文献类型：期刊文献

中文题名：含竞争指标的广义可加混合效应树高-胸径模型

英文题名：Generalized Additive Mixed-Effect Tree Height-Diameter Models with a Competition Index

作者：黄宏超[1] 庞丽峰[1] 符利勇[1] 卢军[1] 雷渊才[1]

第一作者：黄宏超

机构：[1]国家林业和草原局森林经营与生长模拟重点实验室(中国林业科学研究院资源信息研究所),北京100091

年份：2024

卷号：52

期号：6

起止页码：70-78

中文期刊名：东北林业大学学报

外文期刊名：Journal of Northeast Forestry University

收录：CSTPCD;;北大核心:【北大核心2023】；CSCD:【CSCD_E2023_2024】；

基金：“十四五”国家重点研发计划(2022YFD2201005)。

语种：中文

中文关键词：广义可加混合效应模型;竞争因子;树高曲线;非线性混合效应模型

外文关键词：Generalized additive mixed-effect model;Competition factor;Tree height curve;Nonlinear mixed-effect model

分类号：S758

摘要：广义可加混合效应模型(GAMM)兼具参数模型与非参数模型的优点,同时适于处理多层次分组数据。通过运用广义可加混合效应模型模拟胸径及树高之间关系,加入竞争因子作为辅助变量,并与传统非线性混合效应模型进行比较,能够为建立树高曲线及提高模型精度提供新方法。根据吉林省汪清林业局金沟岭林场2块100 m×100 m次生混交林样地中的实测单木数据,按照7∶3比例随机划分建模与验证数据。随机效应设定为林木分级,辅助变量选择大于对象木胸高断面积之和(B_(AL))或简单竞争指数(Hegyi指数,H_(EG)),根据随机效应的设定位置共构建15个广义可加混合效应模型,对照模型以Logistic及Richard方程为基础模型,共构建6个非线性混合效应树高-胸径模型。结果表明:所有广义可加混合效应模型均能较好地描述自变量与树高之间的关系,决定系数(R^(2))为0.8897~0.8998,相对均方根误差(R_(RMSE))为17.87%~18.74%,平均绝对误差(M_(AE))为1.7881~1.8745 m,赤池信息量(A_(IC))为4120.42~4162.23,均优于相同自变量下的非线性混合模型,R^(2)平均提高0.005,相对均方根误差、平均绝对误差、赤池信息量分别平均降低0.46%、0.0587 m、41.49。对于验证数据的预测可以看出,模型5具有最小的预测相对均方根误差,为20.28%,同时具有最小的预测平均绝对误差,为2.1038 m。但部分广义可加混合效应模型的预测表现略差于非线性混合模型。综合考虑参数与非参数估计显著性、模型估计精度及预测能力,所有模型中的最优模型为模型5,即以B_(AL)为辅助变量,考虑唯一全局平滑函数并以具有相同扭曲程度的分组水平平滑函数为基础添加随机效应。竞争因子选择B AL作为辅助变量能够提升树高模型的精度,而选择Hegyi指数为辅助变量的促进效果不明显。研究建立的广义可加混合效应树高胸径模型相较于传统非线性混合效应模型具有更高的估计精度及预测效果,B AL适宜作为树高模型的辅助变量来反映林木竞争状况的影响。
The Generalized Additive Mixed-Effects Model(GAMM)combines the advantages of both parametric and non-parametric models,making it suitable for handling multilevel grouped data.By applying the GAMM to simulate the relationship between tree diameter at breast height(DBH)and tree height,incorporating competition factors as auxiliary variables,and comparing it with traditional nonlinear mixed-effects models,a new method is provided for establishing tree height curves and improving model accuracy.Based on the measured data of individual trees in a 100 m×100 m secondary mixed forest plot in Jingouling Forest Farm,Wangqing Forestry Bureau,Jilin Province,the data was randomly divided into modeling and validation data in a 7∶3 ratio.Random effects were set as tree grades,and auxiliary variables were selected as the sum of basal area larger than the target tree(B_(AL))or the simple competition index(Hegyi index,H_(EG)).Fifteen GAMMs were constructed based on the position of the random effects,while six nonlinear mixed-effects tree height-diameter models were built using Logistic and Richard equations as the base models for comparison.The results showed that all GAMMs can effectively describe the relationship between the independent variables and tree height,with coefficients of determination(R^(2))ranging from 0.8897 to 0.8998,relative root mean square error(R_(RMSE))ranging from 17.87%to 18.74%,mean absolute error(M_(AE))ranging from 1.7881 to 1.8745 m,and Akaike information criterion(A_(IC))ranging from 4120.42 to 4162.23,all of which are superior to the nonlinear mixed-effects models with the same independent variables.The R^(2)increased by an average of 0.005,while the relative root mean square error,mean absolute error,and Akaike information criterion decreased by an average of 0.46%,0.0587 m,and 41.49,respectively.For the validation data,Model 5 showed the lowest predicted relative root mean square error at 20.28%and the lowest predicted mean absolute error at 2.1038 m.However,the predictive performance of some GAMMs was slightly inferior to that of the nonlinear mixed-effects models.Considering the significance of parameter and non-parameter estimation,model estimation accuracy,and predictive ability,the optimal model among all models was Model 5,which used B AL as an auxiliary variable,considered a unique global smooth function,and added random effects based on smooth functions with the same wiggliness.Choosing B_(AL) as the auxiliary variable can enhance the accuracy of the tree height model,while the promotion effect of selecting the Hegyi index as the auxiliary variable is not significant.The established GAMM tree height-diameter models have higher estimation accuracy and good predictive performance compared to traditional nonlinear mixed-effects models,and B AL is suitable as an auxiliary variable in tree height models to reflect the impact of tree competition.