Spatial Assessment of Model Errors from Four Regression Techniques

Abstract

Abstract 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.