基于非线性分位数混合效应构建杉木树高曲线模型

Construction of Cunninghamia lanceolata tree height curve model based on nonlinear quantile mixed effect

【目的】探索树高-胸径模型构建新方法,将分位数回归与非线性混合效应法相结合应用于树高-胸径模型构建,以此提高模型的拟合精度。【方法】利用2018年福建省将乐国有林场30 m×30 m固定样地1306株杉木的实测树高、胸径数据,从4个树高-胸径模型中筛选拟合效果最好的为基础模型,基于基础模型分别采用非线性混合效应、分位数回归以及非线性分位数混合效应构建树高-胸径模型。采用评价指标均方根误差(RMSE)、调整后决定系数(R^(2)_(adj))和均方差(MSE),对各模型的拟合结果进行评价比较,采用赤池信息准则(AIC)、贝叶斯信息准则(BIC)以及对数似然函数值(Loglik)比较各最优模型的拟合精度和预测精度。【结果】根据评价指标对比显示,Logistic模型为基础模型。非线性混合效应模型的拟合效果最优(AIC为3953.986,BIC为3988.199,Loglik为-1969.993),非线性分位数混合效应模型(AIC为3979.418,BIC为4028.293,Loglik为-1979.709)次之。模型拟合效果排序为非线性混合效应模型>非线性分位数混合效应模型>基础模型>分位数回归模型。比较各模型的残差图可知各模型均不存在异方差现象,预测效果排序为非线性混合效应模型>非线性分位数混合效应模型>基础模型>分位数回归模型。【结论】本研究将分位数回归与非线性混合效应法相结合,该方法对分组数据结构中不同分位点个体间的差异与关联做出解释,提高了模型的稳定性以及拟合精度,将该方法应用到树高-胸径关系的研究上是一个可行的思路,为构建树高-胸径模型提供新方法。

[Objective]This paper aims to explore a new method for constructing tree height-DBH model,and combine quantile regression with nonlinear mixed effect method to construct tree height-DBH model,so as to improve the fitting accuracy of the model.[Method]Based on the measured tree height and DBH data of 1306 Cunninghamia lanceolata trees in the 30 m×30 m fixed sample plot of C.lanceolata in Jiangle State-Owned Forest Farm of Fujian Province,eastern China in 2018,the basic model with the best fitting effect was selected from four tree height-DBH models.Based on the basic model,the tree height-DBH model was constructed by nonlinear mixed effect,quantile regression and nonlinear quantile mixed effect.The evaluation indexes of RMSE,R^(2)_(adj) and MSE were used to evaluate and compare the fitting results of each model.Akaike information criterion(AIC),Bayesian information criterion(BIC)and log likelihood(Loglik)were used to compare the fitting accuracy and prediction accuracy of each optimal model.[Result]According to the comparison of evaluation indicators,the Logistic model was the basic model.The fitting effect of nonlinear mixed effect model was the best(AIC=3953.986,BIC=3988.199,Loglik=−1969.993),and the fitting effect of the nonlinear quantile mixed effect model(AIC=3979.418,BIC=4028.293,Loglik=−1979.709)was only slightly lower than that of the nonlinear mixed effect model.The order of model fitting effect was nonlinear mixed effect model>nonlinear quantile mixed effect model>basic model>quantile regression model.By comparing the residual sample plots of each model,it can be seen that there was no heteroscedasticity.The order of prediction effect was nonlinear mixed effect model>nonlinear quantile mixed effect model>basic model>quantile regression model.[Conclusion]This study combines quantile regression with nonlinear mixed effect method.This method explains the differences and associations between individuals at different quantiles in the grouped data structure,and improves the stability and fitting accuracy of the model.It is a feasible idea to apply this method to the study of tree height-diameter relationship,and provides a new method for constructing tree height-DBH model.