Spatial regression modeling of tree height-diameter relationships

Tree height-diameter relationships are usually studied using linear or nonlinear models, but exogenous variables, especially spatially autocorrelated and dependent variables of tree diameter or height, are not often considered in height-diameter modeling. Three types of spatial regression models - spatial lag model, spatial error model, and spatial Durbin process model - are explored in this study. The height-diameter relationships are modeled using the spatial regression models to investigate the effects of spatial dependence and spatial autocorrelation and the roles of the exogenous variables generated by neighboring trees. Case study 1 shows that the spatial lag model should be used to analyze height-diameter relationships, in which heights of neighboring trees, which are exogenous variables, and the endogenous variable DBH significantly affect height growth. Case study 2 shows that the spatial error model performs better than other models, and that height growth is not only affected by its endogenous variable diameter but also by unobserved variables that vary spatially and result in residual spatial autocorrelation. Spatial regression models are an approach to height-diameter modeling that provide insight into how the endogenous variable diameter, the exogenous variables height and (or) diameter of neighboring trees, and locally varied but unobserved environmental or ecological variables contribute to height growth.