Local modeling of tree growth by geographically weighted regression

Abstract

The spatial heterogeneity of multivariate relationships between tree growth and diameter is explored using geographically weighted regression (GWR). GWR attempts to capture spatial variation by calibrating a multiple regression model fitted at each tree in a sample plot, weighting all neighboring trees by a function of distance from the subject tree. GWR produces a set of parameter estimates and model statistics (e.g., model R2) for each tree in the sample plot. It is evident that the GWR model not only predicts individual tree growth better than the traditional ordinary least-squares model, but also provides useful information on the nature of the growth variation caused by neighboring competitors and surrounding environmental factors. The parameter estimates and model statistics of the GWR model can be mapped using visualization tools, such as geographic information systems (GIS), to illustrate local spatial variation in the regression relationship under study. Consequently, the influence of microsite variation, competition status, growth potential, and the impacts of management activities on trees can be evaluated, tested, modeled, and readily visualized. GWR is a useful tool that provides much more information on spatial relationships to assist in model development and further our understanding of spatial processes.