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基于Possion回归混合效应模型的长白落叶松一级枝数量模拟

王曼霖 董利虎 李凤日

王曼霖, 董利虎, 李凤日. 基于Possion回归混合效应模型的长白落叶松一级枝数量模拟[J]. 北京林业大学学报, 2017, 39(11): 45-55. doi: 10.13332/j.1000-1522.20170204
引用本文: 王曼霖, 董利虎, 李凤日. 基于Possion回归混合效应模型的长白落叶松一级枝数量模拟[J]. 北京林业大学学报, 2017, 39(11): 45-55. doi: 10.13332/j.1000-1522.20170204
WANG Man-lin, DONG Li-hu, LI Feng-ri. First-order branch number simulation for Larix olgensis plantation through Poisson regression mixed effect model[J]. Journal of Beijing Forestry University, 2017, 39(11): 45-55. doi: 10.13332/j.1000-1522.20170204
Citation: WANG Man-lin, DONG Li-hu, LI Feng-ri. First-order branch number simulation for Larix olgensis plantation through Poisson regression mixed effect model[J]. Journal of Beijing Forestry University, 2017, 39(11): 45-55. doi: 10.13332/j.1000-1522.20170204

基于Possion回归混合效应模型的长白落叶松一级枝数量模拟

doi: 10.13332/j.1000-1522.20170204
基金项目: 

“十三五”国家重点研发计划课题 2017YFD0600402

详细信息
    作者简介:

    王曼霖。主要研究方向:林分生长与收获模型。Email: 445947011@qq.com   地址: 150040 黑龙江省哈尔滨市和兴路26号东北林业大学林学院

    责任作者:

    李凤日,教授,博士生导师。主要研究方向:林分生长与收获模型。Email: fengrili@126.com   地址:同上

  • 中图分类号: S758.5

First-order branch number simulation for Larix olgensis plantation through Poisson regression mixed effect model

  • 摘要: 利用广义线性混合模型对长白落叶松一级枝条数量进行研究,以黑龙江省佳木斯市孟家岗林场长白落叶松人工林为研究对象,基于7块标准地49株枝解析样木的596个一级枝条测定数据,利用SAS 9.3软件中的PROC GLIMMIX模块,建立了基于Poisson分布的一级枝条数量的最优基础模型。在此基础上考虑树木效应,构建每半米段一级枝条数量的广义线性混合模型,并利用AIC、BIC、-2log likelihood以及LRT检验对收敛模型的拟合优度进行比较。结果表明:任意参数组合的混合效应模型的拟合效果均好于传统模型,最终将含有DINC、LnRDINC、RDINC2这3个随机效应参数的模型作为长白落叶松每半米段一级枝条数量分布的最优混合效应模型。模型拟合结果显示,LnRDINC、CL的参数估计值为正值,DINC、RDINC2、HT/DBH、DBH的参数估计值为负值,每半米段一级枝条分布数量在树冠范围内存在峰值,模型的确定系数R2为0.669,拟合的平均绝对误差为2.250,均方根误差为3.012。从总体上看,所建立的一级枝条分布数量混合模型不但可以反映总体枝条数量的变化趋势,还可以反映树木之间的个体差异,说明广义线性混合模型确实可以提高模型的模拟精度。所得出的混合模型可以很好地预估该研究区内人工长白落叶松每半米段一级枝条数量的分布情况,为定量研究长白落叶松树冠构筑型和三维可视化模拟提供了基础。

     

  • 图  1  人工长白落叶松每半米段一级枝条数量分布

    高径比、冠长模拟值来自胸径为13.5 cm的人工长白落叶松解析木。Simulated values of HT/DBH,CL based on a Larix olgensis with DBH=13.5 cm.

    Figure  1.  Predicted value of number of first-order branches per 0.5 m

    图  2  人工长白落叶松一级枝条数量的实测值与预测值散点图

    Figure  2.  Observed values and predicted values of first-order branch for Larix olgensis planation

    图  3  人工长白落叶松相对冠层深度与每半米段的预测枝条数量关系

    Figure  3.  Relationship between relative distance from tree apex and the number of predicted branches per 0.5 m section for Larix olgensis planation

    表  1  长白落叶松人工林林分因子统计表

    Table  1.   Statistics of stand variables for Larix olgensis planation

    项目
    Item
    年龄/a
    Age/year
    平均胸径
    Mean DBH/cm
    平均树高
    Mean tree height/m
    平均冠幅
    Mean crown width/m
    林分密度/(株·hm-2)
    Stand density/(tree·ha-1)
    坡度
    Slope/(°)
    海拔
    Altitude/m
    最小值Minimum 9 5.40 6.20 1.10 1 016.70 5.00 141.80
    最大值Maximum 33 19.90 24.10 1.60 3 083.30 12.50 260.10
    平均值Mean 19.19 11.30 13.31 1.27 2 223.80 6.30 193.11
    标准差Std 7.53 4.19 5.20 0.19 579.72 2.90 35.35
    变异系数CV/% 39.24 37.08 39.07 14.96 26.07 46.03 18.31
    下载: 导出CSV

    表  2  长白落叶松人工林解析木和枝条分布统计表

    Table  2.   Statistics of sample trees and branch distribution for Larix olgensis planation

    项目
    Item
    胸径
    DBH/cm
    树高
    Tree height
    (HT)/cm
    冠长
    Crown length
    (CL)/m
    冠幅
    Crown width
    (CW)/m
    高径比
    HT/DBH
    每半米段的一级枝个数
    Number of first-order
    branch per 0.5 m
    建模数据(样本数量=40)
    Fitting data(sample size=40)
    最小值Minimum 2.00 3.80 2.30 0.55 0.66 1
    最大值Maximum 27.00 21.50 11.50 3.18 1.41 26
    平均值Mean 13.68 12.45 6.24 1.42 0.85 7.56
    标准差Std 5.42 4.45 2.38 0.56 0.26 4.21
    变异系数CV/% 39.61 35.74 38.14 39.44 30.59 55.69
    检验数据(样本数量=9)
    Validation data(sample size=9)
    最小值Minimum 3.80 5.30 2.52 0.51 0.70 1
    最大值Maximum 25.20 21.30 10.51 3.20 1.39 23
    平均值Mean 14.03 12.86 6.01 1.49 0.81 7.83
    标准差Std 5.88 4.13 2.49 0.59 0.22 3.86
    变异系数CV/% 37.56 32.12 41.43 39.60 27.16 49.30
    下载: 导出CSV

    表  3  长白落叶松一级枝条数量模型所需变量及相关描述

    Table  3.   Symbol and associated description for variables tested in the first-order branch model for Larix olgensis planation

    变量符号
    Variable symbol
    变量描述
    Description
    DINC 冠层深度Distance from tree apex
    RDINC 相对冠层深度Relative distance from tree apex
    LnDINC 冠层深度的对数值Logarithm of distance from tree apex
    LnRDINC 相对冠层深度的对数值Logarithm of relative distance from tree apex
    RDINC2 相对冠层深度的平方Relative distance from tree apex squared
    DBH 树木胸高处的直径Diameter at breast height/cm
    HT 树高Tree height/m
    HT/DBH 树高和胸径的比值Ratio of tree height to diameter at breast height
    CL 树冠冠长Crown length/m
    下载: 导出CSV

    表  4  基于树木效应的混合模型拟合结果

    Table  4.   Fitting results of mixed model based on individual tree effects

    参数个数
    Parameter
    number
    模型
    Model
    随机参数Random parameter AIC BIC -2log
    likelihood
    截距Intercept HT/DBH DINC LnRDINC CL RDINC2 DBH
    7 (7) 无None 2 610.85 2 640.17 2 596.85
    (8) 2 600.01 2 617.92 2 580.11
    (9) 2 599.16 2 619.67 2 582.16
    (10) 2 584.90 2 598.41 2 568.90
    8 (11) 2 600.07 2 618.98 2 581.47
    (12) 2 600.19 2 616.50 2 582.99
    (13) 2 580.35 2 593.86 2 564.35
    (14) 2 599.50 2 616.01 2 586.50
    10 (15) 2 575.01 2 591.90 2 555.01
    (16) 2 571.42 2 588.31 2 551.42
    (17) 2 574.70 2 591.98 2 554.70
    (18) 2 575.65 2 590.85 2 557.65
    (19) 2 576.51 2 593.40 2 556.61
    (20) 2 576.65 2 593.54 2 556.65
    (21) 2 572.97 2 589.86 2 552.97
    (22) 2 574.16 2 591.05 2 554.16
    (23) 2 568.91 2 585.80 2 548.91
    (24) 2 573.76 2 590.65 2 553.76
    (25) 2 573.08 2 589.97 2 553.08
    (26) 2 574.18 2 591.06 2 554.18
    (27) 2 583.32 2 600.20 2 563.32
    (28) 2 574.62 2 591.51 2 554.62
    (29) 2 580.54 2 592.43 2 561.54
    (30) 2 572.95 2 589.84 2 552.95
    13 25(31) 2 568.95 2 590.91 2 542.95
    26(32) 2 566.07 2 588.03 2 540.07
    27(33) 2 570.77 2 592.73 2 544.77
    28(34) 2 568.37 2 590.32 2 542.37
    29(35) 2 565.65 2 587.61 2 539.65
    30(36) 2 572.20 2 594.15 2 546.20
    31(37) 2 569.04 2 590.99 2 543.04
    32(38) 2 567.45 2 589.40 2 541.45
    33(39) 2 565.74 2 587.70 2 539.74
    34(40) 2 568.37 2 590.32 2 542.37
    注:参数个数包括固定效应参数个数、随机效应方差-协方差参数个数;带★变量表示包含此随机参数;表中的模型(7)即正文中的公式(7),即不含随机效应参数的最优基础模型。Notes: the number of parameters includes the fixed parameters, parameters in covariance-structure G for random effect; variables with ★ are included in the random parameters; model (7) in the table is the formula (7) model, which is the optimal basic model without random effect parameters.
    下载: 导出CSV

    表  5  不同参数个数的模型固定参数和方差组成的估计值

    Table  5.   Fixed parameters and variance component estimates of models with different numbers of parameters

    固定参数
    Fixed parameter
    模型(7)
    Model (7)
    模型(13)
    Model (13)
    模型(23)
    Model (23)
    模型(35)
    Model (35)
    截距Int 3.058 2 2.941 7 3.178 4 3.086 6
    DINC -0.002 1 -0.002 1 -0.002 2 -0.002 5
    LnRDINC 0.342 3 0.361 7 0.370 9 0.415 3
    RDINC2 -1.044 4 -1.153 0 -1.129 3 -1.046 1
    HT/DBH -0.282 2 -0.147 1 -0.280 3 -0.245 4
    DBH -0.015 3 -0.004 34 -0.007 4 -0.011 2
    CL 0.094 9 0.080 4 0.076 7 0.105 0
    随机效应方差-协方差结构
    Variance of random effect-covariance
    structure
    [0.279 1] $\left[ {\begin{array}{*{20}{c}} {0.000\;01}&{ - 0.000\;99}\\ { - 0.000\;99}&{1.446\;3} \end{array}} \right]$ $ \left[ {\begin{array}{*{20}{c}} {0.000\;001}&{0.000\;033}&{ - 0.001\;16}\\ {0.000\;033}&{0.004\;852}&{ - 0.011\;22}\\ { - 0.001\;16}&{ - 0.011\;22}&{1.565\;0} \end{array}} \right]$
    LRT 32.5 15.44 9.26
    P <0.001 <0.001 0.026
    Pearson χ2/自由度 1.73 1.50 1.38 1.20
    Pearson χ2/degree
    下载: 导出CSV

    表  6  基于随机参数不同方差-协方差结构的混合模型模拟结果比较

    Table  6.   Comparisons of mixed model based on different variance-covariance structure of random parameters

    方差-协方差结构
    Variance-covariance structure
    参数个数
    Parameter number
    AIC BIC -2log likelihood LRT P
    复合对称矩阵Composite symmetric matrix (CS) 9 2 586.71 2 601.91 2 579.71
    对角矩阵Diagonal matrix (UN(1)) 13 2 580.99 2 597.87 2 560.99 18.72 < 0.001
    无结构矩阵Non-structural matrix (UN) 13 2 565.65 2 587.61 2 539.65 21.34
    下载: 导出CSV

    表  7  检验数据的随机参数估计结果

    Table  7.   Random parameter estimation result of validation data

    检验数据
    Validation data
    随机参数
    Random parameter
    DINC LnRDINC RDINC2
    b1 -0.000 5 -0.013 2 0.383 1
    b2 0.000 6 -0.022 6 -0.971 2
    b3 0.000 9 0.014 7 -1.068 5
    b4 0.000 8 -0.073 4 -1.525 0
    b5 0.000 1 -0.109 2 -1.883 0
    b6 0.000 7 0.044 0 -0.629 0
    b7 -0.001 6 -0.114 4 1.453 0
    b8 -0.001 6 -0.173 4 1.109 1
    b9 0.001 4 0.120 6 -1.083 0
    下载: 导出CSV

    表  8  基础模型和混合效应模型模拟结果比较

    Table  8.   Comparison of based model and mixed-effect model

    评价指标
    Evaluation index
    固定模型
    Fixed model
    混合模型
    Mixed model
    确定系数
    Determination coefficient (R2)
    0.510 0.669
    均方根误差
    Root mean square error (RMSE)
    3.396 3.012
    平均绝对误差
    Average absolute error (MAE)
    2.601 2.250
    下载: 导出CSV
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    [29] ISHⅡ H, MCDOWELL N. Age-related development of crown structure in coastal Douglas-fir trees[J]. Forest Ecology and Management, 2002, 169(3): 257-270. doi: 10.1016/S0378-1127(01)00751-4
    [30] THORPE H C, ASTRUP R, TROWBRIDGE A, et al. Competition and tree crowns: a neighborhood analysis of three boreal tree species[J]. Forest Ecology & Management, 2010, 259(8): 1586-1596. http://cn.bing.com/academic/profile?id=e01e55e9ca64ee12f100228cbeb0efbf&encoded=0&v=paper_preview&mkt=zh-cn
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出版历程
  • 收稿日期:  2017-06-12
  • 修回日期:  2017-10-19
  • 刊出日期:  2017-11-01

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