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R 问卷分析.pdf
Analysis of
Questionnaire
Data with R
Bruno Falissard
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2012 by Taylor & Francis Group, LLC
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Version Date: 20110816
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Contents
Preface..................................................................................................................... vii
Acknowledgments..................................................................................................ix
1 Introduction......................................................................................................1
1.1. About.Questionnaires...........................................................................1
1.2. Principles.of.Analysis............................................................................2
1.2.1. Overviews..................................................................................2
1.2.2.
Specific.Aspects.of.Questionnaire.Data.Analysis................3
1.3. The.Mental.Health.in.Prison.(MHP).Study........................................3
If.You.Are.a.Complete.R.Beginner......................................................4
1.4.
1.4.1. First.Steps...................................................................................4
1.4.2. Functions.from.Optional.Packages........................................7
1.4.3. When.Assistance.Is.Needed....................................................7
1.4.4.
Importing.a.Dataset..................................................................7
1.4.5. More.about.the.R.Language....................................................8
2 Description of Responses..............................................................................9
2.1. Description.Using.Summary.Statistics...............................................9
2.2.
Summary.Statistics.in.Subgroups..................................................... 13
2.3. Histograms............................................................................................ 17
2.4. Boxplots................................................................................................. 21
2.5. Barplots..................................................................................................23
2.6. Pie.Charts.............................................................................................. 24
2.7. Evolution.of.a.Numerical.Variable across Time.
(Temperature.Diagram).......................................................................25
3 Description of Relationships between Variables...................................29
3.1. Relative.Risks.and.Odds.Ratios.........................................................29
3.2. Correlation.Coefficients......................................................................33
3.3. Correlation.Matrices............................................................................34
3.4. Cartesian.Plots...................................................................................... 37
3.5. Hierarchical.Clustering....................................................................... 39
3.6. Principal.Component.Analysis..........................................................42
3.7. A.Spherical.Representation.of.a.Correlation.Matrix.......................47
3.8.
Focused.Principal.Component.Analysis..........................................48
4 Confidence Intervals and Statistical Tests of Hypothesis..................... 51
4.1. Confidence.Interval.of.a.Proportion.................................................. 51
4.2. Confidence.Interval.of.a.Mean...........................................................55
iii
iv
Contents
4.3. Confidence.Interval.of.a.Relative.Risk.or.an.Odds.Ratio...............56
4.4.
Statistical.Tests.of.Hypothesis:.Comparison.of.Two.Percentages....58
Statistical.Tests.of.Hypothesis:.Comparison.of.Two.Means............ 61
4.5.
Statistical.Tests.of.Hypothesis:.Correlation.Coefficient..................64
4.6.
Statistical.Tests.of.Hypothesis:.More.than.Two.Groups.................66
4.7.
Sample.Size.Requirements:.Survey.Perspective..............................71
4.8.
4.9.
Sample.Size.Requirements:.Inferential.Perspective........................72
5 Introduction to Linear, Logistic, Poisson, and Other Regression
Models..............................................................................................................75
5.1. Linear.Regression.Models.for.Quantitative.Outcomes..................75
5.2. Logistic.Regression.for.Binary.Outcome..........................................89
5.3. Logistic.Regression.for.a.Categorical Outcome.with.More.
than.Two.Levels...................................................................................97
5.4. Logistic.Regression.for.an.Ordered.Outcome............................... 101
5.5. Regression.Models.for.an.Outcome.Resulting.from.a.Count...... 104
6 About Statistical Modelling...................................................................... 113
6.1. Coding.Numerical.Predictors.......................................................... 113
6.2. Coding.Categorical.Predictors......................................................... 120
6.3. Choosing.Predictors.......................................................................... 130
6.4.
Interaction.Terms............................................................................... 139
6.5. Assessing.the.Relative.Importance.of.Predictors.......................... 148
6.6. Dealing.with.Missing.Data............................................................... 155
6.7. Bootstrap............................................................................................. 165
6.8. Random.Effects.and.Multilevel.Modelling.................................... 170
7.1.
7.2.
7 Principles for the Validation of a Composite Score.............................. 177
Item.Analysis.(1):.Distribution......................................................... 177
Item.Analysis.(2):.The.Multi-Trait.Multi-Method.Approach.to.
Confirm.a.Subscale.Structure.......................................................... 180
7.3. Assessing.the.Unidimensionality.of.a.Set.of.Items....................... 185
7.4.
Factor.Analysis.to.Explore.the.Structure.of.a.Set.of.Items........... 191
7.5. Measurement.Error.(1):.Internal.Consistency.and.the.
Cronbach.Alpha................................................................................. 197
7.6. Measurement.Error.(2):.Inter-Rater.Reliability.............................. 199
8 Introduction to Structural Equation Modelling...................................205
8.1. Linear.Regression.as.a.Particular.Instance of.Structural.
Equation.Modelling...........................................................................205
Factor.Analysis.as.a.Particular.Instance of.Structural.
Equation.Modelling...........................................................................209
Structural.Equation.Modelling.in.Practice.................................... 212
8.2.
8.3.
Contents
v
9 Introduction to Data Manipulation Using R.........................................223
Importing.and.Exporting.Datasets.................................................223
9.1.
9.2. Manipulation.of.Datasets..................................................................227
9.3. Manipulation.of.Variables................................................................230
9.4. Checking.Inconsistencies..................................................................234
Appendix: The Analysis of Questionnaire Data Using R:
Memory Card....................................................................................................... 241
A.1. Data.Manipulations........................................................................... 241
A.1.1.
Importation/Exportation.of.Datasets................................ 241
A.1.2. Manipulation.of.Datasets.................................................... 241
A.1.3. Manipulation.of.Variables................................................... 241
A.2. Descriptive.Statistics.......................................................................... 242
A.2.1. Univariate............................................................................... 242
A.2.2. Bivariate.................................................................................. 242
A.2.3. Multidimensional................................................................. 243
A.3. Statistical.Inference............................................................................ 243
A.4. Statistical.Modelling.......................................................................... 243
A.5. Validation.of.a.Composite.Score......................................................244
References............................................................................................................ 247
Preface
Most.epidemiologists,.sociologists,.market.research.professionals.and.econo-
mists.are.now.regularly.dealing.with.quantitative.data.obtained.from.ques-
tionnaires..Sometimes.these.data.are.analyzed.by.a.professional.statistician,.
but.most.often.it.is.the.specialist.in.the.particular.field.of.study.who.does.the.
job..In.all.situations,.there.is.an.absolute.need.to.master.statistics,.a.discipline.
often.considered.unpalatable.because.it.lies.at.the.intersection.of.two.some-
what.impenetrable.disciplines—mathematics.and.data.processing.
There.is.obviously.a.misunderstanding.on.this.subject..If.theoretical.sta-
tistics. do. rely. on. mathematics,. the. practice. of. statistics. does. not,. or. in. all.
events.very.little..Statistical.practice.is.in.fact.like.the.process.of.translation,.
a.process.which,.basically,.proceeds.from.a.hypothesis.or.a.question.formu-
lated.by.a.researcher.to.a.series.of.variables.linked.by.means.of.a.statistical.
tool..As with.written.material,.there.is.almost.always.a.loss.or.a.difference.
between.the.meaning.of.the.original.text.and.the.meaning.of.the.translated.
text,.and.many.versions.can.generally.be.suggested,.each.with.their.advan-
tages.and disadvantages.
The. objective. of. this. book. is. to. learn. how. to. “translate”. certain. classic.
research.questions.into.statistical.formulations..As.indicated.in.the.title.of.the.
book,.the.syntax.of.these.statistical.formulations.is.based.on.the.well-known.
R.language..R.has.been.chosen.because.it.is.accessed.freely,.and.widely.used,.
and.above.all.because.of.the.simplicity.and.the.power.of.its.structure:.R.helps.
to.think.statistics.clearly..But.syntax.is.not.the.main.point;.understanding.
the.semantics.is.undoubtedly.our.real.challenge..The.semantics.will.emerge.
.progressively. from. examples. and. experience,. and. only. very. occasionally.
from.mathematical.considerations.
Statistics. are. nothing. without. data.. The. part. devoted. to. the. analysis. and.
the. interpretation. of. examples. is. therefore. important.. These. examples. are.
all.derived.from.the.same.genuinely.implemented.study.(Mental.Health.in.
Prison. study,. 2006). with. hundreds. of. variables. measured. on. hundreds. of.
.subjects..This.is.an.important.particularity.of.questionnaire.data:.the..number.
of. .variables. and. the. number. of. subjects. are. both. generally. very. large. and,.
.curiously,.this.has.many.practical.consequences..The.Mental.Health.in.Prison.
study.data.set.is.available.on.the.companion.website.to.the.book.(http://bruno.
falissard.pagesperso-orange.fr/AQR/index.html),. with. all. the. R. syntaxes,.
so that.it.is.easy.for.the.reader.to.replicate.and.develop.the.analyses.
In. real. life,. data. sets. contain. errors,. inconsistencies. between. answers,.
missing.data,.and.so.forth..Sometimes,.the.interpretation.of.a.result.is.not.
clear.. Sometimes,. there. is. no. statistical. tool. really. suited. to. the. question.
that. is. .nagging. you.. More. often,. the. statistical. tool. that. you. want. to. use.
is.not.formally.appropriate,.and.it.is.difficult.to.assess.to.what.extent.this.
vii
viii
Preface
slight.inadequacy.affects.the.interpretation.of.results..These.are.also.certain.
.common.situations.that.will.be.tackled.in.the.following.pages..
I.hope.that.researchers.and.Master’s.or.PhD.students.will.find.material.
here. that. will. help. them. to. gain. some. insight. into. their. data.. This. is. the.
.ultimate.achievement.for.a.statistician.
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