﻿ 基于非线性混合模型的落叶松树干削度模型
 林业科学  2011, Vol. 47 Issue (4): 101-106 PDF
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#### 文章信息

Jiang Lichun, Liu Ruilong

A Stem Taper Model with Nonlinear Mixed Effects for Dahurian Larch

Scientia Silvae Sinicae, 2011, 47(4): 101-106.

### 作者相关文章

A Stem Taper Model with Nonlinear Mixed Effects for Dahurian Larch
Jiang Lichun, Liu Ruilong
College of Forestry, Northeast Forestry University Harbin 150040
Abstract: 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.
Key words: Larix gmelinii    stem taper    nonlinear mixed model    fixed effects    random effects

1 数据与方法 1.1 数据

1.2 方法 1.2.1 基础模型

 (1)

1.2.2 混合模型

1) 确定参数效应。一般情况下有2种方法确定模型中固定参数和随机参数。一种直观的方法是将样地(树木)间数据分别拟合，然后画出基于每一样地(树木)间参数的置信区间，如果该参数的置信区间重合，则把该参数确定为固定参数，否则认为该参数为混合参数，即包括随机参数。这种方法显然要求有足够的样地(树木)抽样确保削度方程能收敛。此外本文所用削度方程有6个参数，在实际拟合过程中发现对于部分样地(树木)模型很难收敛，因此该方法不适合确定复杂削度方程的参数效应。另一种方法是将不同随机参数组合的模型进行拟合，比较模型拟合的统计量，即比较AIC、BIC和对数似然值指标，这3个指标越小越好。本文选第2种方法确定参数效应。

2) 确定样地(树木)内方差协方差结构(Ri)。本文所使用数据具有层次结构, 包括样地间、树木间和观察值。应采用3层混合模型理论来建立削度模型; 但在一个模型中综合考虑3个层次，模型很难收敛且不能得到完整的方差协方差结构，因此本研究分别考虑2个层次，即样地间和树木间，将样地间随机效应和树木间随机效应分开建模，这样也能体现样地效应和树木效应对削度方程的影响。本研究使用Davidian等(1995)来计算样地(树木)内方差协方差结构：

 (2)

3) 确定样地(树木)间方差协方差结构(D)。样地(树木)间的方差协方差结构反映了组间的变化。本研究所用的方差协方差结构取决于随机参数的个数，以包括2个随机参数(u, v)的方差协方差结构为例，结构如下：

 (3)

1.2.3 模型评价和检验指标

1.2.4 模型检验

 (4)

2 结果与分析 2.1 基本模型

2.2 非线性混合模型 2.2.1 基于样地效应混合模型随机参数确定

2.2.2 基于树木效应混合模型随机参数确定

2.2.3 模型评价

2.2.4 模型检验

 图 1 基本模型、固定效应和随机效应模型的均方根误差 Figure 1 Root mean square error (RMSE) by relative height classes (h/H) for basio model, fixed effects and mixed effects model
3 结论与讨论

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