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Spatial Assessment of Model Errors from Four Regression Techniques

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Forest modelers have attempted to account for the spatial autocorrelations among trees in growth and yield models by applying alternative regression techniques such as linear mixed models (LMM), generalized additive models (GAM), and geographically weighted regression (GWR). However, the model errors are commonly assessed using average errors across the entire study area and across tree size classes. Little attention has been paid to the spatial heterogeneity of model performance. In this study, we used local Moran coefficients to investigate the spatial distributions of the model errors from the four regression models. The results indicated that GAM improved model-fitting to the data and provided better predictions for the response variable. However, it is nonspatial in nature and, consequently, generated spatial distributions for the model errors similar to the ones from ordinary least-squares (OLS). Furthermore, OLS and GAM yielded more clusters of similar (either positive or negative) model errors, indicating that trees in some subareas were either all underestimated or all overestimated for the response variable. In contrast, LMM was able to model the spatial covariance structures in the data and obtain more accurate predictions by accounting for the effects of spatial autocorrelations through the empirical best linear unbiased predictors. GWR is a varying-coefficient modeling technique. It estimated the model coefficients locally at each tree in the example plot and resulted in more accurate predictions for the response variable. Moreover, the spatial distributions of the model errors from LMM and GWR were more desirable, with fewer clusters of dissimilar model errors than the ones derived from OLS and GAM. FOR. SCI. 51(4):334–346.
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Keywords: Spatial autocorrelation and heterogeneity; environmental management; forest; forest management; forest resources; forestry; forestry research; forestry science; generalized additive model; geographically weighted regression; linear mixed model; local indicator of spatial autocorrelation; natural resource management; natural resources; ordinary least-squares

Document Type: Regular Article

Affiliations: 1: Faculty of Forest and Natural Resources Management, College of Environmental Science and Forestry State University of New York One Forestry Drive Syracuse NY 13210 Phone: (315) 470-6558;, Fax: (315) 470-6535, Email: 2: Research Forester USDA Forest Service Northeastern Research Station PO Box 640 Durham NH 03824 Phone: (603) 868-7667, Email:

Publication date: 2005-08-01

More about this publication?
  • 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
    Other SAF Publications
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