Citation: | Wang Baoying, Liang Ruiting, Xie Yunhong, Qiu Siyu, Sun Yujun. Construction of Cunninghamia lanceolata tree height curve model based on nonlinear quantile mixed effect[J]. Journal of Beijing Forestry University, 2023, 45(11): 33-41. DOI: 10.12171/j.1000-1522.20220496 |
This paper aims to explore a new method for constructing tree height-DBH model, and combine quantile regression with nonlinear mixed effect method to construct tree height-DBH model, so as to improve the fitting accuracy of the model.
Based on the measured tree height and DBH data of 1 306 Cunninghamia lanceolata trees in the 30 m × 30 m fixed sample plot of C. lanceolata in Jiangle State-Owned Forest Farm of Fujian Province, eastern China in 2018, the basic model with the best fitting effect was selected from four tree height-DBH models. Based on the basic model, the tree height-DBH model was constructed by nonlinear mixed effect, quantile regression and nonlinear quantile mixed effect. The evaluation indexes of RMSE, R2adj and MSE were used to evaluate and compare the fitting results of each model. Akaike information criterion(AIC), Bayesian information criterion(BIC) and log likelihood (Loglik) were used to compare the fitting accuracy and prediction accuracy of each optimal model.
According to the comparison of evaluation indicators, the Logistic model was the basic model. The fitting effect of nonlinear mixed effect model was the best (AIC = 3 953.986, BIC = 3 988.199, Loglik = −1 969.993), and the fitting effect of the nonlinear quantile mixed effect model (AIC = 3 979.418, BIC = 4 028.293, Loglik = −1 979.709) was only slightly lower than that of the nonlinear mixed effect model. The order of model fitting effect was nonlinear mixed effect model > nonlinear quantile mixed effect model > basic model > quantile regression model. By comparing the residual sample plots of each model, it can be seen that there was no heteroscedasticity. The order of prediction effect was nonlinear mixed effect model > nonlinear quantile mixed effect model > basic model > quantile regression model.
This study combines quantile regression with nonlinear mixed effect method. This method explains the differences and associations between individuals at different quantiles in the grouped data structure, and improves the stability and fitting accuracy of the model. It is a feasible idea to apply this method to the study of tree height-diameter relationship, and provides a new method for constructing tree height-DBH model.
[1] |
杜志, 陈振雄, 李锐, 等. 气候敏感的杉木树高−胸径非线性混合效应模型研建[J]. 北京林业大学学报, 2023, 45(9): 52−61. doi: 10.12171/j.1000-1522.20230052
Du Z, Chen Z X, Li R, et al. Development of climate-sensitive nonlinear mixed-effects tree height-DBH model for Cunninghamia lanceolata[J]. Journal of Beijing Forestry University, 2023, 45(9): 52−61. doi: 10.12171/j.1000-1522.20230052
|
[2] |
陈浩, 罗扬. 马尾松树高−胸径非线性混合效应模型构建[J]. 森林与环境学报, 2021, 41(4): 439−448.
Chen H, Luo Y. Construction of nonlinear mixed effect height-diameter model for Pinus massoniana[J]. Journal of Forest and Environment, 2021, 41(4): 439−448.
|
[3] |
沈子奕, 林杰. 基于哑变量回归和混合效应的杉树树高−胸径模型[J]. 济南大学学报(自然科学版), 2022, 36(1): 80−85.
Shen Z Y, Lin J. Height-diameter at breast height model for Cunninghamia lanceolate based on dummy variable regression and mixed effects[J]. Journal of University of Jinan (Science and Technology), 2022, 36(1): 80−85.
|
[4] |
梁瑞婷, 孙玉军, 李芸. 深度学习和传统方法模拟杉木树高−胸径模型比较[J]. 林业科学研究, 2021, 34(6): 65−72.
Liang R T, Sun Y J, Li Y. Comparison of deep learning and traditional models to simulate the height-DBH relationship of Chinese fir[J]. Forest Research, 2021, 34(6): 65−72.
|
[5] |
孙拥康, 汤景明, 王怡. 基于分位数回归的马尾松青冈栎混交林树高−胸径模型[J]. 中南林业科技大学学报, 2021, 41(12): 18−25.
Sun Y K, Tang J M, Wang Y. Height-diameter model of Pinus massoniana and Cyclobalanopsis glauca mixed forest based on quantile regression[J]. Journal of Central South University of Forestry & Technology, 2021, 41(12): 18−25.
|
[6] |
Misik T, Antal K, Kárász I, et al. Nonlinear height–diameter models for three woody, understory species in a temperate oak forest in Hungary[J]. Canadian Journal of Forest Research, 2015: 46(11): 1337−1342.
|
[7] |
Huang S S, Titus S J, Wiens D P. Comparison of nonlinear height-diameter functions for major Alberta tree species[J]. Canadian Journal of Forest Research, 1992, 22(9): 1297−1304. doi: 10.1139/x92-172
|
[8] |
佟艺玟, 陈东升, 冯健, 等. 基于线性分位数混合效应的辽东山区红松冠幅模型[J]. 应用生态学报, 2022, 33(9): 2321−2330. doi: 10.13287/j.1001-9332.202209.002
Tong Y W, Chen D S, Feng J, et al. Crown width model for planted Korean pine in eastern Liaoning mountains based on mixed effect linear quantile[J]. Chinese Journal of Applied Ecology, 2022, 33(9): 2321−2330. doi: 10.13287/j.1001-9332.202209.002
|
[9] |
Raptis D I, Kazana V, Kechagioglou S, et al. Nonlinear quantile mixed-effects models for prediction of the maximum crown width of Fagus sylvatica L., Pinus nigra Arn. and Pinus brutia Ten[J/OL]. Forests, 2022, 13(4): 499. [2022−10−31]. https://doi.org/10.3390/f13040499.
|
[10] |
李海奎, 法蕾. 基于分级的全国主要树种树高−胸径曲线模型[J]. 林业科学, 2011, 47(10): 83−90. doi: 10.11707/j.1001-7488.20111013
Li H K, Fa L. Height-diameter model for major tree species in China using the classified height method[J]. Scientia Silvae Sinicae, 2011, 47(10): 83−90. doi: 10.11707/j.1001-7488.20111013
|
[11] |
Grégoire T G, Schabenberger O, Barrett J P. Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements[J]. Canadian Journal of Forest Research, 2011, 25(1): 137−156.
|
[12] |
Pinheiro J C, Bates D M. Mixed-effects models in S and S-Plus[M]. New York: Springer, 2000.
|
[13] |
Koenker R, Bassett G. Regression quantiles[J]. Econometrica, 1978, 46(1): 33−50. doi: 10.2307/1913643
|
[14] |
田德超, 李凤日, 董利虎. 依据分位数回归建立的长白落叶松潜在最大冠幅预测模型[J]. 东北林业大学学报, 2019, 47(8): 41−46. doi: 10.3969/j.issn.1000-5382.2019.08.008
Tian D C, Li F R, Dong L H. Potential maximum crown width prediction model of Larix olgensis by quantile regression[J]. Journal of Northeast Forestry University, 2019, 47(8): 41−46. doi: 10.3969/j.issn.1000-5382.2019.08.008
|
[15] |
Delyon B, Lavielle M, Moulines E. Convergence of a stochastic approximation version of EM algorithm[J]. The Annals of Statistics, 1999, 27(1): 94−128.
|
[16] |
Akaike H. A new look at the statistical model identification[J]. IEEE Transactions on Automatic Control, 1974, 19(6): 716−723. doi: 10.1109/TAC.1974.1100705
|
[17] |
王冬至, 张冬燕, 李永宁, 等. 基于贝叶斯法的针阔混交林树高与胸径混合效应模型[J]. 林业科学, 2019, 55(11): 85−94. doi: 10.11707/j.1001-7488.20191110
Wang D Z, Zhang D Y, Li Y N, et al. Height-diameter relationship for conifer mixed forest based on Bayesian nonlinear mixed-effects model[J]. Scientia Silvae Sinicae, 2019, 55(11): 85−94. doi: 10.11707/j.1001-7488.20191110
|
[18] |
Xu H, Sun Y J, Wang X J, et al. Height-diameter models of Chinese fir ( Cunninghamia lanceolata) based on nonlinear mixed effects models in southeast China[J]. Advance Journal of Food Science and Technology, 2014, 6(4): 445−452. doi: 10.19026/ajfst.6.53
|
[19] |
Sun Y X, Gao H L, Li F R. Using linear mixed-effects models with quantile regression to simulate the crown profile of planted Pinus sylvestris var. Mongolica trees[J/OL]. Forests, 2017, 8(11): 446 [2022−11−02]. https://doi.org/10.3390/f8110446.
|
[20] |
邓祥鹏, 许芳泽, 赵善超, 等. 基于贝叶斯法的新疆天山云杉树高−胸径模型研究[J]. 北京林业大学学报, 2023, 45(1): 11−20. doi: 10.12171/j.1000-1522.20220318
Deng X P, Xu F Z, Zhao S C, et al. Tree height-DBH model for Picea schrenkiana in Tianshan Mountain, Xinjiang of northwestern China based on Bayesian method[J]. Journal of Beijing Forestry University, 2023, 45(1): 11−20. doi: 10.12171/j.1000-1522.20220318
|
[21] |
Wang J. Bayesian quantile regression for parametric nonlinear mixed effects models[J]. Statistical Methods and Applications, 2012, 21(3): 279−295. doi: 10.1007/s10260-012-0190-7
|
[22] |
Özçelik R, Cao Q V, Trincado G, et al. Predicting tree height from tree diameter and dominant height using mixed-effects and quantile regression models for two species in Turkey[J]. Forest Ecology and Management, 2018, 419: 240−248.
|
1. |
魏安琪,魏天兴,刘海燕,王莎. 黄土区刺槐和油松人工林土壤微生物PLFA分析. 北京林业大学学报. 2019(04): 88-98 .
![]() | |
2. |
李鹏飞,张兴昌,郝明德,崔勇兴,张燕江,朱世雷. 植被恢复对黄土高原矿区重构土壤理化性质、酶活性以及真菌群落的影响. 水土保持通报. 2019(05): 1-7 .
![]() | |
3. |
陆梅,孙向阳,田昆,任玉连,王邵军,王行,彭淑娴. 纳帕海高原湿地不同退化阶段土壤真菌群落结构特征. 北京林业大学学报. 2018(03): 55-65 .
![]() | |
4. |
张蓉,于亚军. 煤矸山复垦林地和草地土壤微生物多样性和群落组成的差异及其影响因素. 生态学杂志. 2018(06): 1662-1668 .
![]() | |
5. |
张树萌,黄懿梅,倪银霞,钟祺琪. 宁南山区人工林草对土壤真菌群落的影响. 中国环境科学. 2018(04): 1449-1458 .
![]() | |
6. |
李敏敏,魏天兴,李信良,葛海潮. 黄土区蔡家川流域刺槐人工林林下物种多样性. 浙江农林大学学报. 2018(02): 227-234 .
![]() | |
7. |
刘洋,曾全超,黄懿梅. 基于454高通量测序的黄土高原不同乔木林土壤细菌群落特征. 中国环境科学. 2016(11): 3487-3494 .
![]() |