基于非线性混合模型的栓皮栎树高与胸径关系研究

Height-diameter relationship for Quercus variabilis Blume plantations based on nonlinear mixed model

以西北农林科技大学测量的39块栓皮栎样地数据为例,首先选择非线性最小二乘法对6个常用方程进行模拟,找出模拟精度最高的模型作为基础模型。然后,利用基础模型及模拟数据构建非线性混合效应模型,分别考虑区域效应和样地效应,通过变化混合参数个数并利用SAS软件进行模拟,选择对数似然值、AIC和BIC值最小并且收敛的混合模型作为最优模型。最后利用验证数据与传统的非线性最小二乘法进行精度比较。结果表明:由于h=1.3+[(a1+a2BA+a3ha)exp(b1/D)]+ei考虑了林分断面积和优势木平均高,在模拟单木的树高时精度比其他5个模型高,并且该模型对于描述单木树高的生长趋势效果显著,因此作为构建非线性混合模型的基础模型。利用AIC、BIC和对数似然值来评价非线性混合模型的效果,结果表明:考虑区域效应的影响时,a2、a3、b1同时作为混合参数的模拟效果最好;考虑样地效应的影响时,a1、b1同时作为混合参数的模拟效果最好。无论考虑区域效应影响还是考虑样地效应影响,混合模型的拟合精度都比固定模型的模拟精度高,并且考虑样地效应影响要比考虑区域效应影响的精度更高。

In this research, six nonlinear height-diameter equations were evaluated to develop a base model with the highest precision using 39 sample plot data of Quercus variabilis Blume in Northwest A＆F University. Then, the nonlinear mixed model was constructed based on the base model and simulated data. Taking into account of different regional effect and plot effect, the convergence model, in which the values of - 2 Log Likelihood, AIC and BIC were the smallest, was considered as the best model via changing the number of mixed parameters in fitting process. Finally, the precision of mixed models was compared with that of conventional nonlinear least square method based on validation data. Results showed that the precision of the model h=1.3＋[（a1＋a2BA＋a3ha）exp（b1/D）]＋ei was higher than that of the other five models due to the consideration of stand basal area and dominant height. The fitted effects of a2, a3 and b1 simultaneously as mixed parameters were the best when considering different regional effects. The fitted effects of a, and b, simultaneously as mixed parameters were the best when considering the effects of plots. In conclusion, the precision of mixed model is better than that of conventional models whatever considering regional effects or plot effects, moreover, the precision of mixed model considering plot effects is better than that considering regional effects.