关键词: 空间自相关, 胸径, 树高, 自回归模型, 空间滞后

Abstract: [Objective] Considering spatial autocorrelation among individuals, individual diameter-height models based on spatial autocorrelation were constructed. It may provide a theoretical basis for sustainable management of natural mixed forests. [Method] Three simultaneous autoregressive (SAR) models, including spatial lag model (SLM), spatial error model (SEM) and spatial Durbin model (or called spatial mixed model) (SDM) within seven spatial weight matrices, including Delaunay triangulation (DT), inverse distance raised to one power (ID1), inverse distance raised to two powers (ID2), inverse distance raised to five powers (ID5), spherical variogram (SV), gaussian variogram (GV) and exponential variogram (EV), was used to construct individual diameter at breast height and height models of mixed Quercus mongolica broadleaved natural stands in Northeast China, and treating linearization base model (BM) as a benchmark model. Model parameters of BM were estimated by ordinary least squares (OLS), model parameters of three SAR models were estimated by maximum likelihood. Model coefficients β₀ and β₁ of four models were tested by T-test, the autoregressive parameters ρ, γ and λ were all tested by likelihood ratio test. Moran's I (MI) was selected to compared autocorrelation of four model residuals. Three statistics, i.e. coefficient of determination (R²), root mean square error (RMSE) and Akaike information criterion (AIC), were regarded as the appropriate criteria to identify the model fitting among BM, SLM, SDM and SEM. [Result] MI values of BM residuals were larger than 1, when applying SV into BM. Therefore, SV was the unreasonable spatial weight matrix and did not regard as a spatial weight matrix in the following result analysis. MI values of BM and SLM residuals were significantly larger than the expected value I₀ of MI in the all spatial weight matrices (except SV). MI values of SLM residuals were smaller than those of BM using the same spatial weight matrix. The difference between MI values of SDM residuals and I₀ was not significant in other four spatial weight matrices, except GV and ID1. Similarly, the difference between MI values of SEM residuals and I₀ was not significant in other five spatial weight matrices, except ID1. Three criteria of three SAR models were all better than those of BM. Using the same spatial weight matrix, MI values of SDM were very similar to those of SEM, meanwhile, MI values of SDM and SEM were both larger than those of SLM. Different spatial weight matrices (except GV) in SDM and SEM were sorted from best to worst according three criteria and the ranking was: ID2 > DT > ID > ID5 > EV. Model coefficients β₁ of three SAR were very similar to those of BM, regardless of which spatial weight matrix was used. Compared with β₁, model coefficients β₀ of SEM were similar to those of BM, while model coefficients β₀ of SDM and SLM were different to those of BM, and were changed along with the different spatial weight matrix. Among all spatial weight matrices within three SAR models, the autoregressive parameters ρ, γ and λ using ID1 were larger higher than any other spatial weight matrix. GV only applied to SEM, rather than SDM, could make the autoregressive parameter λ significant not equal to zero. The autoregressive parameters ρ, γ and λ were all not equal to zero using five spatial weight matrices (except GV).[Conclusion] Among all spatial weight matrices applied in three SAR models, SV and ID1 are the unreasonable spatial weight matrices. SLM do not remove, but reduce the spatial autocorrelation of model residuals, and slightly improve the model fitting. Model fitting of SLM was worse than those of SDM and SEM. Selecting appropriate spatial weight matrices, SDM and SEM can remove the spatial dependence of model residuals and improve the model fitting. ID2 is the best one among these selected appropriate spatial weight matrices. The diameter-height models of Quercus mongolica, Populus-Betula (Populus davidiana and Betula platyphylla) and Pinus koraiensis were constructed by species dummy variables SAR models based on ID2 and SEM.

Key words: spatial autocorrelation, diameter at breast height, tree height, autoregressive model, spatial lag