IDEAS home Printed from https://ideas.repec.org/a/wly/envmet/v35y2024i1ne2827.html
   My bibliography  Save this article

On the identifiability of the trinomial model for mark‐recapture‐recovery studies

Author

Listed:
  • Simon J. Bonner
  • Wei Zhang
  • Jiaqi Mu

Abstract

Continuous predictors of survival present a challenge in the analysis of data from studies of marked individuals if they vary over time and can only be observed when individuals are captured. Existing methods to study the effects of such variables have followed one of two approaches. The first is to model the joint distribution of the predictor and the observed capture histories, and the second is to draw inference from the likelihood conditional on events that depend only on observed predictor values, called the trinomial model. Previous comparison of these approaches found that joint modelling provided more precise inference about the effect of the covariate while the trinomial model was less prone to issues of model mis‐specification. However, we believe that an important issue was missed. We show through mathematical analysis and numerical simulation that the trinomial model is not identifiable when the predictor has no effect on the survival probability. This also causes inferences from the trinomial model to be imprecise when the effect of the covariate on the survival probability is small. We also analyse data on the effect of body mass on the survival of meadow voles to demonstrate the importance of this issue in real applications.

Suggested Citation

  • Simon J. Bonner & Wei Zhang & Jiaqi Mu, 2024. "On the identifiability of the trinomial model for mark‐recapture‐recovery studies," Environmetrics, John Wiley & Sons, Ltd., vol. 35(1), February.
    • Handle: RePEc:wly:envmet:v:35:y:2024:i:1:n:e2827
    DOI: 10.1002/env.2827
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/env.2827
    Download Restriction: no
    File URL: https://libkey.io/10.1002/env.2827?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. Roger Pradel, 2005. "Multievent: An Extension of Multistate Capture–Recapture Models to Uncertain States," Biometrics, The International Biometric Society, vol. 61(2), pages 442-447, June.
    2. D. L. Borchers & M. G. Efford, 2008. "Spatially Explicit Maximum Likelihood Methods for Capture–Recapture Studies," Biometrics, The International Biometric Society, vol. 64(2), pages 377-385, June.
    3. E. A. Catchpole & B. J. T. Morgan & G. Tavecchia, 2008. "A new method for analysing discrete life history data with missing covariate values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 445-460, April.
    4. S. J. Bonner & C. J. Schwarz, 2006. "An Extension of the Cormack–Jolly–Seber Model for Continuous Covariates with Application to Microtus pennsylvanicus," Biometrics, The International Biometric Society, vol. 62(1), pages 142-149, March.
    5. E. A. Catchpole & B. J. T. Morgan & T. Coulson, 2004. "Conditional methodology for individual case history data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(1), pages 123-131, January.
    6. Paul McLaughlin & Haim Bar, 2021. "A spatial capture–recapture model with attractions between individuals," Environmetrics, John Wiley & Sons, Ltd., vol. 32(1), February.
    7. Alex Diana & Eleni Matechou & Jim E. Griffin & Yadvendradev Jhala & Qamar Qureshi, 2022. "A vector of point processes for modeling interactions between and within species using capture‐recapture data," Environmetrics, John Wiley & Sons, Ltd., vol. 33(8), December.
    8. Mevin B. Hooten & Michael R. Schwob & Devin S. Johnson & Jacob S. Ivan, 2023. "Multistage hierarchical capture–recapture models," Environmetrics, John Wiley & Sons, Ltd., vol. 34(6), September.
    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. 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.
    2. 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.
    3. Simon J. Bonner & Byron J. T. Morgan & Ruth King, 2010. "Continuous Covariates in Mark-Recapture-Recovery Analysis: A Comparison of Methods," Biometrics, The International Biometric Society, vol. 66(4), pages 1256-1265, December.
    4. 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.
    5. Mevin B. Hooten & Michael R. Schwob & Devin S. Johnson & Jacob S. Ivan, 2023. "Multistage hierarchical capture–recapture models," Environmetrics, John Wiley & Sons, Ltd., vol. 34(6), September.
    6. Oliver, Lauren J. & Morgan, Byron J.T. & Durant, Sarah M. & Pettorelli, Nathalie, 2011. "Individual heterogeneity in recapture probability and survival estimates in cheetah," Ecological Modelling, Elsevier, vol. 222(3), pages 776-784.
    7. D. L. Borchers & B. C. Stevenson & D. Kidney & L. Thomas & T. A. Marques, 2015. "A Unifying Model for Capture-Recapture and Distance Sampling Surveys of Wildlife Populations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 195-204, March.
    8. Blanca Sarzo & Ruth King & David Conesa & Jonas Hentati-Sundberg, 2021. "Correcting Bias in Survival Probabilities for Partially Monitored Populations via Integrated Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(2), pages 200-219, June.
    9. Murray G. Efford & Christine M. Hunter, 2018. "Spatial capture–mark–resight estimation of animal population density," Biometrics, The International Biometric Society, vol. 74(2), pages 411-420, June.
    10. Jennifer Pohle & Roland Langrock & Floris M. Beest & Niels Martin Schmidt, 2017. "Selecting the Number of States in Hidden Markov Models: Pragmatic Solutions Illustrated Using Animal Movement," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 270-293, September.
    11. 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.
    12. Russell, Robin E. & Walsh, Daniel P. & Samuel, Michael D. & Grunnill, Martin D. & Rocke, Tonie E., 2021. "Space matters: host spatial structure and the dynamics of plague transmission," Ecological Modelling, Elsevier, vol. 443(C).
    13. Cecilia Soldatini & Yuri Vladimir Albores-Barajas & Bruno Massa & Olivier Gimenez, 2014. "Climate Driven Life Histories: The Case of the Mediterranean Storm Petrel," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-10, April.
    14. Bart J Harmsen & Rebecca J Foster & Howard Quigley, 2020. "Spatially explicit capture recapture density estimates: Robustness, accuracy and precision in a long-term study of jaguars (Panthera onca)," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    15. Murray G. Efford & Matthew R. Schofield, 2020. "A spatial open‐population capture‐recapture model," Biometrics, The International Biometric Society, vol. 76(2), pages 392-402, June.
    16. Michael R. Whitehead & Rod Peakall, 2013. "Short-term but not long-term patch avoidance in an orchid-pollinating solitary wasp," Behavioral Ecology, International Society for Behavioral Ecology, vol. 24(1), pages 162-168.
    17. Robert M Dorazio, 2013. "Bayes and Empirical Bayes Estimators of Abundance and Density from Spatial Capture-Recapture Data," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-12, December.
    18. Xinhai Li & Ning Li & Baidu Li & Yuehua Sun & Erhu Gao, 2022. "AbundanceR: A Novel Method for Estimating Wildlife Abundance Based on Distance Sampling and Species Distribution Models," Land, MDPI, vol. 11(5), pages 1-13, April.
    19. Klaich, M. Javier & Kinas, Paul G. & Pedraza, Susana N. & Coscarella, Mariano A. & Crespo, Enrique A., 2011. "Estimating dyad association probability under imperfect and heterogeneous detection," Ecological Modelling, Elsevier, vol. 222(15), pages 2642-2650.
    20. Meritxell Genovart & Roger Pradel, 2019. "Transience effect in capture-recapture studies: The importance of its biological meaning," PLOS ONE, Public Library of Science, vol. 14(9), pages 1-13, September.

    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:wly:envmet:v:35:y:2024:i:1:n:e2827. 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.interscience.wiley.com/jpages/1180-4009/ .

    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.