A new spatial-attribute weighting function for geographically weighted regression

In recent years, geographically weighted regression (GWR) has become popular for modeling spatial heterogeneity in a regression context. However, the current weighting function used in GWR only considers the geographical distances of trees in a stand, while the attributes (e.g., tree diameter) of the neighboring trees are totally ignored. In this study, we proposed a new weighting function that combines the "geographical space" and "attribute space" between the subject tree and its neighbors, such that (1) neighbors with greater geographical distances from the subject tree are assigned smaller weights, and (2) at a given geographical distance, neighboring trees with sizes that are similar to that of the subject tree are assigned larger weights. The results indicate that the GWR model with the new spatial-attribute weighting function performs better than the one with the spatial weighting function in terms of model residuals and predictions for different spatial patterns of tree locations.