IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v25y2020i1d10.1007_s13253-019-00381-3.html
   My bibliography  Save this article

Right-Censored Mixed Poisson Count Models with Detection Times

Author

Listed:
  • Wen-Han Hwang

    (National Chung Hsing University)

  • Rachel V. Blakey

    (Institute of the Environment and Sustainability, University of California)

  • Jakub Stoklosa

    (The University of New South Wales)

Abstract

Conducting complete surveys on flora and fauna species within a sampling unit (or quadrat) of interest can be costly, particularly if there are several species in high abundance. A commonly used approach, which aims to reduce time and costs, consists of occurrence data reflecting the status of occupancy of a species– e.g., rather than counting every individual, the survey is stopped as soon as one individual has been observed. Although this approach is cheaper to conduct than a complete survey, some statistical efficiency in model estimators is lost. In this study, we consider occurrence data as a special case of right-censored count data where the collecting process stops until some set threshold on the number of observed individuals is reached. We then propose a new class of regression estimation models for right-censored count data that incorporate information from detection times (or catch effort) collected during sampling. First, we show that incorporating ancillary information in the form of detection times can greatly improve statistical efficiency over, say, right-censored Poisson or negative binomial models. Furthermore, the proposed models retain the same cost-effectiveness as censored-type models. We also consider zero-truncated and zero-inflated models for a variety of count data types. These models can be extended to a more general class of mixed Poisson models. We investigate model performance on simulated data and give two examples consisting of plant abundance data and bat acoustics data. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Wen-Han Hwang & Rachel V. Blakey & Jakub Stoklosa, 2020. "Right-Censored Mixed Poisson Count Models with Detection Times," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 112-132, March.
  • Handle: RePEc:spr:jagbes:v:25:y:2020:i:1:d:10.1007_s13253-019-00381-3
    DOI: 10.1007/s13253-019-00381-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-019-00381-3
    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/s13253-019-00381-3?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. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107014169.
    2. Karlis, Dimitris, 2005. "EM Algorithm for Mixed Poisson and Other Discrete Distributions," ASTIN Bulletin, Cambridge University Press, vol. 35(1), pages 3-24, May.
    3. Gurutzeta Guillera-Arroita & José J Lahoz-Monfort & Darryl I MacKenzie & Brendan A Wintle & Michael A McCarthy, 2014. "Ignoring Imperfect Detection in Biological Surveys Is Dangerous: A Response to ‘Fitting and Interpreting Occupancy Models'," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-14, July.
    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. Greene, William, 2008. "Functional forms for the negative binomial model for count data," Economics Letters, Elsevier, vol. 99(3), pages 585-590, June.
    6. Wen-Han Hwang & Richard Huggins, 2016. "Estimating Abundance from Presence–Absence Maps via a Paired Negative-Binomial Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 573-586, June.
    7. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273.
    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. Hossein Kavand & Marcel Voia, 2018. "Estimation of Health Care Demand and its Implication on Income Effects of Individuals," Springer Proceedings in Business and Economics, in: William H. Greene & Lynda Khalaf & Paul Makdissi & Robin C. Sickles & Michael Veall & Marcel-Cristia (ed.), Productivity and Inequality, pages 275-304, Springer.
    2. Sunisa Junnumtuam & Sa-Aat Niwitpong & Suparat Niwitpong, 2022. "A Zero-and-One Inflated Cosine Geometric Distribution and Its Application," Mathematics, MDPI, vol. 10(21), pages 1-22, October.
    3. White-Means, Shelley I. & Osmani, Ahmad Reshad, 2018. "Affordable Care Act and Disparities in Health Services Utilization among Ethnic Minoritiy Breast Cancer Survivors: Evidence from Longitudinal Medical Expenditure Panel Surveys 2008-2015," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 15(9), pages 1-26.
    4. Brendan P. M. McCabe & Christopher L. Skeels, 2020. "Distributions You Can Count On …But What’s the Point?," Econometrics, MDPI, vol. 8(1), pages 1-36, March.
    5. Zhang, Pengcheng & Calderin, Enrique & Li, Shuanming & Wu, Xueyuan, 2020. "On the Type I multivariate zero-truncated hurdle model with applications in health insurance," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 35-45.
    6. Luiz Paulo Fávero & Joseph F. Hair & Rafael de Freitas Souza & Matheus Albergaria & Talles V. Brugni, 2021. "Zero-Inflated Generalized Linear Mixed Models: A Better Way to Understand Data Relationships," Mathematics, MDPI, vol. 9(10), pages 1-28, May.
    7. Riccardo (Jack) Lucchetti & Luca Pedini, 2020. "ParMA: Parallelised Bayesian Model Averaging for Generalised Linear Models," Working Papers 2020:28, Department of Economics, University of Venice "Ca' Foscari".
    8. Landry, Craig E. & Shonkwiler, J. Scott & Whitehead, John C., 2020. "Economic Values of Coastal Erosion Management: Joint Estimation of Use and Existence Values with recreation demand and contingent valuation data," Journal of Environmental Economics and Management, Elsevier, vol. 103(C).
    9. Ghosh, Prasenjit & Rong, Jian & Khanna, Madhu & Wang, Weiwei & Miao, Ruiqing, 2017. "Have They Gone with the Wind? Indirect Effects of Wind Turbines on Bird Abundance," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258100, Agricultural and Applied Economics Association.
    10. Mullahy, John, 2024. "Analyzing health outcomes measured as bounded counts," Journal of Health Economics, Elsevier, vol. 95(C).
    11. Michel Beine & Ilan Noy & Christopher Parsons, 2021. "Climate change, migration and voice," Climatic Change, Springer, vol. 167(1), pages 1-27, July.
    12. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    13. D M Zimmer, 2023. "The effect of food stamps on fibre intake," Economic Issues Journal Articles, Economic Issues, vol. 28(2), pages 71-86, September.
    14. Jasna Atanasijević & Miloš Božović, 2016. "Exchange Rate as a Determinant of Corporate Loan Defaults in a Euroized Economy: Evidence from Micro-Level Data," Eastern European Economics, Taylor & Francis Journals, vol. 54(3), pages 228-250, May.
    15. Syed Muhammad All-E-Raza Rizvi & Marie-Ange Véganzonès-Varoudakis, 2019. "Economic, social, and institutional determinants of domestic conflict in fragile States," Working Papers hal-02340977, HAL.
    16. Kyriakos Drivas & Constantine Iliopoulos, 2017. "An Empirical Investigation in the Relationship Between PDOs/PGIs and Trademarks," Journal of the Knowledge Economy, Springer;Portland International Center for Management of Engineering and Technology (PICMET), vol. 8(2), pages 585-595, June.
    17. J. M. C. Santos Silva & Silvana Tenreyro, 2022. "The Log of Gravity at 15," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 423-437, September.
    18. Vidhura Tennekoon, 2017. "Counting unreported abortions: A binomial-thinned zero-inflated Poisson model," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 36(2), pages 41-72.
    19. Breinlich, Holger & Novy, Dennis & Santos Silva, J. M. C., 2021. "Trade, gravity and aggregation," LSE Research Online Documents on Economics 113858, London School of Economics and Political Science, LSE Library.
    20. Rik L. Rozendaal & Herman R. J. Vollebergh, 2021. "Policy-Induced Innovation in Clean Technologies: Evidence from the Car Market," CESifo Working Paper Series 9422, CESifo.

    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:jagbes:v:25:y:2020:i:1:d:10.1007_s13253-019-00381-3. 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.