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Acta Agronomica Sinica ›› 2021, Vol. 47 ›› Issue (2): 294-304.doi: 10.3724/SP.J.1006.2021.04085


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 Online:2021-02-12 Published:2020-07-15
  • Contact: ZHANG Jiu-Quan E-mail:zhangjiuquan@caas.cn
  • 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)


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

Table 1

Data entry example for Microsoft Excel"

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

Fig. 1

Total N loss varied with leaching times at three N fertilizer treatments The error lines are standard errors (SEs)."

Table 4

Output of F test (type III, ANTE1, soil column experiment)"

Numerator DF
Denominator DF
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

Table 5

Examples of mean comparisons between treatment means"

Code #
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

Table 2

P-value for F test with various covariance structures (III)"

一阶自回归AR(1) 循环相关
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

Table 3

Model fit statistics with various covariance structures (soil column experiment)"

一阶自回归AR(1) 循环相关
-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

Fig. 2

Variance components"

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