• 论文与研究报告 •

### 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

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 Xiaofeng1,2, Ni Chengcai2, Gorden Nigh3, Qin Xianlin1

1. 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

【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。

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.