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    娄明华, 张会儒, 雷相东, 卢军. 天然云冷杉针阔混交林单木胸径树高空间自回归模型研究[J]. 北京林业大学学报, 2016, 38(8): 1-9. DOI: 10.13332/j.1000-1522.20150491
    引用本文: 娄明华, 张会儒, 雷相东, 卢军. 天然云冷杉针阔混交林单木胸径树高空间自回归模型研究[J]. 北京林业大学学报, 2016, 38(8): 1-9. DOI: 10.13332/j.1000-1522.20150491
    LOU Ming-hua, ZHANG Hui-ru, LEI Xiang-dong, LU Jun. An individual height-diameter model constructed using spatial autoregressive models within natural spruce-fir and broadleaf mixed stands.[J]. Journal of Beijing Forestry University, 2016, 38(8): 1-9. DOI: 10.13332/j.1000-1522.20150491
    Citation: LOU Ming-hua, ZHANG Hui-ru, LEI Xiang-dong, LU Jun. An individual height-diameter model constructed using spatial autoregressive models within natural spruce-fir and broadleaf mixed stands.[J]. Journal of Beijing Forestry University, 2016, 38(8): 1-9. DOI: 10.13332/j.1000-1522.20150491

    天然云冷杉针阔混交林单木胸径树高空间自回归模型研究

    An individual height-diameter model constructed using spatial autoregressive models within natural spruce-fir and broadleaf mixed stands.

    • 摘要: 林木间普遍存在着空间自相关,这直接关联着林木间的竞争与相互作用。单木胸径树高模型是森林生长、收获与预测的基础,忽略林木间的空间自相关将会导致胸径树高模型的普通最小二乘(OLS)回归违背残差独立分布假设,导致犯第一类错误的可能性变大,以及模型参数标准差的有偏估计和回归模型估计的有效性降低。因此,本文选择我国东北地区主要森林类型即天然云冷杉针阔混交林为研究对象,考虑林木间的空间自相关,选用合适的线性化单木胸径树高OLS模型为基准模型,利用3个同步自回归(SAR)模型即空间滞后模型(SLM)、空间误差模型(SEM)和空间Durbin模型(SDM),构建该混交林的单木胸径树高模型。与此同时,每个SAR模型分别采用5个不同的空间加权矩阵即Delaunay三角网(DT)矩阵、逆距离一次幂(ID1)、逆距离二次幂(ID2)、逆距离五次幂(ID5)和高斯变异函数(GV)矩阵,利用极大似然(maximum likelihood)估计3个SAR模型的参数。对OLS和3个SAR模型的回归参数进行t检验,对3个SAR模型的自回归参数进行似然比检验。选择Morans I(MI)指数比较分析4个模型的残差空间自相关,选择决定系数(R2)、均方根误差(RMSE)和Akaike信息准则(AIC)3个拟合指标比较分析这4个模型的拟合效果,选择均方误差(MS)检验模型预测效果。结果表明:未考虑空间自相关的OLS模型残差存在正空间自相关;3个SAR模型拟合效果均优于OLS,SDM和SEM的拟合效果最好,SLM最差;无论使用哪个空间加权矩阵,SLM均不能消除模型残差空间自相关,但可降低空间自相关,在一定程度上提高了模型的拟合效果;5个空间矩阵应用于SDM和SEM时,均可以消除模型残差空间自相关,但空间加权矩阵GV只适用于SEM;ID2是5个空间加权矩阵中最好的空间加权矩阵,将ID2应用于4个模型进行预测时,SDM和SEM的预测效果明显优于SLM,但3个SAR模型的预测效果均优于OLS。利用3个SAR模型提高了单木胸径树高模型拟合和预测的精度,为合理经营天然云冷杉针阔混交林提供了理论基础。

       

      Abstract: Spatial autocorrelation is a common phenomenon in forestry. It directly connects competition and interaction among individuals. Individual height-diameter models are fundamentally important for forest growth, yield modeling and forecasting. Violation of residual independent distribution assumption in ordinary least squares (OLS) will inflate type 1 errors, lead to biased estimates of the standard errors of model parameters, and decrease the efficiency of estimation in a regression model, if the spatial autocorrelation among the individuals is ignored. Therefore, three simultaneous autoregressive (SAR) models, including spatial lag model (SLM), spatial error model (SEM) and spatial Durbin model (SDM) within five 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) and Gaussian variogram (GV), were applied to construct individual height-diameter models of natural spruce-fir and broadleaf mixed stands which are the main forest type in northeast China, with linearization individual height-diameter OLS model as a benchmark model. Model parameters of three SAR models were estimated by maximum likelihood. Model coefficients of OLS and three SAR models were tested by t-test, the autoregressive parameters of three SAR models were all tested by likelihood ratio test. Morans I (MI) was selected to compare autocorrelation of four model residuals. Three statistical indices, 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 OLS, SLM, SDM and SEM. Mean square error (MS) was selected to identify the predictive validity among four models. Results show that residuals of OLS were positive spatial dependence for ignoring the spatial autocorrelation among individuals. The model fittings of three SAR models were better than that of OLS. Among the three SAR models, model fitting of SLM was worse than those of SDM and SEM. SLM do not remove but reduce the spatial autocorrelation of model residuals, and slightly improve the model fitting, no matter which spatial weight matrices are used in SLM. All of the spatial weight matrices used in SDM and SEM could remove the spatial autocorrelation of residuals; however, GV was only applicable to SEM. Among all spatial weight matrices, ID2 was the best spatial weight matrix. Using ID2 into four modes, the predictive validity of SDM and SEM was superior to that of SLM, while the predictive validity of three SAR was better than that of OLS. Using three SAR models, fitting and prediction of individual diameter at breast height and height models were improved, and it may provide a theoretical basis for reasonable management of natural spruce-fir and broadleaf mixed stands.

       

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