Welcome to Acta Agronomica Sinica,

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

• CROP GENETICS & BREEDING·GERMPLASM RESOURCES·MOLECULAR GENETICS • Previous Articles     Next Articles

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)

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

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)"

效应
Effect
分子自由度
Numerator DF
分母自由度
Denominator DF
F
F-value
P
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

Table 5

Examples of mean comparisons between treatment means"

语句#
Code #
处理组合
Treatment
差值
Difference
标准误
SE
自由度
DF
t
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

Table 2

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

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

Table 3

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

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

Fig. 2

Variance components"

[1] Wang Z, Goonewardene L A. The use of MIXED models in the analysis of animal experiments with repeated measures data. Can J Animal Sci, 2004,84:1-11.
[2] Kaps M, Lamberson W. Biostatistics for Animal Science, 3rd edn. Wallingford: CABI Publishing, 2017. pp 365-380.
[3] Littell R C, Henry P R, Ammerman C B. Statistical analysis of repeated measures data using sas procedures. J Animal Sci, 1998,76:1216-1231.
[4] SAS Institute. SAS Technique Support. Cary, NC, USA: SAS Institute Inc., 2020. [2020-05-02]. http://support.sas.com/techsup/.
[5] Littell R C, Milliken G A, Stroup W W, Wolfinger R D, Schabenberger O. SAS for Mixed Models, 2nd edn. Cary, NC, USA: SAS Institute Inc., 2006. pp 159-202.
[6] Yossa R, Verdegem M. Misuse of multiple comparison tests and underuse of contrast procedures in aquaculture publications. Aquaculture, 2015,437:344-350.
[7] 王琪, 胡良平, 高辉. 如何用SAS软件正确分析生物医学科研资料: XV. 用SAS软件实现具有一个重复测量的两因素和具有两个重复测量的两因素设计定量资料的统计分析. 中国医药生物技术, 2012,7(1):74-77.
Wang Q, Hu L P, Gao H. How to use SAS software to correctly analyze data of biomedical study: XV. Statistical analysis of quantitative data with one or two factors of repeated measure. Chin Med Biotechnol, 2012,7(1):74-77 (in Chinese).
[8] 周倩, 张晋昕. 含缺失值的重复测量资料分析在SPSS和SAS中的实现. 循证医学, 2013,13(2):120-123.
Zhou Q, Zhang J X. Data analysis for repeated measurements with missing values in SPSS and SAS.[J] Evidence-Based Med, 2013,13(2):120-123 (in Chinese with English abstract).
[9] 冯跃华, 韩钢钢, 赵田径, 董爱玲, 邹应斌, 敖和军. 单因素随机区组试验中重复测量数据分析及其SAS实现方法. 安徽农业科学, 2007,35:11730-11732.
Feng Y H, Han G G, Zhao T J, Dong A L, Zou Y B, Ao H J. Analysis of repeated measure data and its implementations of SAS in single-factor randomized complete block design. J Anhui Agric Sci, 2007,35:11730-11732 (in Chinese with English abstract).
[10] 张军锋, 董海原. 医学论文审稿中常见的统计学错误: 重复测量方法的误用分析. 中国药物与临床, 2017,17:1875-1876.
Zhang J F, Dong H Y. Common statistical errors in medical papers: Mis-use of repeated measure method. Chin Remedies Clinics, 2017,17:1875-1876 (in Chinese).
[11] 施红英, 沈毅. 混合模型在临床试验重复测量资料中的应用. 中国卫生统计, 2007,24(2):140-142.
Shi H Y, Shen Y. Mixed model applications to the analysis of repeated measures data in clinical trials. Chin Health Statistics, 2007,24(2):140-142 (in Chinese).
[12] 余松林, 向慧云. 重复测量资料分析方法与SAS程序. 北京: 科学出版社, 2004. pp 1-252.
Yu S L, Xiang H Y. The Analyse Method and SAS Procudures for Repeated Measure. Beijing: Science Press, 2004. pp 1-252(in Chinese).
[13] SAS Institute. SAS Course Notes on Mixed Model Analysis Using SAS System. Cary, NC, USA: SAS Institute Inc., 2002. pp 120-155.
[14] HJ 636-2012水质总氮的测定——碱性过硫酸钾消解紫外分光光度法. 国家环境保护标准, 2012.
HJ 636-2012 Water quality—Determination of total nitrogen-Alkaline potassium persulfate digestion UV spectrophotometric method. National Standard for Environmental Protection, 2012 (in Chinese).
[15] Littell R C, Stroup W W, Freund R J. SAS System for Linear Models, 4th edn. Cary, North Carolina, USA: SAS Institute Inc., 2002. pp 265-304.
[16] Kenward M G, Roger J H. Small sample inference for fixed effects from restricted maximum likelihood. Biometrics, 1997,53:983-997.
[17] 胡良平, 郭辰仪. 用SAS软件实现具有一个重复测量的单因素设计定量资料的统计分析. 药学服务与研究, 2011,11:409-411.
Hu L P, Guo C Y. Statistical analysis and SAS solutions for quantitative data in single-factor repeated-measurement design. Pharm Care Res, 2011,11:409-411 (in Chinese).
[18] Kiernan K, Tobias R, Gibbs P, Tao J. Contrast and Estimate Statements Made Easy: The LSMESTIMATE Statement. SAS Global Forum. Cary, North Caroina, USA: SAS Institute Inc., 2011. pp 1-19.
[19] Wolfinger R D. Heterogeneous variance covariance structures for repeated measures. J Agric Biol Environ Statistics, 1996,1:205-230.
[20] Guerin L, Stroup W W. A simulation study to evaluate PROC MIXED analysis of repeated measures data. In: Stroup W W eds. Proceedings of the 12th Annual Conference on Applied Statistics in Agriculture. Manhattan, KS: Kansas State University, 2000. pp 170-203.
[21] Huynh H, Feldt L S. Conditions under which mean square ratios in repeated measurements designs have exact F-distributions. J Am Statistical Assoc, 1970,65:1582-1589.
[22] Huynh H, Feldt L S. Estimation of the Box correction for degrees of freedom from sample data in the randomized block and split plot designs. J Education Statistics, 1976,1:15-51.
[23] 樊俊, 谭军, 邓建强, 彭五星, 赵秀云, 郑海洲, 朱宗第. 不同地膜的降解性能及对烟株生长和土壤环境的影响. 中国烟草科学, 2019,40(4):22-29.
Fan J, Tan J, Deng J Q, Peng W X, Zhao X Y, Zheng H Z, Zhu Z D. Degradation property of degradable films and their effects on flue-cured tobacco development and soil ecological environment. Chin Tob Sci, 2019,40(4):22-29 (in Chinese with English abstract).
[24] 侯红乾, 林洪鑫, 刘秀梅, 冀建华, 刘益仁, 蓝贤瑾, 吕真真, 周卫军. 长期施肥处理对双季晚稻叶绿素荧光特征及籽粒产量的影响. 作物学报, 2020,46:280-289.
Hou H Q, Lin H X, Liu X M, Ji J H, Liu Y R, Lan X J, Lyu Z Z, Zhou W J. Influence of long-term fertilizer application on chlorophyll fluorescence characteristics and grain yield of double cropping late rice. Acta Agron Sin, 2020,46:280-289 (in Chinese with English abstract).
[25] 贾国涛, 杨永锋, 杨欣玲, 王宝林, 刘超, 王根发, 申洪涛, 张书伟, 刘向真, 赵森森. 腐熟秸秆对植烟土壤理化性质和酶活性的影响. 中国农业科技导报, 2018,20(9):138-145.
Jia G T, Yang Y F, Yang X L, Wang B L, Liu C, Wang G F, Shen H T, Zhang S W, Liu X Z, Zhao S S. Influence of rotten straw on physical and chemical properties and enzyme activity of soil. J Agric Sci Technol, 2018,20(9):138-145 (in Chinese with English abstract).
[26] 陈峰, 姚晨, 孙高, 任仕泉, 何清波, 苏炳华, 陆守曾. 新药临床试验中重复测量资料的混合效应模型. 中国卫生统计, 2000,17(6):373-376.
Chen F, Yao C, Sun G, Ren S Q, He Q B, Su B H, Lu S Z. Mixed effect model of repeated measurement data in clinical trials of new drugs. Chin J Health Statistics, 2000,17(6):373-376 (in Chinese with English abstract).
[27] 王琪, 胡良平 . 如何用 SAS 软件正确分析生物医学科研资料: XIV. 用SAS软件实现具有一个重复测量的单因素设计定量资料的统计分析. 中国医药生物技术, 2011,6(4):313-320.
Wang Q, Hu L P. How to correctly analyze biomedical research data with SAS software: XIV. Statistical analysis for quantitative data with single factor design and repeated measure by using SAS software. Chin Med Biotechnol, 2011,6(4):313-320 (in Chinese with English abstract).
[28] 王超, 王汝芬, 张淑娴. 混合效应线性模型与单因素方差分析在重复测量数据中的应用比较. 数理医药学杂志, 2006,19(4):355-357.
Wang C, Wang R F, Zhang S X. The application and comparison of mixed effects linear model with single effects of variance in repeated measures data. J Mathematical Med, 2006,19(4):355-357 (in Chinese with English abstract).
[29] Littell R C, Pendergast J, Natarajan R. Modelling covariance strucutre in the analysis of repeated measures data. Statistics Med, 2000,19:1793-1819.
[1] LI Yi-Jun, LYU Hou-Quan. Effect of agricultural meteorological disasters on the production corn in the Northeast China [J]. Acta Agronomica Sinica, 2022, 48(6): 1537-1545.
[2] WANG Juan, ZHANG Yan-Wei, JIAO Zhu-Jin, LIU Pan-Pan, CHANG Wei. Identification of QTLs and candidate genes for 100-seed weight trait using PyBSASeq algorithm in soybean [J]. Acta Agronomica Sinica, 2022, 48(3): 635-643.
[3] MA Yu-BIng, WANG Dan-Li, LI Wei-Jing. Chilling Disaster Factors in Maize Reproductive Stage Based on Crop Growth Model [J]. Acta Agron Sin, 2011, 37(09): 1642-1649.
[4] Jiang Chang-jian; Zhu Qing-sen; Qiu Ze-sen. Statistical Analysis of a Factorial Experiment with Indeterminate Levels [J]. Acta Agron Sin, 1994, 20(02): 229-234.
[5] Li Wei-ming;Wu Wei-ren;Lu Hao-lan. A Method of Detecting Linkage between Quantitative Trait Loci and Genetic Marker and Its Application in wheat [J]. Acta Agron Sin, 1993, 19(02): 97-102.
[6] Sun Zhirong;Ni Pichong; Huang Zhouzhong. Studies on the Analysis of Variance and Major/Minor Factors of Medium Components Influencing the Efficiency of Anther Culture Ability [J]. Acta Agron Sin, 1990, 16(02): 123-130.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!