–Recapture Models in the Presence of Individual Heterogeneity," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 401-418, September.
    9. Mengke Li & Yukun Liu & Pengfei Li & Jing Qin, 2022. "Empirical likelihood meta-analysis with publication bias correction under Copas-like selection model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 93-112, February.
    10. 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.
    11. Paul S. F. Yip & Yan Wang, 2002. "A Unified Parametric Regression Model for Recapture Studies with Random Removals in Continuous Time," Biometrics, The International Biometric Society, vol. 58(1), pages 192-199, March.
    12. John Ashton & Tim Burnett & Ivan Diaz Rainey & Peter L. Ormosi, 2018. "Has the financial regulatory environment improved in the UK? Capture-Recapture approach to estimate detection and deterrence," Working Paper series, University of East Anglia, Centre for Competition Policy (CCP) 2018-03, Centre for Competition Policy, University of East Anglia, Norwich, UK..
    13. Shen-Ming Lee & Truong-Nhat Le & Phuoc-Loc Tran & Chin-Shang Li, 2023. "Estimation of logistic regression with covariates missing separately or simultaneously via multiple imputation methods," Computational Statistics, Springer, vol. 38(2), pages 899-934, June.
    14. Buu-Chau Truong & Nguyen Van Thuan & Nguyen Huu Hau & Michael McAleer, 2019. "Applications of the Newton-Raphson Method in Decision Sciences and Education," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(4), pages 52-80, December.
    15. Matthew R. Schofield & Richard J. Barker & William A. Link & Heloise Pavanato, 2023. "Estimating population size: The importance of model and estimator choice," Biometrics, The International Biometric Society, vol. 79(4), pages 3803-3817, December.
    16. Yee, Thomas W. & Stoklosa, Jakub & Huggins, Richard M., 2015. "The VGAM Package for Capture-Recapture Data Using the Conditional Likelihood," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 65(i05).
    17. Kim-Hung Pho & Tuan-Kiet Tran & Thi Diem-Chinh Ho & Wing-Keung Wong, 2019. "Optimal Solution Techniques in Decision Sciences A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 114-161, March.
    18. Stoklosa, Jakub & Huggins, Richard M., 2012. "A robust P-spline approach to closed population capture–recapture models with time dependence and heterogeneity," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 408-417.
    19. Shen‐Ming Lee & Wen‐Han Hwang & Jean de Dieu Tapsoba, 2016. "Estimation in closed capture–recapture models when covariates are missing at random," Biometrics, The International Biometric Society, vol. 72(4), pages 1294-1304, December.
    20. Stoklosa, Jakub & Dann, Peter & Huggins, Richard M. & Hwang, Wen-Han, 2016. "Estimation of survival and capture probabilities in open population capture–recapture models when covariates are subject to measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 74-86.

    More about this item

    Statistics

    Access and download statistics

    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:bla:biomet:v:77:y:2021:i:3:p:1050-1060. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    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.