Spatially assessing model errors of four regression techniques for three types of forest stands

Abstract

Summary In this study, three types of forest stands with different spatial patterns of tree locations were used to investigate the spatial autocorrelation and heterogeneity in model errors from four regression techniques: ordinary least squares (OLS), linear mixed model (LMM), generalized additive model (GAM) and geographically weighted regression (GWR). In uneven-aged stands of softwood and hardwood, trees were clustered or randomly distributed over space. Tree variables were signifi cantly correlated, and the relationship between tree height and diameter was non-stationary across the study area. GAM fi tted the data well, but it generated spatial patterns for model errors similar to OLS because GAM is no-spatial in nature. In contrast, LMM and GWR took spatial autocorrelation into account for estimating the model coeffi cients and the standard errors of the coeffi cients. Consequently, they produced more accurate predictions for the response variable, as well as more desirable spatial distributions of model errors than those derived from OLS and GAM. The model errors from GWR were not only smaller in spatial autocorrelation but also lower in spatial heterogeneity than those from LMM. In the pine plantation, trees were more uniform in size, and regularly distributed over space. The relationship between tree height and diameter was also stationary or homogeneous across the study area. In this case, applying spatial models such as LMM and GWR may not have obvious advantages and benefi ts, while OLS and GAM may be appropriate for fi tting the data and predicting the response variable equally well.