Multiple Factor Analysis by Example Using R

Cover......Page 1
Semi-Title......Page 2
Series Title......Page 3
Title......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 12
1.2 Objectives......Page 14
1.2.1 Studying Individuals......Page 15
1.2.2 Studying Variables......Page 16
1.3.1 The Cloud of Individuals......Page 18
1.3.2 Fitting the Cloud of Individuals......Page 20
1.3.3 Representation of the Variables as an Aid for Interpreting the Cloud of Individuals......Page 24
1.4.1 The Cloud of Variables......Page 26
1.4.2 Fitting the Cloud of Variables......Page 27
1.5 Relationships between the Two Representations NI and NK......Page 29
1.6.1 Numerical Indicators......Page 30
1.6.2 Supplementary Elements......Page 33
1.6.3 Automatic Description of the Components......Page 37
1.7 Implementation with FactoMineR......Page 38
1.8.1 Testing the Significance of the Components......Page 39
1.8.3 Simultaneous Representation: Biplots......Page 40
1.8.6 Varimax Rotation......Page 41
1.9.1 Data Description -- Issues......Page 42
1.9.3 Implementation of the Analysis......Page 44
1.10.2 Analysis Parameters......Page 57
1.10.3 Implementation of the Analysis......Page 59
1.11.1 Data Description -- Issues......Page 64
1.11.3 Implementation of the Analysis......Page 65
2.1 Data -- Notation -- Examples......Page 72
2.2.1 Objectives......Page 74
2.2.2 Independence Model and X2 Test......Page 75
2.2.3 The Independence Model and CA......Page 77
2.3.1 Clouds of Row Profiles......Page 78
2.3.2 Clouds of Column Profiles......Page 79
2.3.3 Fitting Clouds NI and NJ......Page 81
2.3.4 Example: Women\'s Attitudes to Women\'s Work in France in 1970......Page 82
2.3.5 Superimposed Representation of Both Rows and Columns......Page 85
2.4.1 Inertias Associated with the Dimensions (Eigenvalues)......Page 90
2.4.2 Contribution of Points to a Dimension\'s Inertia......Page 93
2.4.3 Representation Quality of Points on a Dimension or Plane......Page 94
2.4.4 Distance and Inertia in the Initial Space......Page 95
2.5 Supplementary Elements (= Illustrative)......Page 96
2.6 Implementation with FactoMineR......Page 99
2.7 CA and Textual Data Processing......Page 101
2.8.1 Data Description -- Issues......Page 105
2.8.2 Implementation of the Analysis......Page 107
2.9.1 Data Description -- Issues......Page 114
2.9.3 Inertia......Page 117
2.9.4 Representation on the First Plane......Page 119
2.10.1 Data Description -- Issues......Page 122
2.10.2 Margins......Page 124
2.10.3 Inertia......Page 125
2.10.4 First Dimension......Page 128
2.10.5 Plane 2-3......Page 130
2.10.6 Projecting the Supplementary Elements......Page 134
2.10.7 Conclusion......Page 138
3.1 Data -- Notation -- Examples......Page 140
3.2.1 Studying Individuals......Page 141
3.2.2 Studying the Variables and Categories......Page 142
3.3.2 Distances between the Categories......Page 143
3.4.1 Relationship between MCA and CA......Page 145
3.4.2 The Cloud of Individuals......Page 146
3.4.3 The Cloud of Variables......Page 147
3.4.4 The Cloud of Categories......Page 148
3.4.5 Transition Relations......Page 151
3.5.1 Numerical Indicators......Page 153
3.5.2 Supplementary Elements......Page 155
3.5.3 Automatic Description of the Components......Page 156
3.6 Implementation with FactoMineR......Page 158
3.7.1 Analysing a Survey......Page 161
3.7.2 Description of a Categorical Variable or a Subpopulation......Page 163
3.7.3 The Burt Table......Page 167
3.8.1 Data Description -- Issues......Page 168
3.8.2 Analysis Parameters and Implementation with FactoMineR......Page 171
3.8.3 Analysing the First Plane......Page 172
3.8.4 Projection of Supplementary Variables......Page 173
3.9.1 Data Description -- Issues......Page 175
3.9.3 Representation of Individuals on the First Plane......Page 177
3.9.4 Representation of Categories......Page 178
3.9.5 Representation of the Variables......Page 179
4.1 Data -- Issues......Page 181
4.2.1 Similarity between Individuals......Page 185
4.2.2 Similarity between Groups of Individuals......Page 188
4.3.1 Classic Agglomerative Algorithm......Page 189
4.4 Ward\'s Method......Page 191
4.4.1 Partition Quality......Page 192
4.4.2 Agglomeration According to Inertia......Page 193
4.4.3 Two Properties of the Agglomeration Criterion......Page 195
4.4.4 Analysing Hierarchies, Choosing Partitions......Page 196
4.5.1 Data -- Issues......Page 197
4.5.2 Principle......Page 198
4.5.3 Methodology......Page 199
4.6 Partitioning and Hierarchical Clustering......Page 0
4.7 Clustering and Principal Component Methods......Page 200
4.7.2 Simultaneous Analysis of a Principal Component Map and Hierarchy......Page 201
4.8.2 Analysis Parameters......Page 202
4.8.3 Implementation of the Analysis......Page 203
4.9.2 Constructing the AHC......Page 209
4.9.3 Defining the Clusters......Page 211
4.10 Dividing Quantitative Variables into Classes......Page 214
A.1 Percentage of Inertia Explained by the First Component or by the First Plane......Page 217
A.2.1 Introduction......Page 222
A.2.2 The Rcmdr Package......Page 226
A.2.3 The FactoMineR Package......Page 228
Bibliography of Software Packages......Page 233
Bibliography......Page 235