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Variance estimation for integrated population models

Author

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  • Panagiotis Besbeas

    (Athens University of Economics and Business
    University of Kent)

  • Byron J. T. Morgan

    (University of Kent)

Abstract

State-space models are widely used in ecology. However, it is well known that in practice it can be difficult to estimate both the process and observation variances that occur in such models. We consider this issue for integrated population models, which incorporate state-space models for population dynamics. To some extent, the mechanism of integrated population models protects against this problem, but it can still arise, and two illustrations are provided, in each of which the observation variance is estimated as zero. In the context of an extended case study involving data on British Grey herons, we consider alternative approaches for dealing with the problem when it occurs. In particular, we consider penalised likelihood, a method based on fitting splines and a method of pseudo-replication, which is undertaken via a simple bootstrap procedure. For the case study of the paper, it is shown that when it occurs, an estimate of zero observation variance is unimportant for inference relating to the model parameters of primary interest. This unexpected finding is supported by a simulation study.

Suggested Citation

  • Panagiotis Besbeas & Byron J. T. Morgan, 2017. "Variance estimation for integrated population models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 439-460, October.
    • Handle: RePEc:spr:alstar:v:101:y:2017:i:4:d:10.1007_s10182-017-0304-5
    DOI: 10.1007/s10182-017-0304-5
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    References listed on IDEAS

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    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, December.
    2. S. C. Barry & S. P. Brooks & E. A. Catchpole & B. J. T. Morgan, 2003. "The Analysis of Ring-Recovery Data Using Random Effects," Biometrics, The International Biometric Society, vol. 59(1), pages 54-65, March.
    3. Toby A. Patterson & Alison Parton & Roland Langrock & Paul G. Blackwell & Len Thomas & Ruth King, 2017. "Statistical modelling of individual animal movement: an overview of key methods and a discussion of practical challenges," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 399-438, October.
    4. P. Besbeas & J.‐D. Lebreton & B. J. T. Morgan, 2003. "The efficient integration of abundance and demographic data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 95-102, January.
    5. P. Besbeas & S. N. Freeman & B. J. T. Morgan & E. A. Catchpole, 2002. "Integrating Mark–Recapture–Recovery and Census Data to Estimate Animal Abundance and Demographic Parameters," Biometrics, The International Biometric Society, vol. 58(3), pages 540-547, September.
    6. Bengtsson, Thomas & Cavanaugh, Joseph E., 2006. "An improved Akaike information criterion for state-space model selection," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2635-2654, June.
    7. Wang, Ji-Ping Z. & Lindsay, Bruce G., 2005. "A Penalized Nonparametric Maximum Likelihood Approach to Species Richness Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 942-959, September.
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