• 论文与研究报告 •

### 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

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: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 Xiaofeng1,2, Li Qiushi2, Ni Chengcai2, Qin Xianlin1, Nigh Gorden3

1. 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

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.