From Experimental Network to Meta-analysis: Methods and Applications with R for Agronomic and Environmental Sciences

160 Pages·2019·5.947 MB·English

by  David Makowski, François Piraux, François Brun

David Makowski
François Piraux
François Brun
From Experimental
Network to
Meta-analysis
Methods and Applications with R
for Agronomic and Environmental Sciences
Éditions Cirad, Ifremer, Inra, Irstea
www.quae.com
From Experimental Network to Meta-analysis
(cid:129)
David Makowski François Piraux
François Brun
From Experimental Network
to Meta-analysis
Methods and Applications with R for
Agronomic and Environmental Sciences
DavidMakowski FrançoisPiraux
INRA,CIRED,CIRAD,AgroParisTech ArvalisInstitutduvégétal
UniversityParis-Saclay Boigneville,France
Thiverval-Grignon,Nogent-sur-Marne
France
FrançoisBrun
ACTA
CastanetTolosan,France
ISBN978-94-024-1695-4 ISBN978-94-024-1696-1 (eBook)
https://doi.org/10.1007/978-94-024-1696-1
ÉditionsQuæ,R10,78026Versaillescedex,France
©ÉditionsQuæ2019
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Acknowledgments
Theauthorsaregratefultotheirhomeinstitutions:
(cid:129) INRA, French National Institute for Agricultural Research (http://www.inra.fr/
en)
(cid:129) ARVALIS, the French arable crops R&D institute (https://www.english.
arvalisinstitutduvegetal.fr/index.html)
(cid:129) ACTA,headofthenetworkofFrenchTechnicalInstitutesforAgriculture(http://
www.acta.asso.fr/en.html)
The authors would like to thank Jean Boiffin who has supported us since the
beginningofthisproject.Thiseditionwaspartlyfundedby:
(cid:129) NetworkDataScienceandModelingforAgriculture(www.modelia.org),funded
byagrantfromtheFrenchMinistryforAgricultureandFisheries
(cid:129) #DigitAg – Digital Agriculture Convergence Lab (https://www.hdigitag.fr/en),
fundedbyagrantofFrenchNationalResearchAgency(ANR-16-CONV-0004)
v
Contents
1 IntroductionandExamples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 ObjectivesofExperimentalNetworkAnalysis
andMeta-analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Data. . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . 3
1.3 Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 PrincipalSteps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 ObjectiveofThisBook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.6 ASimpleExampleofaMixedModel. . . . . . . . . . . . . . . . . . . . 6
1.6.1 Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.6.2 Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6.3 DefinitionoftheModel. . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6.4 Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.6.5 ComparisonwithaFixed-EffectModel. . . . . . . . . . . . . . 11
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
PartI AnalysisofExperimentalNetworks
2 BasicNotions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 Experimentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 ExperimentalNetworks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.3 TheNotionof“Environment”. . . . . . . . . . . . . . . . . . . . . 18
2.2.4 ObjectivesofanExperimentalNetwork. . . . . . . . . . . . . . 20
2.3 Notionofa“PopulationofEnvironments”. . . . . . . . . . . . . . . . . 20
2.4 Notionof“Interaction”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
vii
viii Contents
3 AnalysisofaNetworkofRandomizedCompleteBlock
DesignExperimentswithOneFactor. . . . . . . . . . . . . . . . . . . . . . . . 25
3.1 ObjectiveoftheChapter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Example“Wheat”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.1 ModelwithExperimentasaRandomEffect. . . . . . . . . . 27
3.3.2 ModelwithExperimentasaFixedEffect. . . . . . . . . . . . 28
3.3.3 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.4 ShouldExperimentEffectbeConsideredFixed
orRandom?. . . . . . .. . . . . . . . . . . .. . . . . . . . . . . . .. . 32
3.4 EvaluationoftheModel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.1 Normality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.2 Homoscedasticity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.3 Independence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4.4 SuspectData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 ComparisonsofMeans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.1 HypothesisTests:TestsofEquality. . . . . . . . . . . . . . . . . 35
3.5.2 ConfidenceIntervals. . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.3 HypothesisTests:TestsofEquivalence. . . . . . . . . . . . . . 38
3.5.4 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.6 Analysisofthe“Wheat”ExampleandRScript. . . . . . . . . . . . . . 44
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 AdvancedMethodsforNetworkAnalysis. . . . . . . . . . . . . . . . . . . . . 59
4.1 AnalysisofMeanData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.1 Step1:AnalysisofIndividualExperiments
toEstimateTreatmentMeans. . . . . . . . . . . . . . . . . . . . . 60
4.1.2 Step2:AnalysisofMeanData. . . . . . . . . . . . . . . . . . . . 60
4.1.3 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1.4 AVariant:AnalysisofMeanDatawithaFixed-Effects
Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.1.5 EstimationofVariancefortheTreatment
(cid:1)ExperimentInteraction. . . . . . . . . . . . . . . . . . . . . . . . 65
4.1.6 RScript.. . . .. . . .. . . .. . . .. . . .. . .. . . .. . . .. . . .. 67
4.2 ExperimentswithHeterogeneousVariances. . . . . . . . . . . . . . . . 69
4.2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2.2 Example“Wheat”. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2.3 GoingFurther.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3 MissingData. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3.1 OriginofMissingData. . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.3.2 AdjustedMeans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.4 TheFactors“Site”and“Year”. . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.1 Objective. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. 84
4.4.2 The“Wheat_Multi”Example. . . . . . . . . . . . . . . . . . . . . 84
Contents ix
4.4.3 ModelfortheAnalysisofMeanData. . . . . . . . . . . . . . . 85
4.4.4 EstimationoftheVarianceoftheTreatment
(cid:1)Year(cid:1)SiteInteraction. . . . . . . . . . . . . . . . . . . . . . . . 86
4.4.5 VarianceoftheDifferenceBetweenTwo
Treatments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.4.6 Analysisofthe“Wheat_Multi”Example,
withRScript. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5 PlanninganExperimentalNetwork. . . . . . . . . . . . . . . . . . . . . . . . . 95
5.1 Objective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.2 ComparisonofTwoTreatments. . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2.1 CaseofaMultisiteNetwork. . . . . . . . . . . . . . . . . . . . . . 96
5.2.2 CaseofaMultisiteandMultiyearNetwork. . . . . . . . . . . 98
5.3 OtherContrasts. . . . . . .. . . . . . . . . .. . . . . . . . .. . . . . . . . . .. 100
5.3.1 ComparisontotheMeanofSeveralControls. . . . . . . . . . 100
5.3.2 ComparisonwiththeGeneralMean. . . . . . . . . . . . . . . . 101
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
PartII Meta-analysis
6 BasicConceptsinMeta-analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.1 Definition,OriginandPrincipalStepsofMeta-analysis. . . . . . . . 105
6.2 EstimationofMeanEffectSize. . . . . . . . . . . . . . . . . . . . . . . . . 107
6.2.1 Objective. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. 107
6.2.2 SystematicSearchforStudies,SelectionofReferencesand
DataExtraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.2.3 EstimationofMeanEffectSizewithaFixed-EffectsModel 109
6.2.4 EstimationoftheMeanEffectSizewithaRandom-Effects
Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.3 Meta-regression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.3.1 Objective. . . . .. . . .. . . .. . . . .. . . .. . . .. . . . .. . . .. 116
6.3.2 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.3.3 RegressionModelswithandWithoutRandomEffects. . . 118
6.3.4 Example(Continued). . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.4 CriticalAnalysisoftheResults. . . . . . . . . . . . . . . . . . . . . . . . . 123
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7 StatisticalProblemsSpecifictoMeta-analysis. . . . . . . . . . . . . . . . . . 127
7.1 DefinitionofEffectSize. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.1.1 CorrectionofBiasesLinkedtotheUseofRatios. . . . . . . 127
7.1.2 DifferenceBetweenObservationMeans. . . . . . . . . . . . . 128
7.1.3 EffectSizesforBinaryandCountData. . . . . . . . . . . . . . 128
7.1.4 CorrelationCoefficient. . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.1.5 EffectSizesBasedonVariance. . . . . . . . . . . . . . . . . . . . 130
x Contents
7.2 GeneralizedLinearModelsfortheAnalysisofDiscrete
Data. . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . 131
7.2.1 BinomialLogitRandom-EffectsModel
forAnalyzingtheEffectofaTreatment. . . . . . . . . . . . . . 131
7.2.2 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.3 Non-linearMixedModels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.3.1 UtilityandDefinition. . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.3.2 Example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.4 BayesianModels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.4.1 Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.4.2 Example:Meta-analysiswithMCMCglmm. . . . . . . . . . . 140
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Appendix:RResourcestoImplementNetworkAnalysis
andMeta-analysisMethods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Chapter 1
Introduction and Examples
1.1 Objectives of Experimental Network Analysis
and Meta-analysis
Many experiments are performed each year to analyze the effects of agricultural
practicesonproductionandtheenvironment.Anexperimentconsistsofexperimen-
taltreatmentsappliedtoexperimentalplotsforoneorseveralyears.Dependingon
the objective of the experiment, these experimental treatments may correspond to
different types of agricultural practices, such as pest control methods, fertilization
practices, different sowing dates, crop rotations or varieties. In these experiments,
oneorseveralvariablesaremeasuredforeachtreatment,withtheaimofcharacter-
izing the plant cover (yield, product quality, leaf area, etc.) or environment (soil
characteristics, greenhouse gas emissions, water pollution, impact on biodiversity,
etc.)ofthecrop.Theseexperimentsgeneratevaluableresults,providinginsightinto
the effects of agricultural practices on crops and environmental risks. They are
performed by various organizations: research institutes, technical institutes, cham-
bersofagricultureandcompanies.
The results of agronomic experiments are likely to differ strongly between sites
and between years. The effects of agricultural practices depend on local factors
linked,inparticular,toclimateandsoilcharacteristics.Agronomicexperimentsare
often performed in networks, to make it possible to evaluate the variability of the
effects of agricultural practices. In such networks, the same set of experimental
treatmentsistestedatseveralsites,inseveralyears,toassessthevariabilityofeffects
and to estimate mean effect size. Variety testing is a classic example of an experi-
mental network. In this particular case, different varieties are cultivated at several
sites,inseveralyears,andtheirmeanperformancesandvariabilityareanalyzed.In
©ÉditionsQuæ2019 1
D.Makowskietal.,FromExperimentalNetworktoMeta-analysis,
https://doi.org/10.1007/978-94-024-1696-1_1