异速生长模型的误差结构和误差函数

摘要

[目的]基于异速生长模型,构建兴安落叶松和樟子松立木材积模型,分析材积模型的误差结构和误差函数.[方法]采用Ballantyne(2013)提出的似然分析法判断兴安落叶松和樟子松立木材积模型的误差结构.为了对比,利用S-PLUS软件的广义非线性GNLS模块拟合非线性模型.针对模型拟合产生的异方差现象,采用误差方差函数(固定方差、指数函数、幂函数和常数加幂函数)消除异方差.采用确定系数(R2)、均方根误差(RMSE)、绝对误差(Bias)和平均相对误差(MRE)对立木材积模型精度进行综合比较分析.[结果]1)经似然分析法判断,兴安落叶松和樟子松立木材积模型的误差结构是相乘的.2)为了描述立木材积模型构建过程中产生的异方差现象,将固定方差、指数函数、幂函数和常数加幂函数加入到立木材积模型中,所有方差函数都能降低材积模型的异方差性.幂函数消除兴安落叶松材积模型的异方差效果最好,常数加幂函数消除樟子松材积模型的异方差效果最好.3)非线性(相加误差结构)及线性(相乘误差结构)拟合和检验统计量的比较表明,对于两树种,相加和相乘立木材积模型拟合评价指标非常接近,具有相加误差结构的立木材积模型的拟合和检验精度略高于相乘误差结构的立木材积模型.[结论]兴安落叶松和樟子松立木材积模型的误差结构是相乘的.根据非线性及线性模型的拟合和检验评价指标对比发现,对数转换的线性模型并没有表现出绝对优势,而非线性回归却略优于对数转换的线性回归.本文并没有给出绝对和一致的结论,如果模型的预测是最重要的,建议对比非线性和对数转换的线性模型,选择精度较高的误差结构.针对兴安落叶松和樟子松立木材积模型的详细对比分析,建议选择非线性回归分析,即相加的误差结构.%[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.