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    王君杰, 姜立春. 利用分位数组合预测兴安落叶松枝下高[J]. 北京林业大学学报, 2021, 43(3): 9-17. DOI: 10.12171/j.1000-1522.20200075
    引用本文: 王君杰, 姜立春. 利用分位数组合预测兴安落叶松枝下高[J]. 北京林业大学学报, 2021, 43(3): 9-17. DOI: 10.12171/j.1000-1522.20200075
    Wang Junjie, Jiang Lichun. Predicting height to crown base for Larix gmelinii using quantile groups[J]. Journal of Beijing Forestry University, 2021, 43(3): 9-17. DOI: 10.12171/j.1000-1522.20200075
    Citation: Wang Junjie, Jiang Lichun. Predicting height to crown base for Larix gmelinii using quantile groups[J]. Journal of Beijing Forestry University, 2021, 43(3): 9-17. DOI: 10.12171/j.1000-1522.20200075

    利用分位数组合预测兴安落叶松枝下高

    Predicting height to crown base for Larix gmelinii using quantile groups

    • 摘要:
        目的  本文使用分位数回归和分位数组合对枝下高进行建模和预测,为单木枝下高模型的构建提供新的思路和方法。
        方法  利用大兴安岭新林区4个林场的兴安落叶松天然林实测数据,采用非线性回归构建枝下高基础和广义模型并分别扩展到分位数回归。使用三分位数组合(\tau \text = 0.1, 0.5, 0.9)、五分位数组合(\tau \text = 0.1, 0.3, 0.5, 0.7, 0.9)、九分位数组合(\tau \text = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9)和4种抽样设计(抽最大树、抽最小树、抽平均木、随机抽取)进行预测,比较不同分位数组合的预测效果并分析不同抽样设计对预测精度的影响。同时使用双重交叉检验对非线性回归、最优位数回归和最优分位数组合进行比较。模型拟合和检验的评价指标主要包括平均绝对误差(MAE)、均方根误差(RMSE)、相对误差(MPE)和调整确定系数(R_\rmadj^2)。
        结果  (1)无论是非线性回归还是分位数回归,广义模型的拟合MAE较基础模型可降低6% ~ 12%,RMSE可降低6% ~ 10%,检验效果也优于基础模型。枝下高与胸径呈负相关、与样地优势高和每公顷断面积呈正相关。(2)中位数回归在所有分位数中拟合能力最好,且效果与非线性回归相似。分位数回归可以描述枝下高的分布。(3)3种分位数组合都可以对枝下高模型进行预测且效果相差不大,三分位数组合就可以满足枝下高的预测精度。中位数回归的交叉检验结果与非线性回归相似,三分位数组合的预测能力最优,MAE和MPE较非线性回归和中位数回归分别下降了20%和4%左右,R_\rmadj^2提高了16%左右。(4)基础和广义分位数组合的最优抽样设计分别为抽平均木5株和抽大树7株。
        结论  本研究基于三分位数组合(\tau \text = 0.1, 0.5, 0.9)的枝下高模型可以提高预测精度,具体应用基础和广义分位数组合模型的最优抽样设计分别为抽平均木5株和抽大树7株。综合预测精度和调查成本的考虑,在实践中应用分位数组合时,推荐在样地中抽取5 株平均木对枝下高进行预测。

       

      Abstract:
        Objective  Quantile regression and quantile groups were used in this article to model and predict height to crown base, which provided new ideas and methods for the construction of height to crown base models.
        Method  The data were collected from the measured data of natural forests of Larix gmelinii in 4 forest farms of Xinlin in Daxing’ anling of northeastern China. Nonlinear regression was used to build the basic and generalized models of the height to crown base and then extended to quantile regression. Four types of sampling designs (the largest DBH tree sampling, the smallest DBH tree sampling, the mean DBH tree sampling and random sampling) and three quantile group (\tau \text = 0.1, 0.5, 0.9), five quantile group (\tau \text = 0.1, 0.3, 0.5, 0.7, 0.9), nine quantile group (\tau \text = 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9) were used to predict height to crown base. The prediction effects of different quantile groups were compared as well as the impact of different sampling designs. Two-fold evaluation was used to compare the prediction effects of nonlinear regression, optimal quantile regression and optimal quantile group. Model evaluation criteria included mean absolute error (MAE), root mean square error (RMSE), mean percentage of error (MPE) and adjustment determination coefficient (R_\rmadj^2).
        Result  (1)Whether it is nonlinear regression or quantile regression, the fitting MAE of generalized models can be reduced by 6% to 12%, RMSE can be reduced by 6% to 10% compared with basic models. And the validation effects of generalized models were also better than basic models. There was a negative correlation between height to crown base and DBH, and a positive correlation between height to crown base and HDOM and BA. (2) Median regression had the best fitting ability among all quantiles, and the effects of median regression were similar to that of nonlinear regression. Quantile regression can describe the distribution of height to crown base. (3) All three quantile groups can predict height to crown base and the effect was not much different. The three quantile group was sufficient to predict height to crown base. The results of two-fold evaluation for median regression were similar to that of nonlinear regression, while three quantile group’s prediction ability was the best. Compared with nonlinear regression and median regression, the MAE and MPE of three quantile group decreased about 20% and 4% respectively, R_\rmadj^2 increased about 16%. (4) The optimal sampling designs for basic and generalized quantile groups were five mean DBH trees and seven largest trees, respectively.
        Conclusion  The height to crown base models based on three quantile group (\tau \text = 0.1, 0.5, 0.9) in this study can improve the prediction accuracy. The optimal sampling design of the basic and generalized quantile groups is 5 mean DBH tree sampling and 7 largest DBH tree sampling, respectively. Considering the accuracy of prediction and the cost of investigation, it is recommended to select 5 medium trees from the sample plot to predict the height to crown base when quantile groups are applied in practice.

       

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