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A model for analyzing clustered occurrence data

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  • Wen‐Han Hwang
  • Richard Huggins
  • Jakub Stoklosa

Abstract

Spatial or temporal clustering commonly arises in various biological and ecological applications, for example, species or communities may cluster in groups. In this paper, we develop a new clustered occurrence data model where presence–absence data are modeled under a multivariate negative binomial framework. We account for spatial or temporal clustering by introducing a community parameter in the model that controls the strength of dependence between observations thereby enhancing the estimation of the mean and dispersion parameters. We provide conditions to show the existence of maximum likelihood estimates when cluster sizes are homogeneous and equal to 2 or 3 and consider a composite likelihood approach that allows for additional robustness and flexibility in fitting for clustered occurrence data. The proposed method is evaluated in a simulation study and demonstrated using forest plot data from the Center for Tropical Forest Science. Finally, we present several examples using multiple visit occupancy data to illustrate the difference between the proposed model and those of N‐mixture models.

Suggested Citation

  • Wen‐Han Hwang & Richard Huggins & Jakub Stoklosa, 2022. "A model for analyzing clustered occurrence data," Biometrics, The International Biometric Society, vol. 78(2), pages 598-611, June.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:2:p:598-611
    DOI: 10.1111/biom.13435
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    References listed on IDEAS

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    1. Péter Sólymos & Subhash Lele & Erin Bayne, 2012. "Conditional likelihood approach for analyzing single visit abundance survey data in the presence of zero inflation and detection error," Environmetrics, John Wiley & Sons, Ltd., vol. 23(2), pages 197-205, March.
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    3. J. Andrew Royle, 2004. "N-Mixture Models for Estimating Population Size from Spatially Replicated Counts," Biometrics, The International Biometric Society, vol. 60(1), pages 108-115, March.
    4. Wen-Han Hwang & Richard Huggins & Lu-Fang Chen, 2017. "A Note on the Inverse Birthday Problem With Applications," The American Statistician, Taylor & Francis Journals, vol. 71(3), pages 191-201, July.
    5. Dorazio, Robert M. & Royle, J. Andrew, 2005. "Estimating Size and Composition of Biological Communities by Modeling the Occurrence of Species," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 389-398, June.
    6. Dunstan, Piers K. & Foster, Scott D. & Darnell, Ross, 2011. "Model based grouping of species across environmental gradients," Ecological Modelling, Elsevier, vol. 222(4), pages 955-963.
    7. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    8. 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.
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