Exploratory multivariate analysis by example using R:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fl. [u.a.]
CRC Press
2011
|
| Series: | Chapman & Hall/CRC computer science and data analysis
A Chapman & Hall book |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XII, 228 S. Ill., graph. Darst. |
| ISBN: | 9781439835807 |
Staff View
MARC
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| 245 | 1 | 0 | |a Exploratory multivariate analysis by example using R |c François Husson ; Sébastien Lê ; Jérôme Pagès |
| 264 | 1 | |a Boca Raton, Fl. [u.a.] |b CRC Press |c 2011 | |
| 300 | |a XII, 228 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Chapman & Hall/CRC computer science and data analysis | |
| 490 | 0 | |a A Chapman & Hall book | |
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| 650 | 4 | |a R (Computer program language) | |
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| adam_text | Contents
Preface
χι
1 Principal
Component
Analysis (PCA)
1
1.1
Data
—
Notation
—
Examples
................. 1
1.2
Objectives
............................ 1
1.2.1
Studying Individuals
................... 2
1.2.2
Studying Variables
.................... 3
1.2.3
Relationships between the Two Studies
........ 5
1.3
Studying Individuals
...................... 5
1.3.1
The Cloud of Individuals
................ 5
1.3.2
Fitting the Cloud of Individuals
............ 7
1.3.2.1
Best Plane Representation of Nj
....... 7
1.3.2.2
Sequence of Axes for Representing
N¡
.... 9
1.3.2.3
How Are the Components Obtained?
.... 10
1.3.2.4
Example
.................... 10
1.3.3
Representation of the Variables as an Aid for
Interpreting the Cloud of Individuals
.......... 11
1.4
Studying Variables
........................ 13
1.4.1
The Cloud of Variables
................. 13
1.4.2
Fitting the Cloud of Variables
.............. 14
1.5
Relationships between the Two Representations
N¡
and NK
16
1.6
Interpreting the Data
...................... 17
1.6.1
Numerical Indicators
................... 17
1.6.1.1
Percentage of Inertia Associated with a
Component
................... 17
1.6.1.2
Quality of Representation of an Individual or
Variable
..................... 18
1.6.1.3
Detecting Outliers
............... 19
1.6.1.4
Contribution of an Individual or Variable to
the Construction of a Component
...... 19
1.6.2
Supplementary Elements
................. 20
1.6.2.1
Representing Supplementary Quantitative
Variables
.................... 21
1.6.2.2
Representing Supplementary Categorical
Variables
.................... 22
1.6.2.3
Representing Supplementary Individuals
. . 23
vi
Exploratory
Multivariate
Analysis by Example Using
R
1.6.3
Automatic Description of the Components
....... 24
1.7
Implementation with FactoMineR
............... 25
1.8
Additional Results
........................ 26
1.8.1
Testing the Significance of the Components
...... 26
1.8.2
Variables: Loadings versus Correlations
........ 27
1.8.3
Simultaneous Representation: Biplots
......... 27
1.8.4
Missing Values
...................... 28
1.8.5
Large
Datasets
...................... 28
1.8.6
Varimax Rotation
.................... 28
1.9
Example: The Decathlon
Dataset
............... 29
1.9.1
Data Description
—
Issues
............... 29
1.9.2
Analysis Parameters
................... 31
1.9.2.1
Choice of Active Elements
.......... 31
1.9.2.2
Should the Variables Be Standardised?
... 31
1.9.3
Implementation of the Analysis
............. 31
1.9.3.1
Choosing the Number of Dimensions to
Examine
.................... 32
1.9.3.2
Studying the Cloud of Individuals
...... 33
1.9.3.3
Studying the Cloud of Variables
....... 36
1.9.3.4
Joint Analysis of the Cloud of Individuals and
the Cloud of Variables
............. 39
1.9.3.5
Comments on the Data
............ 43
1.10
Example: The Temperature
Dataset
.............. 44
1.10.1
Data Description
—
Issues
............... 44
1.10.2
Analysis Parameters
................... 44
1.10.2.1
Choice of Active Elements
.......... 44
1.10.2.2
Should the Variables Be Standardised?
... 45
1.10.3
Implementation of the Analysis
............. 46
1.11
Example of Genomic Data: The Chicken
Dataset
...... 51
1.11.1
Data Description
—
Issues
............... 51
1.11.2
Analysis Parameters
................... 52
1.11.3
Implementation of the Analysis
............. 52
2
Correspondence Analysis (CA)
59
2.1
Data
—
Notation
—
Examples
................. 59
2.2
Objectives and the Independence Model
............ 61
2.2.1
Objectives
......................... 61
2.2.2
Independence Model and
χ2
Test
............ 62
2.2.3
The Independence Model and CA
........... 64
2.3
Fitting the Clouds
........................ 65
2.3.1
Clouds of Row Profiles
.................. 65
2.3.2
Clouds of Column Profiles
................ 66
2.3.3
Fitting Clouds iV/ and Nj
................ 68
2.3.4
Example: Women s Attitudes to Women s Work in France
in
1970 .......................... 69
Contents
vii
2.3.4.1
Column Representation (Mother s Activity)
. 70
2.3.4.2
Row Representation (Partner s Work)
.... 72
2.3.5
Superimposed Representation of Both Rows and
Columns
.......................... 72
2.4
Interpreting the Data
...................... 77
2.4.1
Inertias Associated with the Dimensions (Eigenvalues)
77
2.4.2
Contribution of Points to a Dimension s Inertia
.... 80
2.4.3
Representation Quality of Points on a Dimension or
Plane
........................... 81
2.4.4
Distance and Inertia in the Initial Space
........ 82
2.5
Supplementary Elements
(=
Illustrative)
........... 83
2.6
Implementation with FactoMineR
............... 86
2.7
CA and Textual Data Processing
................ 88
2.8
Example: The Olympic Games
Dataset
............ 92
2.8.1
Data Description
—
Issues
............... 92
2.8.2
Implementation of the Analysis
............. 94
2.8.2.1
Choosing the Number of Dimensions to
Examine
.................... 95
2.8.2.2
Studying the Superimposed Representation
. 96
2.8.2.3
Interpreting the Results
............ 96
2.8.2.4
Comments on the Data
............ 100
2.9
Example: The White Wines
Dataset
.............. 101
2.9.1
Data Description
—
Issues
............... 101
2.9.2
Margins
.......................... 104
2.9.3
Inertia
........................... 104
2.9.4
Representation on the First Plane
........... 106
2.10
Example: The Causes of Mortality
Dataset
.......... 109
2.10.1
Data Description
—
Issues
............... 109
2.10.2
Margins
...........................
Ill
2.10.3
Inertia
........................... 112
2.10.4
First Dimension
..................... 115
2.10.5
Plane
2-3......................... 117
2.10.6
Projecting the Supplementary Elements
........ 121
2.10.7
Conclusion
........................ 125
3
Multiple Correspondence Analysis (MCA)
127
3.1
Data
—
Notation
—
Examples
................. 127
3.2
Objectives
............................ 128
3.2.1
Studying Individuals
................... 128
3.2.2
Studying the Variables and Categories
......... 129
3.3
Defining Distances between Individuals and Distances between
Categories
............................ 130
3.3.1
Distances between the Individuals
........... 130
3.3.2
Distances between the Categories
............ 130
3.4
CA on the Indicator Matrix
.................. 132
viii
Exploratory
Multivariate
Analysis by Example Using
R
3.4.1
Relationship between MCA and CA
.......... 132
3.4.2
The Cloud of Individuals
................ 133
3.4.3
The Cloud of Variables
................. 134
3.4.4
The Cloud of Categories
................. 135
3.4.5
Transition Relations
................... 138
3.5
Interpreting the Data
...................... 140
3.5.1
Numerical Indicators
................... 140
3.5.1.1
Percentage of Inertia Associated with a
Component
................... 140
3.5.1.2
Contribution and Representation Quality of
an Individual or Category
........... 141
3.5.2
Supplementary Elements
................. 142
3.5.3
Automatic Description of the Components
....... 143
3.6
Implementation with FactoMineR
............... 145
3.7
Addendum
............................ 148
3.7.1
Analysing a Survey
.................... 148
3.7.1.1
Designing a Questionnaire: Choice of Format
148
3.7.1.2
Accounting for Rare Categories
........ 150
3.7.2
Description of a Categorical Variable or a
Subpopulation
...................... 150
3.7.2.1
Description of a Categorical Variable by a
Categorical Variable
.............. 150
3.7.2.2
Description of
a Subpopulation
(or a
Category) by a Quantitative Variable
.... 151
3.7.2.3
Description of
a Subpopulation
(or a
Category) by the Categories of a Categorical
Variable
..................... 152
3.7.3
The
Burt
Table
...................... 154
3.8
Example: The Survey on the Perception of Genetically
Modified Organisms
....................... 155
3.8.1
Data Description
—
Issues
............... 155
3.8.2
Analysis Parameters and Implementation with
FactoMineR
........................ 158
3.8.3
Analysing the First Plane
................ 159
3.8.4
Projection of Supplementary Variables
......... 160
3.8.5
Conclusion
........................ 162
3.9
Example: The Sorting Task
Dataset
.............. 162
3.9.1
Data Description
—
Issues
............... 162
3.9.2
Analysis Parameters
................... 164
3.9.3
Representation of Individuals on the First Plane
. . . 164
3.9.4
Representation of Categories
.............. 165
3.9.5
Representation of the Variables
............. 166
Contents ix
4
Clustering
169
4.1 Data —
Issues
.......................... 169
4.2
Formalising the Notion of Similarity
.............. 173
4.2.1
Similarity between Individuals
............. 173
4.2.1.1
Distances and Euclidean Distances
...... 173
4.2.1.2
Example of Non-Euclidean Distance
..... 174
4.2.1.3
Other Euclidean Distances
.......... 175
4.2.1.4
Similarities and Dissimilarities
........ 175
4.2.2
Similarity between Groups of Individuals
....... 176
4.3
Constructing an Indexed Hierarchy
.............. 177
4.3.1
Classic Agglomerative Algorithm
............ 177
4.3.2
Hierarchy and Partitions
................. 179
4.4
Ward s Method
......................... 179
4.4.1
Partition Quality
..................... 180
4.4.2
Agglomeration According to Inertia
.......... 181
4.4.3
Two Properties of the Agglomeration Criterion
.... 183
4.4.4
Analysing Hierarchies, Choosing Partitions
...... 184
4.5
Direct Search for Partitions: K-means Algorithm
....... 185
4.5.1
Data
—
Issues
...................... 185
4.5.2
Principle
......................... 186
4.5.3
Methodology
....................... 187
4.6
Partitioning and Hierarchical Clustering
............ 187
4.6.1
Consolidating Partitions
................. 188
4.6.2
Mixed Algorithm
..................... 188
4.7
Clustering and Principal Component Methods
........ 188
4.7.1
Principal Component Methods Prior to AHC
..... 189
4.7.2
Simultaneous Analysis of a Principal Component Map
and Hierarchy
....................... 189
4.8
Example: The Temperature
Dataset
.............. 190
4.8.1
Data Description
—
Issues
............... 190
4.8.2
Analysis Parameters
................... 190
4.8.3
Implementation of the Analysis
............. 191
4.9
Example: The Tea
Dataset
................... 197
4.9.1
Data Description
—
Issues
............... 197
4.9.2
Constructing the AHC
.................. 197
4.9.3
Defining the Clusters
................... 199
4.10
Dividing Quantitative Variables into Classes
......... 202
Appendix
205
A.I Percentage of Inertia Explained by the First Component or by
the First Plane
.......................... 205
A.2
R
Software
............................ 210
A.2.1 Introduction
....................... 210
A.2.2 The Rcmdr Package
................... 214
A.2.3 The FactoMineR Package
................ 216
χ
Exploratory Multivariate Analysis by Example Using
R
Bibliography of Software Packages
221
Bibliography
223
Index
225
|
| any_adam_object | 1 |
| author | Husson, François Lê, Sébastien Pagès, Jérôme |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.5/3502855133 |
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| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV037236981 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:54:08Z |
| institution | BVB |
| isbn | 9781439835807 |
| language | English |
| lccn | 2010040339 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021150545 |
| oclc_num | 711828203 |
| open_access_boolean | |
| owner | DE-M49 DE-BY-TUM DE-824 DE-473 DE-BY-UBG DE-83 |
| owner_facet | DE-M49 DE-BY-TUM DE-824 DE-473 DE-BY-UBG DE-83 |
| physical | XII, 228 S. Ill., graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Chapman & Hall/CRC computer science and data analysis A Chapman & Hall book |
| spelling | Husson, François Verfasser (DE-588)1063387078 aut Exploratory multivariate analysis by example using R François Husson ; Sébastien Lê ; Jérôme Pagès Boca Raton, Fl. [u.a.] CRC Press 2011 XII, 228 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC computer science and data analysis A Chapman & Hall book Includes bibliographical references and index Multivariate analysis R (Computer program language) MATHEMATICS / Probability & Statistics / General bisacsh Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Komponentenanalyse (DE-588)4133251-9 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s Komponentenanalyse (DE-588)4133251-9 s R Programm (DE-588)4705956-4 s b DE-604 Lê, Sébastien Verfasser aut Pagès, Jérôme Verfasser (DE-588)171367057 aut Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021150545&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Husson, François Lê, Sébastien Pagès, Jérôme Exploratory multivariate analysis by example using R Multivariate analysis R (Computer program language) MATHEMATICS / Probability & Statistics / General bisacsh Multivariate Analyse (DE-588)4040708-1 gnd Komponentenanalyse (DE-588)4133251-9 gnd R Programm (DE-588)4705956-4 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4133251-9 (DE-588)4705956-4 |
| title | Exploratory multivariate analysis by example using R |
| title_auth | Exploratory multivariate analysis by example using R |
| title_exact_search | Exploratory multivariate analysis by example using R |
| title_full | Exploratory multivariate analysis by example using R François Husson ; Sébastien Lê ; Jérôme Pagès |
| title_fullStr | Exploratory multivariate analysis by example using R François Husson ; Sébastien Lê ; Jérôme Pagès |
| title_full_unstemmed | Exploratory multivariate analysis by example using R François Husson ; Sébastien Lê ; Jérôme Pagès |
| title_short | Exploratory multivariate analysis by example using R |
| title_sort | exploratory multivariate analysis by example using r |
| topic | Multivariate analysis R (Computer program language) MATHEMATICS / Probability & Statistics / General bisacsh Multivariate Analyse (DE-588)4040708-1 gnd Komponentenanalyse (DE-588)4133251-9 gnd R Programm (DE-588)4705956-4 gnd |
| topic_facet | Multivariate analysis R (Computer program language) MATHEMATICS / Probability & Statistics / General Multivariate Analyse Komponentenanalyse R Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021150545&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hussonfrancois exploratorymultivariateanalysisbyexampleusingr AT lesebastien exploratorymultivariateanalysisbyexampleusingr AT pagesjerome exploratorymultivariateanalysisbyexampleusingr |