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A note on the difficulties associated with the analysis of capture-recapture experiments with heterogeneous capture probabilities

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  • Huggins, Richard

Abstract

A variety of methods have been proposed to estimate the size of a closed population non-parametrically using capture-recapture data when the capture probabilities are heterogeneous. None of the methods have been proven to be unbiased in all circumstances and in simulations they tend to perform well in some cases but poorly in others. Here we examine random effects models and conclude that if the capture probabilities are heterogeneous then without the imposition of conditions the population size is not identifiable. A necessary condition for identifiability is given, with the derivation of a sufficient condition remaining an open problem.

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  • 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.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:2:p:147-152
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    References listed on IDEAS

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    1. 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.
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    1. 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.
    2. Liqun Xi & Ray Watson & Paul S. F. Yip, 2008. "The Minimum Capture Proportion for Reliable Estimation in Capture–Recapture Models," Biometrics, The International Biometric Society, vol. 64(1), pages 242-249, March.
    3. 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.
    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. Chang Xuan Mao & Robert K. Colwell & Jing Chang, 2005. "Estimating the Species Accumulation Curve Using Mixtures," Biometrics, The International Biometric Society, vol. 61(2), pages 433-441, June.
    6. 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.
    7. 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.
    8. 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.
    9. Anne Chao & Robin L. Chazdon & Robert K. Colwell & Tsung-Jen Shen, 2006. "Abundance-Based Similarity Indices and Their Estimation When There Are Unseen Species in Samples," Biometrics, The International Biometric Society, vol. 62(2), pages 361-371, June.
    10. Gimenez, Olivier & Rossi, Vivien & Choquet, Rémi & Dehais, Camille & Doris, Blaise & Varella, Hubert & Vila, Jean-Pierre & Pradel, Roger, 2007. "State-space modelling of data on marked individuals," Ecological Modelling, Elsevier, vol. 206(3), pages 431-438.
    11. 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.
    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. William A. Link, 2006. "The author replied as follows:," Biometrics, The International Biometric Society, vol. 62(3), pages 936-939, September.

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