基于分位数回归和哑变量模型的大兴安岭兴安落叶松树高-胸径模型

Height-diameter models for Larix gmelinii in Daxing’anling based on quantile regression and dummy variable model

【目的】基于Richards方程比较分位数回归和哑变量模型对树高-胸径方程预测精度的影响,为林业树高-胸径模型的构建提供新的思路和方法。【方法】利用大兴安岭4个区域的兴安落叶松Larix gmelinii伐倒木胸径/树高实测数据,采用分位数回归和哑变量模型构建树高-胸径模型,并与基本模型进行对比分析。评价指标采用平均绝对误差(MAE)、均方根误差(RMSE)、确定系数(R2)、赤池信息量(AIC)、贝叶斯信息量(BIC)、平均预测误差百分比(MPE)、平均绝对百分比误差(MAPE)、均方根百分比误差(RMSPE),同时利用非线性额外平方和法进行区域性检验。【结果】1)Richards树高-胸径模型在9个不同的分位点(τ=0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9)都能收敛,且每个区域都有其对应的最优分位数模型,区域1、2、3和4的最优分位数模型所对应的分位数分别是τ=0.7、τ=0.3、τ=0.5和τ=0.3,各区域最优分位数模型与哑变量模型所得结果差异不大,都优于基本模型。2)F检验结果表明哑变量模型的构造是有必要的,区域2和区域4没有显著不同,其他5对区域都有显著不同。3)模型检验结果表明区域1、3、4的最优分位数回归模型都要优于哑变量模型,区域2的哑变量模型没有通过正态性检验(P=0.0286),因此区域2的最优模型仍然为τ=0.3时的分位数模型。【结论】分位数回归模型和哑变量模型都能够反映不同区域树高-胸径关系的变化,在拟合和检验统计量等方面都表现较好,适合于大兴安岭落叶松树高预测。在进行方法选择时,可以根据数据特征和研究目的进行选择。

【Objective】Quantile regression and dummy variable model were compared for accuracy of tree height-diameter models based on Richards function,which provides new methods for the construction of tree height-diameter models.【Method】Height-diameter models were developed using quantile regression and dummy variable model based on the felled diameter/height data of Larix gmelinii from four regions in Daxing’anling.Mean absolute error(MAE),root mean square error(RMSE),coefficient determination(R2),Akaike information criterion(AIC),Bayesian Information Criterion(BIC),mean prediction percentage error(MPE),mean absolute percentage error(MAPE)and root mean square percentage error(RMSPE)were used to compare among different models.At the same time,the nonlinear extra sum of square method was used to compare the difference of the height-diameter relationships among different regions【.Result】1)The Richards height-diameter models converged at 9 different quantiles(τ=0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9),and each region had its corresponding optimal quantile model.The best quantile models for region 1,2,3,and 4 wereτ=0.7,τ=0.3,τ=0.5 andτ=0.3,respectively.The fitting ability of the best quantile model and dummy variable model in each region had little difference and were superior to the basic model.2)The results of F-test indicating that it is necessary to construct the dummy variable model for different regions.With the exception of region 2 and region 4,there were significant differences in the other 5 regions.It shows that there is no obvious difference between region 2 and region 4,which can be fitted by the reduced model.4)The model validation results showed that the optimal quantile regression model of region 1,3 and 4 was better than that of dummy variable model.The dummy variable model for region 2 did not pass the normality test(P=0.0286).Therefore,the best model of region 2 was still the quantile model ofτ=0.3.【Conclusion】Both quantile regression model and dummy variable model can reflect the variation of the relationship between height and diameter in different regions.They are suitable for height prediction of Larix gmelinii in Daxing’anling because of its good performance in fitting and validation statistics.In the process of method selection,it can be selected according to data characteristics and research purposes.