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

doi:10.11707/j.1001-7488.20150304

林业科学 ›› 2015, Vol. 51 ›› Issue (3): 25-33.doi: 10.11707/j.1001-7488.20150304

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

祖笑锋^1,2, 倪成才², Gorden Nigh³, 覃先林¹

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:2014-05-20 修回日期:2014-09-19 出版日期:2015-03-25 发布日期:2015-04-10
通讯作者: 倪成才
基金资助:
国防科工局重大专项项目(21-Y30B05-9001-13/15)。

Based on Mixed-Effects Model and Empirical Best Linear Unbiased Predictor to Predict Growth Profile of Dominant Height

Zu Xiaofeng^1,2, Ni Chengcai², Gorden Nigh³, Qin Xianlin¹

1. Institute of Forest Resources 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:2014-05-20 Revised:2014-09-19 Online:2015-03-25 Published:2015-04-10

摘要/Abstract

摘要：

【目的】基于加拿大哥伦比亚省美国黄松79株解析木数据,研究如何用经验线性无偏最优预测法(EBLUP)预测优势木树高生长过程,并分析预测精度与观测次数、观测间隔和预测时长的关系。【方法】随机抽取49株解析木数据拟合树高生长混合效应模型,30株解析木数据用于EBLUP的预测分析。树高生长模型以Richards,Logistic,Korf等为基础模型,选用AIC,BIC及Loglik 3个统计量评价模型的拟合效果。模型拟合用R软件的nlme函数实现,预测分析以预测误差均方(MSPE)为评价标准。在分析观测间隔、观测次数和预测时长对MSPE的影响时,为分离出1个因素的影响效果,将2个因素保持不变,以分析第3个因素的影响作用。在R软件拟合结果的基础上,用SAS的IML过程进行EBLUP预测分析。【结果】拟合结果表明,Logistic方程的拟合精度最高,选为EBLUP预测分析的基本模型。预测分析结果表明,观测次数、观测间隔和预测时长对预测精度均有显著影响。随着观测次数的增加,MSPE一般表现出减少的趋势,但下降幅度与观测间隔有关:当间隔较大时,不同的观测值可以提供更充分的生长过程信息,因而可以显著降低MSPE值;但当间隔较小时,观测值所提供的生长信息相互重叠,对提高预测精度的增益有限。从预测时长角度看,在观测值附近一定区域内,EBLUP预测结果非常精确,但随着预测时长增加,预测误差呈逐渐增加的趋势。【结论】 EBLUP预测相当于两阶段拟合过程的第二阶段。第一阶段拟合为估计混合参数模型确定参数的过程,而第二阶段则是在第一阶段拟合结果的基础上,依据一个特定林分的若干树高观测值用EBLUP法预测此林分的随机效应值,并进一步预测树高生长过程。

关键词: 混合效应模型, 经验线性无偏最优预测法, 树高生长模型, 美国黄松

Abstract:

【Objective】 This study analyzed prediction accuracy of empirical best linear unbiased predictor(EBLUP), and effects of previous observations, age interval of observations and prediction span on prediction accuracy, based upon height data from 79 dominant trees of ponderosa pine in British Columbia, Canada. 【Method】We randomly selected 49 trees for fitting mixed-effects models and 30 trees for validating EBLUP. The base models were Richards, Logistic, and Korf. Fit statistics, AIC, BIC and Loglik, were used as evaluation criteria, and mean squared prediction error (MSPE) for analyzing effects of previous observations, age interval of observations and prediction span on prediction accuracy. We used the nlme function in R for model fitting, and the IML procedure in SAS for analyzing EBLUP prediction. To isolate the effect of one factor, we kept two other factors fixed.【Result】Fitting results showed the Logistic model had the best criteria among the three models of under investigation, indicating that it was the best-fitted model and was chosen for EBLUP prediction analysis. In the analysis of EBLUP prediction, we first introduced how to use EBLUP to predict random effects associated with a stand through a detailed example. Data from six trees, which deviated significantly from population-mean growth process, were used to present relationships among individual growth, population-mean growth, and adjusted values given by EBLUP. The results indicated that EBLUP prediction could fully follow individual growth process, given that there were multiple previous observations with long-enough age intervals. EBLUP analysis results also presented the number of previous observations, age interval of observations and prediction span significantly affected prediction accuracy. MSPE decreased as the number of previous observations increased, particularly when observations separated long enough in age so that they could give more efficient growth information. With respect to prediction span, prediction accuracy decreased as prediction span extended further away from the ages at which observations were obtained. 【Conclusion】 We concluded that EBLUP could be taken as the second stage of a two-stage fitting process. The first stage was used to estimate fixed model parameters, whereas the second stage to predict random effects associated with a stand on the basis of parameter estimators obtained in the first stage, and then to predict the height growth process of the stand.

Key words: mixed-effects model, EBLUP, dominant height growth model, ponderosa pine

中图分类号:

S758

祖笑锋, 倪成才, Gorden Nigh, 覃先林. 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[J]. 林业科学, 2015, 51(3): 25-33.

Zu Xiaofeng, Ni Chengcai, Gorden Nigh, Qin Xianlin. Based on Mixed-Effects Model and Empirical Best Linear Unbiased Predictor to Predict Growth Profile of Dominant Height[J]. Scientia Silvae Sinicae, 2015, 51(3): 25-33.

参考文献

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. Establishment of tree height growth model based on mixed and nlmixed of SAS. Forest Research, 17(3): 279-283.[in Chinese])
吕萍,朱钰. 2009. 基于最佳线性无偏估计的模型权数的小域估计.统计与决策,(1): 9-11.
(Lü P, Zhu Y. 2009. Estimate based on the number of best linear unbiased estimate of the model right small domains. Statistics & Decision, (1): 9-11.[in Chinese])
孟宪宇. 1994. 测树学.2版.北京:中国林业出版社.
(Meng X Y.1944. Forest mensuration. 2^nd edition.Beijing: China Forestry Publishing House.[in Chinese])
赵磊,倪成才,Gordon Nigh. 2012. 加拿大哥伦比亚省美国黄松广义代数分型地位指数模型.林业科学,48(3): 74-81.
(Zhao L, Ni C C, Nigh G. 2012. Generalized algebraic difference site index model for ponderosa pine in British Columbia,Canada. Scientia Silvae Sinicae, 48(3): 74-81.[in Chinese])
Bailey R L, Clutter J L.1974. Base-age invariant polymorphic sitecurves.Forest Science, 20(2): 155-159.
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.
Cieszewski C J, Bailey R L.2000a. Generalized algebraic difference approach: theory based derivation of dynamic site equations with polymorphism and variable asymptotes.Forest Science,46(1): 116-126.
Cieszewski C J, Harrison M,Martin S T. 2000b.Examples of practicalmethods for unbiased parameter estimation in self-referencingfunction//Cieszewski C J. Proceedings of the first international conferenceon measurements and quantitative methods management.Jekyll Island, Georgia,November 17-18.
Clutter J L. 1963. Compatible growth and yield models for loblolly pine.Forest Science,9(3): 354-371.
Davidian M, Giltinan D M.1995.Nonlinear models for repeated measurement data. Chapman and Hall, London,62: 359.
Fang Z, Bailey R L. 2001. Nonlinear mixed effects modeling for slash pine Dominant height growth following intensive silvi cultural treatments. Forest Science,47(3): 287-300.
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(1):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 mixedwoods. 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.
Littell R C, Milliken G A, Stroup W W, et al. 1966. SAS system for mixed models. SAS Institute Inc. Cary, NC, 633.
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.
Meng S X, Huang S, Yang Y, et al. 2009. Evaluation of population-averaged and subject-specific approaches for modeling the dominant or codominant height of lodgepole pine trees. Can J For Res, 39(6): 1148-1158.
Ni C C,Nigh G. 2011. An analysis and comparison of predictors of random parameters demonstrated on planted loblolly pine diameter growth prediction. Forestry, 85(2): 271-280.
Nigh G. 2004. A comparison of fitting techniques for ponderosa pine height-age models in British Columbia. Ann For Sci,61(7): 609-615.
Pinheiro J C, Bales D M. 2000. Mixed effects models in S and S-plus Springer Verlag. New York.
Tang S Z, Meng F R. 2001. Analyzing parameters of growth and yield models for Chinese Fir —145. provenances with a inearmixed approach.Silvae Genetica,50(3/4): 140-145.
Yang Y,Huang S. 2011. Comparison of different methods for fitting nonlinear mixed forest models and for making predictions. Can J For Res,41(8): 1671-1686.

[1]	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.
[2]	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.
[3]	李春明. 基于混合效应模型的杉木人工林蓄积联立方程系统[J]. 林业科学, 2012, 48(6): 80-88.
[4]	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.
[5]	赵磊;倪成才;Gordon Nigh. 加拿大哥伦比亚省美国黄松广义代数差分型地位指数模型[J]. 林业科学, 2012, 48(3): 74-81.
[6]	陈东升;李凤日;孙晓梅;贾炜玮. 基于线性混合模型的落叶松人工林节子大小预测模型[J]. 林业科学, 2011, 47(11): 121-128.
[7]	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.
[8]	李春明. 混合效应模型在森林生长模型中的应用[J]. 林业科学, 2009, 12(4): 131-138.
[9]	段杰马履一贾黎明侯雅琴公宁宁 . 北京低山地区油松人工林立地指数表的编制及应用[J]. 林业科学, 2009, 12(3): 7-12.
[10]	雷相东　李永慈　向玮. 基于混合模型的单木断面积生长模型[J]. 林业科学, 2009, 12(1): 74-80.
[11]	李科友唐德瑞朱海兰赵忠郭蔼光. 美国黄松离体胚培养条件下不定芽的形成与根产生的研究[J]. 林业科学, 2004, 40(4): 63-67.

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

Based on Mixed-Effects Model and Empirical Best Linear Unbiased Predictor to Predict Growth Profile of Dominant Height

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 11

编辑推荐

Metrics

本文评价

作者中心

期刊获奖

引证指标

联系方式