基于线性混合效应模型的杉木树高-胸径模型

Height-diameter model for Chinese fir based on linear mixed model

【目的】利用线性混合效应模型分析杉木树高与胸径的关系,为杉木树高测量提供支持。【方法】收集688组有效杉木研究数据,利用最小二乘法构建树高(H)和胸径(DBH)的线性基础模型,同时考虑林分密度效应和海拔效应,在R 3.2.2软件中拟合混合模型,比较基础模型和2种混合模型的赤池信息规则(AIC)、贝叶斯信息规则(BIC)和-2倍对数似然值(-2log lik),在此基础上,引入误差效应方差协方差矩阵及指数函数、幂函数和恒等式函数,筛选较好的混合模型;基于独立验证数据对模型进行验证,选取R^2、|E|、RMSE3个评价指标对模型精度进行评价。【结果】固定模型的AIC=2 089.731,BIC=2 102.151,-2log lik=2 083.732,均大于混合模型,即混合效应模型拟合效果优于固定模型;考虑模型误差效应方差协方差矩阵,加入恒等式异方差函数能够显著提高模型的精度,且含有不同随机参数的混合模型精度不同,引入海拔随机效应的混合模型拟合精度(R^2=0.804 4,|E|=1.553 9,RMSE=2.143 0)高于含有林分密度效应的混合模型(R^2=0.797 0,|E|=1.576 6,RMSE=2.183 0)。【结论】考虑随机效应的混合模型既能反映杉木树高的总体变化趋势,还能体现不同组分间的差异,在估测精度和通用性上均优于固定模型。

[Objective] Relationship between height （H） and diameter at breast-height （DBH） of Chi- nese fir （Cunninghamia lanceolata） was studied using linear mixed model to provide support for height measurement. [Method] Data of 688 Chinese fir plants were collected and least square method was used to established the H-DBH linear model. Considering stand density and altitude effects, the Akaike informa- tion criterion （AIC）,Bayesian information criterion （BIC） and the -2 time of logarithm likelihood value （-2log lik） are compared between the basic model and the 2 mixed models. Based on this,the exponential function （Exp）, power function （Power）, and identity heteroscedasticity function （Ident） were added to se- lect the better mixing models. The accuracy of the model was evaluated using of R2 , ｜ E｜ and RMSE as in- dexes in R 3.2.2 software. [Result] The Akaike information criterion （2 089. 731）, Bayesian information criterion （2 102. 151） ,and - 2 times of logarithm likelihood value （2 083. 732） were higher than the mixed model,indicating that the mixed model was better. Considering the error variance-covariance matrix and adding identity heteroscedasticity function （Ident） significantly improved the model accuracy. Compared with the density-level mixed model （R2= 0. 797 0, ｜E｜= 1. 576 6, RMSE = 2. 183 0）, the altitude-level mixed model had better precision （R2 =0. 804 4,｜E｜=1. 553 9 ,RMSE= 2. 143 0）. [Conclusion] The mixed model with the consideration of random effects was better than fixed model since it can reveal both overall trends and differences between different groups of Chinese fir plantations.