Considering Spatial Correlations between Binary Response Variables in Forestry: An Example Applied to Tree Harvest Modeling
Authors: Mathieu Fortin, Simon Delisle-Boulianne, David Pothier
Source: Forest Science
Publisher: Society of American Foresters
Abstract: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.
Keywords: Farlie-Gumbel-Morgenstern copula, Spearman's correlation coefficient, spatial dependence, correlated binary outcomes, maximum likelihood estimator
Appeared or available online: May 24, 2012