以黑龙江省带岭林业局大青川林场84株人工落叶松解析木数据为例,采用Max和Burkhart分段削度模型作为基础模型,利用SAS软件中的似乎不相关回归过程得到该分段削度模型的4个参数和2个拐点参数同时估计。参数估计显著性检验(P<0.000 1)以及模型检验(F=31 392.30,P<0.000 1)都证明该分段模型能较好地描述落叶松树干干形变化。然后以该分段模型为基础模型,采用非线性混合模型的方法,建立落叶松人工林树干削度混合效应模型。结果表明: 当考虑样地效应影响时, b1,b2同时作为混合参数时模型拟合最好; 当考虑树木效应影响时, b2,b4同时作为混合参数时模型拟合最好。无论考虑样地效应影响还是考虑树木效应影响,混合模型的拟合精度都比基本模型的拟合精度高, 并且考虑树木效应影响要比考虑样地效应影响的精度更高。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。
In this study, the sample data were based on stem analysis of 84 trees from Dahurian Larch (Larix gmelinii) plantations located in Dailing Forest Bureau in Heilongjiang Province. Max and Burkhart segmented taper model was used to model tree stem taper. Parameters estimates of 4 parameters and 2 inflection points were obtained simultaneously using Seemingly unrelated regression procedure in SAS. This model is suitable for describing dahurian larch stem taper based on significant test of parameter estimates and F-test. Then, a nonlinear mixed-effects modeling approach was used to model stem taper based on the base model. The best performances were obtained for this model with parameters b1 and b2 as mixed effects when considering plot effects and with parameters b2 and b4 as mixed effects when considering tree effects. The mixed-effects models provided better model fitting than original model, moreover, the precision of mixed-effects model when considering tree effects is better than that when considering plot effects. Validation confirmed that the mixed model with calibration of random parameters could provide more accurate and precise prediction.