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林业科学 ›› 2009, Vol. 12 ›› Issue (1): 74-80.doi: 10.11707/j.1001-7488.20090113

• 论文 • 上一篇    下一篇

基于混合模型的单木断面积生长模型

雷相东1 李永慈2 向玮1   

  1. (1.中国林业科学研究院资源信息研究所 北京 100091;2.北京林业大学理学院 北京 100083)
  • 收稿日期:2008-03-14 修回日期:1900-01-01 出版日期:2009-01-25 发布日期:2009-01-25

Individual Basal Area Growth Model Using Multi-Level Linear Mixed Model with Repeated Measures

Lei Xiangdong1,Li Yongci1,Xiang Wei1   

  1. (1. Institute of Forest Resources Information Techniques, CAF Beijing 100091; 2. College of Science, Beijing Forestry University Beijing 100083)
  • Received:2008-03-14 Revised:1900-01-01 Online:2009-01-25 Published:2009-01-25

摘要:

摘 要:森林生长观测数据常常具有层次结构、重复测量等特点,因而不满足普通回归分析中的独立性假设,会得到有偏的参数估计,包含随机效应的混合模型可以灵活地处理这一问题。本文采用混合模型方法,建立东北近天然落叶松云冷杉林中落叶松、红松、云杉、冷杉、慢阔(色木、水曲柳、椴树和枫桦)和中阔(白桦、榆树和杂木)6个树种组的单木5年断面积生长模型。数据来自于20个长期固定观测样地,共得到10 756个观测数据,其中随机抽取15个样地的8 034个数据用于建模,其他5个样地的2 722个数据用于模型验证。建立的模型与距离无关,不需要年龄和立地指数。结果表明:起初胸径、林分密度、立地因子和与距离无关的竞争指数都是显著影响林木生长的因子,在实际调查中,这些数据很容易得到;样地内的树木效应在所有模型中均显著;样地间的随机效应只在落叶松模型中显著。与传统的固定效应模型相比,考虑层次结构的混合效应模型显著地改善了模型的表现,决定系数从0.38~0.64提高到0.85~0.89,误差、均方根误差及其相对值均显著减少。模型有一定的生物学意义和统计可靠性。

关键词: 关键词:竞争指数, 林分密度, 单木断面积生长, 混合效应模型

Abstract:

Abstract: Forest growth data are generally repeatedly observed with hierarchical structure, which result in lack of independence among observations and produce biased parameter estimation if ordinary regression analysis was used. Mixed model with random parameters could solve the problem. Individual basal area growth models for larch, spruce and fir, Korean pine and two deciduous groups were developed using linear mixed models in semi-natural larix-spruce-fir forest in northeast China. The data came from 20 permanent sample plots with 10 756 observations, of which 8 034 observations from 15 plots are randomly used for model development and 2 722 observations from rest 5 plots for model validation. These models were independent of age and site index. They may have wide use in that initial diameter at breast height, stand basal area, site factors and distance-dependent competition index were included in them which are easily accessible in forest inventory. Random effects within plots showed significant in all models, and the effects among plots not besides larch model, however. The inclusion of random parameters in these models greatly improved the fixed models. The coefficients of determination reached0.85~0.89 from 0.38~0.64. Errors and RMSEs were also significantly decreased. These models are biologically and statistically reliable.

Key words: words: competition index, stand density, individual tree basal area growth, mixed effect model