基于Possion回归混合效应模型的长白落叶松一级枝数量模拟

First-order branch number simulation for Larix olgensis plantation through Poisson regression mixed effect model

利用广义线性混合模型对长白落叶松一级枝条数量进行研究,以黑龙江省佳木斯市孟家岗林场长白落叶松人工林为研究对象,基于7块标准地49株枝解析样木的596个一级枝条测定数据,利用SAS 9.3软件中的PROC GLIMMIX模块,建立了基于Poisson分布的一级枝条数量的最优基础模型。在此基础上考虑树木效应,构建每半米段一级枝条数量的广义线性混合模型,并利用AIC、BIC、-2log likelihood以及LRT检验对收敛模型的拟合优度进行比较。结果表明:任意参数组合的混合效应模型的拟合效果均好于传统模型,最终将含有DINC、LnRDINC、RDINC2这3个随机效应参数的模型作为长白落叶松每半米段一级枝条数量分布的最优混合效应模型。模型拟合结果显示,LnRDINC、CL的参数估计值为正值,DINC、RDINC2、HT/DBH、DBH的参数估计值为负值,每半米段一级枝条分布数量在树冠范围内存在峰值,模型的确定系数R2为0.669,拟合的平均绝对误差为2.250,均方根误差为3.012。从总体上看,所建立的一级枝条分布数量混合模型不但可以反映总体枝条数量的变化趋势,还可以反映树木之间的个体差异,说明广义线性混合模型确实可以提高模型的模拟精度。所得出的混合模型可以很好地预估该研究区内人工长白落叶松每半米段一级枝条数量的分布情况,为定量研究长白落叶松树冠构筑型和三维可视化模拟提供了基础。

In this study, the generalized linear mixed model was used to study the distribution of number of first-order branch for planted Larix olgensis trees. The modeling data were based on 596 first-order branches of 49 branch analysis trees selected from 7 permanent sample plots in Larix olgensis plantation from Mengjiagang Forest Farm, Jiamusi City, Heilongjiang Province of northeastern China. Poisson model was introduced to develop the optimal basic model with the PROC GLIMMIX procedure of SAS. Considering the different tree effects, the generalized linear mixed model of number of first-order branch per 0.5 m was developed on the selected optimal basic model. AIC, BIC, - 2log likelihood and LRT test were selected to compare the goodness-of-fit statistics of the models. The results showed that all of the convergence mixed models with the combination of random coefficients fitted better than the basic model. Finally, the one with three random coefficients （including DINC, LnRDINC, RDINC2） was selected as the optimal mixed model to describe the distribution of number of first-order branch per 0.5 m for planted Larix olgensis trees. In this model, the parameter values for LnRDINC and CL were positive; the ones for DINC, RDINC2, HT/DBH, DBH were negative. Moreover,there was a peak value for the number of first-order branch per 0.5 m. The fitting result of model showed that the coefficient of determination （R2 ） was 0. 669 and the mean absolute error was 2. 250 and the root mean square error was 3. 012. All in all,not only could the mixed model describe the mean trend of the branch distribution, but also it reflected the differences among sample trees. It was shown that the generalized linear mixed model could improve the simulation accuracy of the model. As a result, the optimal mixed model would be suitable for predicting the first-order branch quantity and will provide theoretic basis to modeling crown architecture and three-dimension visualization for Larix olgensis plantation.