• 论文与研究报告 •

### 异速生长模型的误差结构和误差函数

1. 东北林业大学林学院 哈尔滨 150040
• 收稿日期:2016-05-17 修回日期:2016-11-15 出版日期:2018-02-25 发布日期:2018-03-30
• 基金资助:
"十三五"国家重点研发计划资助项目（2017YFB0502700）；国家自然科学基金项目（31570624）。

### Error Structure and Variance Function of Allomatric Model

Ma Yanyan, Jiang Lichun

1. College of Forestry, Northeast Forestry University Harbin 150040
• Received:2016-05-17 Revised:2016-11-15 Online:2018-02-25 Published:2018-03-30

Abstract: [Objective] Based on allometric model, individual tree volume model was developed for Larix gmelinii and Pinus sylvestris var. mongolica in Daxing'anling. Error structure and variance function were studied.[Method] Ballantyne(2013)provides the method how to test the error structure by likelihood analysis. For comparison, nonlinear model was fitted using GNLS in S-PLUS. Variance functions (fixed variance, exponential function, power function and constant plus power function) were incorporated into general nonlinear model to reduce heteroscedasticity. Coefficient determination (R2), root mean square error (RMSE), mean absolute bias (Bias), and mean relative error (MRE), were employed to evaluate the precision of different individual volume models.[Result] 1) Through likelihood analysis, error structure of individual tree volume model is multiplicative, therefore, linear regression on the log-transformed data is suitable for individual tree volume model. 2) In order to describe the variance phenomenon in the process of individual tree volume model, variance functions (fixed variance, exponential function, power function and constant plus power function) were incorporated into volume model,and all variance functions could reduce heteroscedasticity, power function and constant plus power function are best for Larix gmelinii and Pinus sylvestris var. mongolica respectively. 3) Model fitting and validation indicated that the result were pretty similar for both error structures of this two species, however, volume model with additive error structure is slightly better than multiplicative error structure.[Conclusion] Error structures of individual tree volume model are multiplicative for this two species. However, through the comparison of model fitting and validation, nonlinear regression is better than linear regression on the log-transformed data. This study did not give an absolute and consistent conclusion from comparison. If model prediction is the first, error structure should be selected based on prediction precision. In summary, additive error structure was favored for individual tree volume model of Larix gmelinii and Pinus sylvestris var. mongolica.