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Estimating population size: The importance of model and estimator choice

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  • Matthew R. Schofield
  • Richard J. Barker
  • William A. Link
  • Heloise Pavanato

Abstract

We consider estimator and model choice when estimating abundance from capture–recapture data. Our work is motivated by a mark–recapture distance sampling example, where model and estimator choice led to unexpectedly large disparities in the estimates. To understand these differences, we look at three estimation strategies (maximum likelihood estimation, conditional maximum likelihood estimation, and Bayesian estimation) for both binomial and Poisson models. We show that assuming the data have a binomial or multinomial distribution introduces implicit and unnoticed assumptions that are not addressed when fitting with maximum likelihood estimation. This can have an important effect in finite samples, particularly if our data arise from multiple populations. We relate these results to those of restricted maximum likelihood in linear mixed effects models.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:biomet:v:79:y:2023:i:4:p:3803-3817
    DOI: 10.1111/biom.13828
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    1. Bernard W. Silverman, 2020. "Multiple‐systems analysis for the quantification of modern slavery: classical and Bayesian approaches," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 691-736, June.
    2. 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.
    3. R. M. Fewster & P. E. Jupp, 2009. "Inference on population size in binomial detectability models," Biometrika, Biometrika Trust, vol. 96(4), pages 805-820.
    4. Ruth King & Sheila M. Bird & Antony M. Overstall & Gordon Hay & Sharon J. Hutchinson, 2014. "Estimating prevalence of injecting drug users and associated heroin-related death rates in England by using regional data and incorporating prior information," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 177(1), pages 209-236, January.
    5. 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.
    6. Anne Chao & Wenten Chu & Chiu-Hsieh Hsu, 2000. "Capture–Recapture When Time and Behavioral Response Affect Capture Probabilities," Biometrics, The International Biometric Society, vol. 56(2), pages 427-433, June.
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