Spatial Autoregressive Models for Stand Top and Stand Mean Height Relationship in Mixed Quercus mongolica Broadleaved Natural Stands of Northeast China

Abstract

The relationship of stand top and stand mean height is important for forest growth and yield modeling, but it has not been explored for natural mixed forests. Observations of stand top and stand mean height can present spatial dependence or autocorrelation, which should be considered in modeling. Simultaneous autoregressive (SAR) models, including spatial lag model (SLM), spatial Durbin model (SDM) and spatial error model (SEM), within nine spatial weight matrices were utilized to model the stand top and stand mean height relationship in the mixed Quercus mongolica Fisch. ex Ledeb. broadleaved natural stands of Northeast China, using ordinary least squares (OLS) as a benchmark model. The results showed that there was a high linear relationship between stand top and stand mean height and that there was a positive spatial autocorrelation pattern in model residuals of OLS. Moreover, SEM and SDM performed better than OLS in terms of reducing the spatial dependence of model residuals and model fitting, regardless of which spatial weight matrix was used. SEM was better than SDM. SLM scarcely reduced the spatial autocorrelation of model residuals. Among nine spatial matrices in SEM, rook contiguous matrix performed best in model fitting, followed by inverse distances raised to the second power (1/d2) and local statistics model matrix (LSM).