以黑龙江省五营林业局丽林林场30株人工落叶松2 190个枝条长度和角度数据为例,利用逐步回归技术建立落叶松枝条长度和角度模型:BL=b1+b2DINC+b3DINC2+b4DBH·DINC2, BA=b1+b2DINC+b3DINC2+b4DBH·DINC。利用S-PLUS软件中的LME模块,考虑树木效应拟合线性枝条长度和角度模型。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:当拟合枝条长度和角度模型时,b1,b2,b3同时作为混合参数时模型拟合最好。为了描述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长度和角度混合模型中。指数函数显著提高了枝条长度混合模型的拟合效果,幂函数显著提高了角度混合模型的拟合效果,并且消除了异方差现象。模型检验结果表明:混合模型通过校正随机参数值能提高模型的预测精度。因此,混合模型在应用上不但能反映总体枝条长度和角度预测,而且能通过方差协方差结构校正随机参数来反映树木之间的差异。
In this study, the sample data was based on 2 190 branch length and angle samples of 30 trees from dahurian larch(Larix gmelinii)plantations located in Wuying Forest Bureau in Heilongjiang Province. The stepwise regression techniques were used to develop branch length and branch angle models: BL=b1+b2DINC+b3DINC2+b4DBH·DINC2, BA=b1+b2DINC+b3DINC2+b4DBH·DINC. Then, the developed models were 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 showed that the branch length and branch angle models with parameters b1, b2, b3as mixed effects showed the best performance. Exponential and power functions were incorporated into mixed branch length and branch angle model. The addition of the exponential and power functions significantly improved the mixed-effects model. The plots of standardized residuals indicated that the mixed-effects model with exponential and power functions showed more homogeneous residual variance than the mixed-effects model. Validation confirmed that the mixed model with calibration of random parameters could provide more accurate and precise prediction. Therefore, the application of mixed model not only showed the mean trends of branch length and branch angle, but also showed the individual difference based on variance-covariance structure.