基于非线性分位数回归的落叶松树干削度方程

Stem Taper Function for Larix gmelinii Based on Nonlinear Quantile Regression

【目的】采用非线性分位数回归法构建落叶松树干削度方程,比较分析不同分位数(τ=0.1、0.2、0.3、0.4、0.5、0.6、0.7、0.8、0.9)及其组合分位数的拟合及检验结果,以提高模型预测精度。【方法】基于大兴安岭落叶松干形数据,采用Koenker和Bassett提出的分位数回归法,利用SAS软件的NLP拟合基于各分位数的Max-Burkhart分段削度方程,选取确定系数(R^2)、平均误差(MAB)、均方根误差(RMSE)、相对误差(MPB)和预估精度(P%)对削度方程进行对比分析。【结果】1)Max-Burkhart分段削度方程在9个不同分位点(τ=0.1、0.2、0.3、0.4、0.5、0.6、0.7、0.8、0.9)均能收敛,说明分位数回归可以提供许多不同分位数的估计结果,进而可预测任意分位点处干形的变化趋势;2)基本模型和分位点处(τ=0.4、0.5、0.6)的分位数模型拟合结果相近,分位数组合(3、5、7、9)可提高模型拟合效果,其中基于3个分位数组合(τ=0.3、0.5、0.7)、5个分位数组合(τ=0.3、0.4、0.5、0.6、0.7)、7个分位数组合(τ=0.1、0.2、0.4、0.5、0.6、0.8、0.9)、9个分位数组合(τ=0.1、0.2、0.3、0.4、0.5、0.6、0.7、0.8、0.9)在分位数组合相同时分别表现最优;3)模型检验表明,大多数分位数回归组合的检验统计量都优于基本模型和各分位数模型,相对于基本模型,5个分位数组合(τ=0.3、0.4、0.5、0.6、0.7)模型的MPB、MAB、RMSE分别降低13.9%、13.9%、13%。【结论】分位数回归能够提高模型预测精度,基于5个分位数组合的Max-Burkhart分段削度方程在拟合及检验统计量等方面表现较好,适合于大兴安岭落叶松树干削度预测。

【Objective】The aim of this study was to develop stem taper equation for Larix gmelinii in Daxing’anling based on quantile regression models,and the results were used to compare and analyze for fitting and validation of different quantiles(τ=0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9)and quantile groups.【Method】Stem taper data of Larix gmelinii were collected from Daxing’anling.NLP method in SAS software was used to fit Max and Burkhart segmented taper equation which was based on quantile regression(Koenker and Bassett,1978),and the performances of all models were evaluated by use of these evaluation statistics:coefficient of determination(R^2),mean absolute bias(MAB),root mean square error(RMSE),mean percentage of bias(MPB),and prediction accuracy(P%).【Result】1)The results showed that Max and Burkhart segmented taper equations could converge based on nine different quantiles(τ=0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9),showing that quantile regression could provide many different quantile estimates,and predict stem profile for different quantiles.2)The base model was similar to the models with quantile equal to 0.4,0.5,and 0.6.Comparing with based model,we found that all of different quantile groups(3,5,7,9)could improve the prediction precision.The quantile regression based on three quantiles group(τ=0.3,0.5,0.7),five quantiles group(τ=0.3,0.4,0.5,0.6,0.7),seven quantiles group(τ=0.1,0.2,0.4,0.5,0.6,0.8,0.9)and nine quantiles group(τ=0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9)were better than the others with the same quantile groups.The quantile regression with five quantiles group(τ=0.3,0.4,0.5,0.6,0.7)were the most accurate in predicting taper equation of Larix gmelinii based on fitting statistics.3)Model validation showed that statistical criteria of most quantile regression groups were superior to those of the base model and the individual quantile model.Relative to the base model,MPB,MAB and RMSE of five quantile combination(τ=0.3,0.4,0.5,0.6,0.7)model reduced by 13.9%,13.9%,13% respectively.【Conclusion】Quantile regression models could improve the prediction precision.Based on the five quantile group(τ=0.3,0.4,0.5,0.6,0.7),Max and Burkhart segmented taper equation showed good performances on fitting and validation statistics,and was suitable for predicting stem taper of Larix gmelinii in Daxing’anling.