基于非线性分位数回归的落叶松树干削度方程

doi:10.11707/j.1001-7488.20191008

Abstract

Abstract:

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 (R²), 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. Objective: 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.

Key words: Larix gmelinii, nonlinear regression, quantile regression, taper equation

CLC Number:

S757

Yanyan Ma,Lichun Jiang. Stem Taper Function for Larix gmelinii Based on Nonlinear Quantile Regression[J]. Scientia Silvae Sinicae, 2019, 55(10): 68-75.

Figures/Tables 5

Table 1

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Table 3

Fig.1

Table 4

References 0

	姜立春, 马英莉, 李耀翔. 大兴安岭不同区域兴安落叶松可变指数削度方程. 林业科学, 2016. 52 (2): 17- 25.
	Jiang L C , Ma Y L , Li Y X . Inside bark diameter prediction models for Dahurian larch. Scientia Silvae Sinicae, 2016. 52 (2): 17- 25.
	孟宪宇. 削度方程和出材率表的研究. 南京林产工业学院学报, 1982. (1): 122- 133.
	Meng X Y . Studies of taper equations and the table of merchantable volumes. Journal of Nanjing Technological College of Forest Products, 1982. (1): 122- 133.
	胥辉, 孟宪宇. 天山云杉削度方程与材种出材率表的研究. 北京林业大学学报, 1995. 18 (3): 21- 30.
	Xu H , Meng X Y . Study on taper function and merchantable volume yielding rate tables of Picea schrenkiana var. tianshanica. Journal of Beijing Forestry University, 1995. 18 (3): 21- 30.
	Bi H . Trigonometric variable-form taper equations for Australian eucalypts. Forest Science, 2000. 46 (3): 397- 409.
	Brooks J R , Jiang L , Clark A . Compatible stem taper, volume, and weight equations for young longleaf pine plantations in southwest Georgia. Southern Journal of Applied Forestry, 2007. 31 (4): 187- 191. doi: 10.1093/sjaf/31.4.187
	Burkhart H E , Tomé M . Modeling forest trees and stands. Springer Netherlands, 2012. 191 (4): S28.
	Cao Q V , Wang J . Evaluation of methods for calibrating a tree taper equation. Forest Science, 2014. 61 (2): 213- 219.
	Corralrivas J J , DiéGuezaranda U , Corral R S , et al. A merchantable volume system for major pine species in El Salto, Durango(Mexico). Forest Ecology and Management, 2007. 238 (1): 118- 129.
	Garber S M , Maguire D A . Modeling stem taper of three central Oregon species using nonlinear mixed effects models and autoregressive error structures. Forest Ecology and Management, 2003. 179 (1): 507- 522.
	Jiang L , Brooks J R . Taper, volume, and weight equations for red pine in west Virginia. Northern Journal of Applied Forestry, 2008. 25, 151- 153. doi: 10.1093/njaf/25.3.151
	Jiang L , Brooks J R , Wang J . Compatible taper and volume equations for yellow-poplar in west Virginia. Forest Ecology and Management, 2005. 213 (1): 399- 409.
	Koenker R , Bassett G . Regression quantiles. Econometrica, 1978. 46 (1): 33- 50. doi: 10.2307/1913643
	Koenker R , Hallock K F . Quantile regression. Journal of Economic Perspectives, 2001. 15 (4): 143- 156. doi: 10.1257/jep.15.4.143
	Kozak A . My last words on taper equations. Forestry Chronicle, 2004. 80 (4): 507- 515. doi: 10.5558/tfc80507-4
	Leites L P , Robinson A P . Improving taper equations of loblolly pine with crown dimensions in a mixed-effects modeling framework. Forest Science, 2004. 50 (2): 204- 212.
	Li R X , Weiskittel A R . Comparison of model forms for estimating stem taper and volume in the primary conifer species of the north American Acadian region. Annals of Forest Science, 2010. 67 (3): 302- 302. doi: 10.1051/forest/2009109
	Max T A , Burkhart H E . Segmented polynomial regression applied to taper equations. Forest Science, 1976. 22 (3): 283- 289.
	Rodriguez F , Lizarralde I , Fernández-Landa A , et al. Non-destructive measurement techniques for taper equation development: a study case in the Spanish Northern Iberian Range. European Journal of Forest Research, 2014. 133 (2): 213- 223. doi: 10.1007/s10342-013-0739-5
	Rojo A , Perales X , Sánchez-Rodríguez F , et al. Stem taper functions for maritime pine(Pinus pinaster, Ait.)in Galicia(Northwestern Spain). European Journal of Forest Research, 2005. 124 (3): 177- 186. doi: 10.1007/s10342-005-0066-6
	Sabatia C O . Use of upper stem diameters in a polynomial taper equation for New Zealand radiata pine: an evaluation. New Zealand Journal of Forestry Science, 2016. 46 (1): 14.
	Schröder T , Arnoni Costa E , Felipe Valério A , et al. Taper equations for Pinus elliottii Engelm. in Southern Paraná, Brazil. Forest Science, 2015. 61 (2): 311- 319. doi: 10.5849/forsci.14-054
	Tasissa G , Burkhart H E . An application of mixed effects analysis to modeling thinning effects on stem profile of loblolly pine. Forest Ecology and Management, 1998. 103 (1): 87- 101. doi: 10.1016/S0378-1127(97)00179-5
	Trincado G , Burkhart H E . A Generalized approach for modeling and localizing stem profile curves. Forest Science, 2006. 52 (6): 670- 682.
	Valentine H T , Gregoire T G . A switching model of bole taper. Canadian Journal of Forest Research, 2001. 31 (8): 1400- 1409. doi: 10.1139/x01-061
	Yang Y Q , Huang S M , Trincado G , et al. Nonlinear mixed-effects modeling of variable-exponent taper equations for lodgepole pine in Alberta, Canada. European Journal of Forest Research, 2009a. 128 (4): 415- 429. doi: 10.1007/s10342-009-0286-2
	Yang Y Q , Huang S M , Meng S X . Development of a tree-specific stem profile model for white spruce: a nonlinear mixed model approach with a generalized covariance structure. Forestry, 2009b. 82 (82): 541- 555.

分组 Group	变量 Variable	样木数 Number	平均值 Mean	最小值 Min.	最大值 Max.	标准差 Std.	变动系数 CV
建模数据 Fitting data	直径DBH/cm	114	23.8	16.9	32.4	2.8	11.7
建模数据 Fitting data	树高Tree height/m	114	20.4	14.9	23.9	1.5	7.2
检验数据 Validation data	直径DBH/cm	28	23.9	17.1	29.9	3	12.4
检验数据 Validation data	树高Tree height/m	28	21	18.7	23	1.1	5.3

参数估计方法Parameter estimate method	β₁	β₂	β₃	β₄	a₁	a₂
非线性回归Nonlinear regression	-5.734 8	2.708 2	-2.717 7	119.097 6	0.860 4	0.078 6
分位数回归Quantile regression
τ=0.1	-5.349 0	2.620 4	-2.153 3	99.019 3	0.889 6	0.069 0
τ=0.2	-5.557 2	2.653 1	-2.229 9	99.310 7	0.911 2	0.070 0
τ=0.3	-7.553 0	3.707 8	-3.315 0	99.145 9	0.912 0	0.068 1
τ=0.4	-5.893 7	2.842 3	-2.789 7	100.075 9	0.853 8	0.079 2
τ=0.5	-5.793 2	2.643 3	-2.389 9	99.698 0	0.930 4	0.073 9
τ=0.6	-4.639 0	2.104 2	-2.178 6	99.125 7	0.833 4	0.083 8
τ=0.7	-4.987 2	2.254 1	-2.379 1	100.295 2	0.847 1	0.085 4
τ=0.8	-5.025 6	2.214 1	-2.407 2	99.468 4	0.860 3	0.088 7
τ=0.9	-4.220 2	1.719 9	-2.071 8	98.772 0	0.841 9	0.095 3

模型Model	MAB	RMSE	R²
基本模型Basic model	0.049 0	0.070 4	0.968 6
各分位数模型Individual quantile model
τ=0.1	0.081 9	0.110 4	0.922 8
τ=0.2	0.064 1	0.092 0	0.946 4
τ=0.3	0.056 0	0.084 0	0.955 3
τ=0.4	0.049 9	0.073 4	0.965 9
τ=0.5	0.050 4	0.074 1	0.965 3
τ=0.6	0.050 1	0.071 7	0.967 4
τ=0.7	0.054 5	0.075 9	0.963 5
τ=0.8	0.065 1	0.086 8	0.952 3
τ=0.9	0.090 4	0.115 6	0.915 4
分位数组合Quantile groups
τ=0.1，0.5，0.9	0.023 4	0.033 7	0.992 8
τ=0.2，0.5，0.8	0.023 9	0.040 5	0.989 6
τ=0.3，0.5，0.7	0.030 1	0.051 0	0.983 5
τ=0.4，0.5，0.6	0.037 2	0.060 1	0.977 1
τ=0.1，0.2，0.5，0.8，0.9	0.015 8	0.027 2	0.995 3
τ=0.1，0.3，0.5，0.7，0.9	0.015 7	0.027 0	0.995 4
τ=0.1，0.4，0.5，0.6，0.9	0.018 1	0.029 2	0.994 6
τ=0.3，0.4，0.5，0.6，0.7	0.028 8	0.050 7	0.983 7
τ=0.2，0.3，0.5，0.7，0.8	0.020 9	0.039 2	0.990 3
τ=0.2，0.4，0.5，0.6，0.8	0.021 2	0.039 3	0.990 2
τ=0.1，0.2，0.3，0.5，0.7，0.8，0.9	0.012 8	0.025 2	0.996 0
τ=0.1，0.3，0.4，0.5，0.6，0.7，0.9	0.014 2	0.026 3	0.995 6
τ=0.2，0.3，0.4，0.5，0.6，0.7，0.8	0.019 7	0.038 9	0.990 4
τ=0.1，0.2，0.4，0.5，0.6，0.8，0.9	0.013 1	0.025 4	0.995 9
τ=0.1，0.2，0.3，0.4，0.5，0.6，0.7，0.8，0.9	0.011 6	0.024 7	0.996 2

模型Model	MPB	MAB	RMSE	P%
基本模型Basic model	4.652 5	0.785 5	1.070 3	99.511 5
各分位数模型Individual quantile model
τ=0.1	8.936 7	1.508 9	1.852 4	99.078 8
τ=0.2	6.662 6	1.124 9	1.456 1	99.300 1
τ=0.3	5.710 4	0.964 2	1.296 5	99.387 4
τ=0.4	4.802 9	0.810 9	1.111 4	99.483 5
τ=0.5	4.900 5	0.827 4	1.095 3	99.501 9
τ=0.6	4.701 5	0.793 8	1.074 6	99.515 6
τ=0.7	5.130 4	0.866 2	1.153 0	99.488 1
τ=0.8	6.180 5	1.043 5	1.354 3	99.411 1
τ=0.9	8.592 7	1.450 8	1.785 7	99.246 9
分位数组合Quantile groups
τ=0.1，0.5，0.9	4.325 2	0.730 3	0.975 6	99.565 2
τ=0.2，0.5，0.8	5.031 2	0.849 5	1.126 1	99.501 5
τ=0.3，0.5，0.7	4.003 8	0.676 0	0.929 4	99.576 5
τ=0.4，0.5，0.6	8.536 9	1.441 4	2.374 6	98.962 6
τ=0.1，0.2，0.5，0.8，0.9	4.325 4	0.730 3	0.975 7	99.565 2
τ=0.1，0.3，0.5，0.7，0.9	4.336 6	0.732 2	0.977 9	99.564 3
τ=0.1，0.4，0.5，0.6，0.9	4.316 3	0.728 8	0.974 3	99.565 7
τ=0.3，0.4，0.5，0.6，0.7	4.003 7	0.676 0	0.929 0	99.576 6
τ=0.2，0.3，0.5，0.7，0.8	5.034 1	0.850 0	1.127 4	99.501 0
τ=0.2，0.4，0.5，0.6，0.8	5.025 9	0.848 6	1.125 5	99.501 7
τ=0.1，0.2，0.3，0.5，0.7，0.8，0.9	4.328 3	0.730 8	0.977 2	99.564 6
τ=0.1，0.3，0.4，0.5，0.6，0.7，0.9	4.336 5	0.732 2	0.977 5	99.564 4
τ=0.2，0.3，0.4，0.5，0.6，0.7，0.8	5.034 0	0.850 0	1.127 1	99.501 1
τ=0.1，0.2，0.4，0.5，0.6，0.8，0.9	4.320 1	0.729 4	0.975 0	99.565 4
τ=0.1，0.2，0.3，0.4，0.5，0.6，0.7，0.8，0.9	4.328 2	0.730 8	0.976 9	99.564 7

[1]	Shahzad Muhammad, Khurra Han, Feifei Jiang. Effects of Different Sampling Methods on Predict Precision of Individual Tree Volume Equation for Dahurian Larch [J]. Scientia Silvae Sinicae, 2018, 54(8): 99-105.
[2]	Ma Yanyan, Jiang Lichun. Error Structure and Variance Function of Allomatric Model [J]. Scientia Silvae Sinicae, 2018, 54(2): 90-97.
[3]	Wang Lixiang, Liu Xiaobo, Ren Lili, Shi Juan, Luo Youqing. Variety of Endophytic Fungi Associated with Conifers in Mixed Conifer Forests Invaded by Sirex noctilio [J]. Scientia Silvae Sinicae, 2017, 53(9): 81-89.
[4]	Ma Li, Mu Changcheng, Wang Biao, Zhang Yan, Li Na. Effects of Wetland Drainage for Forestation on Carbon Source or Sink of Temperate Marshes Wetlands in Xiaoxing'an Mountains of China [J]. Scientia Silvae Sinicae, 2017, 53(10): 1-12.
[5]	Yang Liu, Sun Huizhen. Analysis of Water Management Strategy for Larix gmelinii [J]. Scientia Silvae Sinicae, 2016, 52(6): 149-156.
[6]	Jiang Lichun, Ma Yingli, Li Yaoxiang. Variable-Exponent Taper Models for Dahurian Larch in Different Regions of Daxing'anling [J]. Scientia Silvae Sinicae, 2016, 52(2): 17-25.
[7]	Pang Lifeng, Jia Hongyan, Lu Yuanchang, Niu Changhai, Fu Liyong. Comparison of Two Parameters Estimation Methods for Segmented Taper Equations [J]. Scientia Silvae Sinicae, 2015, 51(12): 141-148.
[8]	Qu Aiyu;;Fang Guigan. Forecasting Methods of Pulping Properties of Fast-Growing Woods with Multiple Nonlinear Regression [J]. Scientia Silvae Sinicae, 2009, 12(10): 113-119.
[9]	Hu Xinsheng;Richard A.Ennos. SCORING THE MATING SYSTEMS OF NATURAL POPULATIONS OF THREE LARIX TAXA IN CHINA: L.GMELINII (RUPR.) RUPR., L.OLGENSIS HENRY AND L.PRINCIPIS RUPPRECHTII MAYR. [J]. , 1999, 35(1): 21-31.
[10]	Zeng Weisheng;Liao Zhiyun. A STUDY ON TAPER EQUATION [J]. , 1997, 33(2): 127-132.
[11]	Jiang Yiyin;Li fengri. A STUDY ON THE GROWTH AND YIELD OF NATURAL DAHURIAN LARCH STANDS [J]. , 1989, 25(5): 477-482.

Stem Taper Function for Larix gmelinii Based on Nonlinear Quantile Regression

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