非线性混合效应生长模型的拟合、随机效应预测和应变量预测间对应关系

doi:10.11707/j.1001-7488.20161009

林业科学 ›› 2016, Vol. 52 ›› Issue (10): 72-79.doi: 10.11707/j.1001-7488.20161009

非线性混合效应生长模型的拟合、随机效应预测和应变量预测间对应关系

祖笑锋^1,2, 李秋实², 倪成才², 覃先林¹, Nigh Gorden³

1. 中国林业科学研究院资源信息研究所北京 100091;
2. 北华大学林学院吉林 132013;
3. British Columbia Ministry of Forests, Lands and Natural Resources Operations, Forest Analysis and Inventory Branch, P.O.BOX9512, Stn.Prov.Govt.Victoria, B.C.V8W 9C2, Canada

收稿日期:2015-07-07 修回日期:2015-11-23 出版日期:2016-10-25 发布日期:2016-11-09
通讯作者: 倪成才
基金资助:
民用航天预研项目“基于多源空间数据的森林火灾综合监测技术与应用示范”；国防科工局重大专项项目（21-Y30B05-9001-13/15）。

Analysis and Comparison of Combinations among Fitting NLME and Predictors of Random Parameters and Response Variables

Zu Xiaofeng^1,2, Li Qiushi², Ni Chengcai², Qin Xianlin¹, Nigh Gorden³

1. Research Institute of Forest Resource Information Techniques, CAF Beijing 100091;
2. College of Forestry, Beihua University Jilin 132013;
3. British Columbia Ministry of Forests, Lands and Natural Resources Operations, Forest Analysis and Inventory Branch, P. O. BOX9512, Stn. Prov. Govt. Victoria, B. C. V8W 9C2, Canada

Received:2015-07-07 Revised:2015-11-23 Online:2016-10-25 Published:2016-11-09

摘要/Abstract

摘要： [目的] 在非线性混合效应模型的拟合、随机效应预测和应变量预测3个环节上，常用一阶泰勒近似法将非线性模型线性化，泰勒近似的基点一般为随机效应参数的数学期望或迭代终值。在林业中，3个环节的基点常常并不完全一致，并可能影响预测精度。本研究以树高生长过程为例，分析了不一致的基点对预测精度的影响程度。[方法] 以加拿大哥伦比亚省美国黄松解析木数据为基础，以三参数Logistic为基本模型，随机抽取49株用于拟合，30株用于验证。采用R语言的nlme函数和SAS的nlmixed过程拟合模型。nlme函数以随机效应的数学期望为基点，而nlmixed过程则以迭代终值为基点。利用SAS的IML过程预测随机效应与应变量，并计算预测精度。以预测误差均方（MSPE）、平均相对误差（MPE）、平均相对误差绝对值（MAPE）作为评价预测精度的指标。[结果] 预测随机效应与预测应变量的基点不同，预测精度将大幅度下降。[结论] 预测随机效应和预测应变量的基点必须一致，且仅需二者一致，与模型拟合的基点基本无关。如果二者一致，以数学期望或迭代终值为基点对预测精度基本上无显著影响；如果预测随机效应和预测应变量的基点不同，将显著降低预测精度。

关键词: 非线性混合效应模型, 生长与收获预测, Logistic方程

Abstract: [Objective] Fitting non-linear mixed effects models (NLME), predicting the random effects parameters, as well as predicting the response variable, often involve a Taylor series expansion for linearization, based upon either the expected value of the random effects or final iterative value. In forestry, however, the linearization bases are not always consistent as they should be, and probably reduced the accuracy of prediction. In this paper, we investigated the tree height growth and discussed the effects of inconsistency among the linearization bases for fitting, predicting random effects the response.[Method] We randomly selected 49 trees for NLME-fitting and 30 trees for validation from 79 dominant trees of ponderosa pine in British Columbia, Canada. The base model was three-parameter Logistic. We used the nlme function in R and the nlmixed procedure in SAS for model fitting, respectively corresponding linearization based upon the expected value and the final iterative value. The IML procedure in SAS was employed for predicting the random effects and the response. Mean squared prediction error (MSPE), mean percentage error (MPE), and mean absolute percentage error (MAPE) were used as evaluation criteria.[Result] The results showed that inconsistent linearization bases between the random effects and the response significantly decreased the accuracy of the response prediction.[Conclusion] The linearization bases between the random effects and the response had to be consistent, and enough for obtaining predictions as accurate as possible. The accuracy of prediction was invariant to the linearization base for model-fitting and to either the expected value or the final iterative value, which was used as a linearization base.

Key words: non-linear mixed effects(NLME), growth and yield prediction, Logistic function

中图分类号:

S757

祖笑锋, 李秋实, 倪成才, 覃先林, Nigh Gorden. 非线性混合效应生长模型的拟合、随机效应预测和应变量预测间对应关系[J]. 林业科学, 2016, 52(10): 72-79.

Zu Xiaofeng, Li Qiushi, Ni Chengcai, Qin Xianlin, Nigh Gorden. Analysis and Comparison of Combinations among Fitting NLME and Predictors of Random Parameters and Response Variables[J]. Scientia Silvae Sinicae, 2016, 52(10): 72-79.

参考文献

符利勇, 张会儒, 唐守正. 2012. 基于非线性混合模型的杉木优势木平均高. 林业科学, 48(7):66-71.
(Fu L Y, Zhang H R, Tang S Z. 2012. Dominant height for Chinese fir plantation using nonlinear mixed effects model based on linearization algorithm. Scientia Silvae Sinicae, 48(7):66-71.[in Chinese])
符利勇, 孙华. 2013. 基于混合效应模型的杉木单木冠幅预测模型. 林业科学, 49(8):65-74.
(Fu L Y, Sun H. 2013. Individual crown diameter prediction for Cunninghamia lanceolata forests based on mixed effects models. Scientia Silvae Sinicae, 49(8):65-74.[in Chinese])
姜立春, 刘瑞龙. 2011. 基于非线性混合模型的落叶松树干削度模型. 林业科学, 47(4):101-106.
(Jiang L C, Liu R L. 2011. A stem taper model with nonlinear mixed effects for dahurian larch. Scientia Silvae Sinicae, 47(4):101-106.[in Chinese])
李春明, 张会儒. 2010. 利用非线性混合模型模拟杉木林优势木平均高. 林业科学, 46(3):89-95.
(Li C M, Zhang H R. 2010. Modeling dominant height for Chinese Fir plantation using a nonlinear mixed-effects modeling approach. Scientia Silvae Sinicae, 46(3):89-95.[in Chinese])
李永慈, 唐守正. 2004. 用Mixed和Nlmixed过程建立混合生长模型. 林业科学研究, 17(3):279-283.
(Li Y C, Tang S Z. 2004. Establishment of tree height growth model based on mixed and Nlmixed of SAS. Forest Research, 17(3):279-283.[in Chinese])
祖笑锋, 倪成才, Nigh Gorden, 等. 2015. 基于混合效应模型及 EBLUP 预测美国黄松林分优势木树高生长过程. 林业科学, 51(3):25-33.
(Zu X F, Ni C C, Nigh G, et al. 2015. Based on mixed-effects model and empirical best linear unbiased predictor to predict growth profile of dominant height. Scientia Silvae Sinicae, 51(3):89-95.[in Chinese])
Calama R, Montero G. 2004. Interregional nonlinear height-diameter model with random coefficients for stone pine in Spain. Can J For Res, 34(1):150-163.
Calegario N, Daniels R F, Maestri R, et al. 2005. Modeling dominant height growth based on nonlinear mixed-effects model:a clonal eucalyptus plantation case study. Forest Ecology and Management, 204(1):11-21.
Ni C, Nigh G. 2012. An analysis and comparison of predictors of random parameters demonstrated on planted loblolly pine diameter growth prediction. Forestry, 85(2):271-280.
Davidian M, Giltinan D M. 1993. Analysis of repeated measurement data using the nonlinear mixed effects model. Chemom. Intell Lab Syst, 20(1):1-24.
Davidian M, Giltinan D M. 1995. Nonlinear models for repeated measurement data. Chapman & Hall, New York, NY, 359.
Fang Z, Bailey R L. 2001. Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments. Forest Science, 47(3):287-300.
Nigh G. 2004. A comparison of fitting techniques for ponderosa pine height-age models in British Columbia. Ann For Sci, 61(7):609-615
Hall D B, Bailey R L. 2001. Modeling and prediction of forest growth variables based on multilevel nonlinear mixed models. For Sci, 47(3):311-321.
Hall D B, Clutter M. 2004. Multivariate multilevel nonlinear mixed effects models for timber yield predictions. Biometrics, 60:16-24.
Huang S, Meng S X, Yang Y. 2009a. Estimating a non-linear mixed volume-age model with and without taking into account serially-correlated errors:differences and implications. Modern Appl Sci, 3(5):3-20.
Huang S, Wiens D P, Yang Y, et al. 2009b. Assessing the impacts of species composition, top height and density on individual tree height prediction of quaking aspen in boreal mixed woods. For Ecol Manage, 258(7):1235-1247.
Jiang L, Li Y. 2010. Application of nonlinear mixed-effects modeling approach in tree height prediction. J Computers, 5(10):1575-1580.
Lappi J, Bailey R L. 1988. A height prediction model with random stand and tree parameter:an alternative to traditional site methods. Forest Science, 34(4):907-927.
Lindstrom M L, Bates D M. 1990. Nonlinear mixed effects models for repeated measures data. Biometrics, 46(3):673-687.
Meng S X, Huang S. 2009. Improved calibration of nonlinear mixed-effects models demonstrated on a height growth function. For Sci, 55(3):238-248.
Sharma M, Parton J. 2007. Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach. For Ecol Manage, 249(3):187-198.
Sharma M, Parton J. 2009. Modeling stand density effects on taper for jack pine and black spruce plantations using dimensional analysis. For Sci, 55(3):268-282.
Temesgen H, Monleon V J, Hann D W. 2008. Analysis and comparison of nonlinear tree height prediction strategies for Douglas-fir forests. Can J For Res, 38(3):553-565.
Wolfinger R D, Lin X. 1997. Two taylor-series approximation methods for nonlinear mixed models. Comput Stat Data Anal, 25(4):465-490.
Yang Y, Huang S. 2013. On the statistical and biological behaviors of nonlinear mixed forest models. European Journal of Forest Research, 132(5/6):727-736.

[1]	符利勇;张会儒;李春明;唐守正. 非线性混合效应模型参数估计方法分析[J]. , 2013, 49(1): 114-119.
[2]	符利勇;李永慈;李春明;唐守正. 利用2种非线性混合效应模型(2水平) 对杉木林胸径生长量的分析[J]. 林业科学, 2012, 48(5): 36-43.
[3]	卢军;李凤日;张会儒;张守攻. 帽儿山天然次生林主要树种冠长率模型[J]. 林业科学, 2011, 47(6): 70-76.
[4]	李春明张会儒. 利用非线性混合模型模拟杉木林优势木平均高[J]. 林业科学, 2010, 46(3): 89-95.
[5]	彭方仁. 大叶樟苗木的高生长及与^{环境因子的相关性}[J]. , 1992, 28(3): 261-266.

非线性混合效应生长模型的拟合、随机效应预测和应变量预测间对应关系

Analysis and Comparison of Combinations among Fitting NLME and Predictors of Random Parameters and Response Variables

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