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Considering Spatial Correlations Between Binary Response Variables in Forestry: An Example Applied to Tree Harvest Modeling

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In forestry, many phenomena, such as tree mortality or harvesting, are thought to be spatially correlated. However, the statistical methods that account for spatial correlations with Bernoulli-distributed response variables are not well known. In this study, we implement a new approach recently developed by Bhat and Sener (2009). This approach is based on the Farlie-Gumbel-Morgenstern (FGM) copula family and was tested in a context of tree harvest modeling. Empirical and estimated Spearman's correlation coefficients (SCC) were compared to assess the goodness of fit of the model. The empirical SCCs showed decreasing correlations as the distance increased between the trees. A copula including a correlation function based on a negative exponential function accounted for this trend. Although the FGM copula is limited to cases in which the dependence is moderate, it worked fairly well in this case study and resulted in a model that had a better fit than a traditional generalized linear mixed model. The comparison between this copula and other families of copula remains to be investigated.
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Keywords: Farlie-Gumbel-Morgenstern copula; Spearman's correlation coefficient; correlated binary outcomes; maximum likelihood estimator; spatial dependence

Document Type: Research Article

Publication date: 2013-06-24

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    Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2016 Impact Factor: 1.782 (Rank 17/64 in forestry)

    Average time from submission to first decision: 62.5 days*
    June 1, 2016 to Feb. 28, 2017

    Also published by SAF:
    Journal of Forestry
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