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A Variance Partitioning Multi-level Model for Forest Inventory Data with a Fixed Plot Design

Author

Listed:
  • Isa Marques

    (University of Göttingen, Chair of Statistics)

  • Paul F. V. Wiemann

    (University of Göttingen, Chair of Statistics
    Texas A &M University, College Station)

  • Thomas Kneib

    (University of Göttingen, Chair of Statistics)

Abstract

Forest inventories are often carried out with a particular design, consisting of a multi-level structure of observation plots spread over a larger domain and a fixed plot design of exact observation locations within these plots. Consequently, the resulting data are collected intensively within plots of equal size but with much less intensity at larger spatial scales. The resulting data are likely to be spatially correlated both within and between plots, with spatial effects extending over two different areas. However, a Gaussian process model with a standard covariance structure is generally unable to capture dependence at both fine and coarse scales of variation as well as for their interaction. In this paper, we develop a computationally feasible multi-level spatial model that accounts for dependence at multiple scales. We use a data-driven approach to determine the weight of each spatial process in the model to partition the variability of the measurements. We use simulated and German small tree inventory data to evaluate the model’s performance.Supplementary material to this paper is provided online.

Suggested Citation

  • Isa Marques & Paul F. V. Wiemann & Thomas Kneib, 2023. "A Variance Partitioning Multi-level Model for Forest Inventory Data with a Fixed Plot Design," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(4), pages 706-725, December.
    • Handle: RePEc:spr:jagbes:v:28:y:2023:i:4:d:10.1007_s13253-023-00548-z
    DOI: 10.1007/s13253-023-00548-z
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    References listed on IDEAS

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    1. Finley, Andrew O. & Banerjee, Sudipto & MacFarlane, David W., 2011. "A Hierarchical Model for Quantifying Forest Variables Over Large Heterogeneous Landscapes With Uncertain Forest Areas," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 31-48.
    2. Samuel A. Morris & Brian J. Reich & Emeric Thibaud, 2019. "Exploration and Inference in Spatial Extremes Using Empirical Basis Functions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 555-572, December.
    3. Finley, Andrew O. & Banerjee, Sudipto & Gelfand, Alan E., 2015. "spBayes for Large Univariate and Multivariate Point-Referenced Spatio-Temporal Data Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i13).
    4. Finn Lindgren & Håvard Rue & Johan Lindström, 2011. "An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 423-498, September.
    5. Krnjajić, Milovan & Draper, David, 2014. "Bayesian model comparison: Log scores and DIC," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 9-14.
    6. Matthias Katzfuss, 2017. "A Multi-Resolution Approximation for Massive Spatial Datasets," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 201-214, January.
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