基于线性混合模型的落叶松枝条基径模型

以黑龙江省五营林业局丽林林场30株人工落叶松2 190个枝条基径数据为例,利用逐步回归技术建立了落叶松枝条基径模型:BD=b1+b2DINC+b3DINC2+b4DBH.DINC2。然后,利用S-PLUS软件中的LME过程,拟合线性枝基径模型。采用AIC、BIC、对数似然值和似然比检验等模型评价统计指标对不同模型的拟合效果进行比较分析。结果表明:当拟合枝条基径模型时,b1、b2、b3同时作为混合参数时模型拟合最好。为了矫正混合模型构建过程中产生的异方差现象,把幂函数和指数函数加入到枝条基径混合模型中。指数函数显著提高了枝条基径混合模型的拟合效果,并且消除了异方差现象。模型模拟表明:对于大小相同树木,枝条基径随着着枝深度(DINC)的增加而增大,对于大小不同的树木,枝条基径随着胸径(DBH)的增加而增大。林木的胸径变量很好地反映了不同大小树木的枝条基径的变化。在不知道详细林分信息的前提下,可以利用树木变量合理地预测兴安落叶松人工林的枝条基径的变化规律。

Modeling Branch Diameter with Linear Mixed Effects for Dahurian Larch

In this study, based on the data of 2190 branch diameter samples of 30 trees from Dahurian larch (Larix gmelini Rupr.) plantations located in Wuying Forest Bureau in Heilongjiang Province, the stepwise regression techniques were used to develop a branch diameter model: BD=b₁+b₂DINC+b₃DINC²+b₄DBH·DINC². The developed model was fitted using linear mixed-effects modeling approach based on LME procedure of S-PLUS software. Evaluation statistics, such as AIC, BIC, Log Likelihood and likelihood ratio test were used for model comparisons. The results indicated that the branch diameter model with parameters b₁, b₂, b₃as mixed effects showed the best performance. Exponential and power functions were incorporated into the mixed branch diameter model. The addition of the power function significantly improved the mixed-effects model. The plots of residuals indicated that the mixed-effects model with power function showed more homogeneous residual variance than the mixed-effects model. Branch diameters increased with the depth into crown (DINC) increasing for trees with similar DBH. Branch diameters increased with the DBH increasing for different trees. DBH is adequate variable of tree for describing branch diameter variations with different trees. Branch diameters can be predicted from the measurement of some tree-level variables without detailed knowledge of the stand history for Dahurian larch plantations.