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作物学报

作物学报 ›› 2021, Vol. 47 ›› Issue (2): 294-304.doi: 10.3724/SP.J.1006.2021.04085

• 作物遗传育种·种质资源·分子遗传学 • 上一篇    下一篇

运用广义线性混合模型分析随机区组重复测量的试验资料

张久权1,*(), 闫慧峰1, 褚继登1, 李彩斌2   

  1. 1中国农业科学院烟草研究所 / 农业农村部烟草生物学与加工重点实验室, 山东青岛 266101
    2贵州省烟草公司毕节市公司, 贵州毕节 551700
  • 收稿日期:2020-04-01 接受日期:2020-07-02 出版日期:2021-02-12 网络出版日期:2020-07-15
  • 通讯作者: 张久权
  • 基金资助:
    国家重点研发计划项目(2018YFD201104);四川省烟草公司重点项目(SCYC201702);四川省烟草公司凉山州公司项目(LSYC201601);贵州省烟草公司毕节市公司项目(2018520500240059)

Statistical analysis of randomized complete block design with repeated measure data using Generalized Linear Mixed Models (GLIMMIX)

ZHANG Jiu-Quan1,*(), YAN Hui-Feng1, CHU Ji-Deng1, LI Cai-Bin2   

  1. 1Tobacco Research Institute, Chinese Academy of Agriculture Sciences / Key Laboratory of Tobacco Biology and Processing, Ministry of Agriculture and Rural Affairs, Qingdao 266101, Shandong, China
    2Bijie Tobacco Company of Guizhou Province, Bijie 551700, Guizhou, China
  • Received:2020-04-01 Accepted:2020-07-02 Published:2021-02-12 Published online:2020-07-15
  • Contact: ZHANG Jiu-Quan
  • Supported by:
    National Key Research and Development Program of China(2018YFD201104);Sichuan Provincial Tobacco Company(SCYC201702);Liangshan Tobacco Company of Sichuan Province(LSYC201601);Bijie Tobacco Company of Guizhou Province(2018520500240059)

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摘要：

重复测量试验对同一受试对象进行多次测量, 各时间点数据间存在自相关性, 进行方差分析和均值比较时需要进行特殊处理。虽然此方法在农业等研究领域运用十分广泛, 但目前有效地相关统计方法鲜见。为了建立操作简单、实用性强、结果可靠的统计分析方法, 本研究采用SAS的广义线性混合模型(Generalized Linear Mixed Models, GLIMMIX), 以随机区组重复测量试验资料为例, 说明了协方差结构筛选、方差分析和均值比较的具体方法。结果表明, 用传统的裂区设计、多变量统计等方法会造成资料信息浪费, 统计功效降低, 缺区无法处理等问题, 甚至会导致错误的结论。GLIMMIX能很好地处理自相关问题, 功能强大, 结果可靠, 使用简单, 允许缺区, 是进行重复测量试验资料方差分析和均值比较的理想方法。目前在国内将其运用到农学类试验数据的统计分析的相关报道鲜见, 该文在本领域具有很强的实用性和创新性。

关键词: 重复测量, 随机区组, 广义线性混合模型, 方差分析, 均值比较, SAS

Abstract:

Multiple measurements of the same subject are conducted, and there is autocorrelations among the data at each time point. Some special treatment is required for statistical analysis of repeated measure data. Although the repeated measure is widely used in agricultural and other research fields, the relevant and effective statistical methods are rare. In order to establish a simple, easy to use, and reliable statistical method, generalized linear mixed models (GLIMMIX) of SAS was adapted. Selection of covariance structure, variance analysis, and means comparison processes were showed by using RCB data. Traditional split plot and MANOVA methods wasted large amounts of information, reduced the power of the test, and could not handle missing data effectively, even resulting in incorrect conclusions. GLIMMIX was the best choice for variance analysis and means comparison of repeated measure data, because it was easy to use, and had powerful function, high reliability, and ability to handle missing data. At present, there was few relevant report in China, and this method would be very practical and innovative in this field.

Key words: repeated measure, randomized complete block, GLIMMIX, analysis of variance, mean comparison, SAS

表1

数据Microsoft Excel输入表示例"

Rain N Block Core Times Y
1 1 1 1 6 20.20
1 1 1 1 7 7.37
1 1 1 1 8 5.75
1 1 1 1 9 4.25
1 1 1 1 10 2.42
1 1 1 1 11 4.69
1 1 1 1 12 5.13
1 1 2 2 6 20.45
1 1 2 2 7 12.33
… … … … …
3 3 3 27 12 6.16

图1

3种施肥处理总氮淋失量随淋洗次数的变化 误差线为标准误。"

表4

F检验结果(III型, ANTE1, 土柱试验)"

效应
Effect		 分子自由度
Numerator DF		 分母自由度
Denominator DF		 F值
F-value		 P值
P-value
Rain 2 28.62 30.49 <0.0001
N 2 28.62 22.89 <0.0001
Rain*N 4 28.62 1.34 0.2806
Times 6 29.40 36.54 <0.0001
Rain*Times 12 39.27 0.90 0.5509
N*Times 12 39.27 4.21 0.0003
Rain*N*Times 24 47.73 0.48 0.9725

表5

处理均值两两比较示例"

语句#
Code #		 处理组合
Treatment 		差值
Difference		 标准误
SE		 自由度
DF		 t值
t-value		 Pr > |t|
(4a) (1)定位法Positional 8.05 4.32 17.85 1.87 0.0786
(4b) (1)非定位法Non-positional 8.05 4.32 17.85 1.87 0.0786
(5) (2) 10.94 3.19 20.36 3.43 0.0026
(6) (3) 6.38 1.73 33.37 3.70 0.0008
(7) (4) 0.94 0.60 31.51 1.58 0.1248
(8) (5) 1.78 0.77 28.62 2.31 0.0285

表2

采用不同协方差结构模型时F检验P值(III型检验)"

效应
Effect		 方差分量
VC		 复合对称
CS		 不规则
UN		 空间幂相关
SP		 一阶自回归AR(1) 循环相关
TOEP		 一阶前依赖ANTE(1)
Rain <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
N <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.0001 <0.0001
Rain*N 0.2375 0.2609 0.2809 0.3023 0.3023 0.3161 0.2822
Times <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
Rain*Times 0.0033 0.0038 0.6167 0.0059 0.0059 0.0172 0.5533
N*Times <0.0001 <0.0001 0.0017 <0.0001 <0.0001 <0.0001 0.0003
Rain*N*Times 0.8526 0.8537 0.9457 0.8584 0.8584 0.9225 0.9727

表3

不同协方差结构模型拟合性(土柱试验)"

准则
Criteria		 方差分量
VC		 复合对称
CS		 不规则
UN		 空间幂相关
SP		 一阶自回归AR(1) 循环相关
TOEP		 一阶前依赖ANTE(1)
-2logL 790.7 790.7 638.5 790.4 790.4 677.0 790.7
AIC 792.7 794.7 694.5 794.4 794.4 703.0 792.7
AICC 792.7 794.8 711.3 794.5 794.5 706.3 792.7
BIC 794.0 797.2 730.8 797.0 792.6 691.3 794.0
CAIC 795.0 799.2 758.8 799.0 794.6 704.3 795.0
HQIC 793.0 795.4 705.3 795.2 790.8 679.5 793.0

图2

方差分量结构"

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