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## Book Description

Multiple factor analysis (MFA) enables users to analyze tables of individuals and variables in which the variables are structured into quantitative, qualitative, or mixed groups. Written by the co-developer of this methodology, Multiple Factor Analysis by Example Using R brings together the theoretical and methodological aspects of MFA. It also includes examples of applications and details of how to implement MFA using an R package (FactoMineR).

The first two chapters cover the basic factorial analysis methods of principal component analysis (PCA) and multiple correspondence analysis (MCA). The next chapter discusses factor analysis for mixed data (FAMD), a little-known method for simultaneously analyzing quantitative and qualitative variables without group distinction. Focusing on MFA, subsequent chapters examine the key points of MFA in the context of quantitative variables as well as qualitative and mixed data. The author also compares MFA and Procrustes analysis and presents a natural extension of MFA: hierarchical MFA (HMFA). The final chapter explores several elements of matrix calculation and metric spaces used in the book.

1. Preliminaries
2. Preface
3. Chapter 1 Principal Component Analysis
1. 1.1 Data, Notations
2. 1.2 Why Analyse a Table with PCA?
3. 1.3 Clouds of Individuals and Variables
4. 1.4 Centring and Reducing
5. 1.5 Fitting Clouds NI and NK
1. 1.5.1 General Principles and Formalising Criteria
2. 1.5.2 Interpreting Criteria
3. 1.5.3 Solution
4. 1.5.4 Relationships Between the Analyses of the Two Clouds
5. 1.5.5 Representing the Variables
6. 1.5.6 Number of Axes
7. 1.5.7 Vocabulary: Axes and Factors
6. 1.6 Interpretation Aids
1. 1.6.1 Percentage of Inertia Associated with an Axis
2. 1.6.2 Contribution of One Point to the Inertia of an Axis
3. 1.6.3 Quality of Representation of a Point by an Axis
7. 1.7 First Example: 909 Baccalaureate Candidates
1. 1.7.1 Projected Inertia (Eigenvalues)
2. 1.7.2 Interpreting the Axes
3. 1.7.3 Methodological Remarks
8. 1.8 Supplementary Elements
9. 1.9 Qualitative Variables in PCA
10. 1.10 Second Example: Six Orange Juices
11. 1.11 PCA in FactoMineR
1. Drop-Down Menu in R Commander
2. Examples of Commands
3. Remark
4. Script for Analysing the Orange Juice Data
4. Chapter 2 Multiple Correspondence Analysis
1. 2.1 Data
2. 2.2 Complete Disjunctive Table
3. 2.3 Questioning
4. 2.4 Clouds of Individuals and Variables
1. 2.4.1 Cloud of Individuals
2. 2.4.2 Cloud of Categories
3. 2.4.3 Qualitative Variables
5. 2.5 Fitting Clouds NI and NK
6. 2.6 Representing Individuals, Categories and Variables
7. 2.7 Interpretation Aids
8. 2.8 Example: Five Educational Tools Evaluated by 25 Students
1. 2.8.1 Data
2. 2.8.2 Analyses and Representations
3. 2.8.3 MCA/PCA Comparison for Ordinal Variables
9. 2.9 MCA in FactoMineR
5. Chapter 3 Factorial Analysis of Mixed Data
1. 3.1 Data, Notations
2. 3.2 Representing Variables
3. 3.3 Representing Individuals
4. 3.4 Transition Relations
5. 3.5 Implementation
6. 3.6 Example: Biometry of Six Individuals
7. 3.7 FAMD in FactoMineR
1. Drop-Down Menu in R Commander
2. Graphical Options (see Figure 3.6)
3. Examples of Commands
6. Chapter 4 Weighting Groups of Variables
1. 4.1 Objectives
2. 4.2 Introductory Numerical Example
3. 4.3 Weighting Variables in MFA
4. 4.4 Application to the Six Orange Juices
5. 4.5 Relationships with Separate Analyses
6. 4.6 Conclusion
7. 4.7 MFA in FactoMineR (First Results)
7. Chapter 5 Comparing Clouds of Partial Individuals
1. 5.1 Objectives
2. 5.2 Method
3. 5.3 Application to the Six Orange Juices
4. 5.4 Interpretation Aids
5. 5.5 Distortions in Superimposed Representations
1. 5.5.1 Example (Trapeziums Data)
2. 5.5.2 Geometric Interpretation
3. 5.5.3 Algebra Approach
6. 5.6 Superimposed Representation: Conclusion
7. 5.7 MFA Partial Clouds in FactoMineR
8. Chapter 6 Factors Common to Different Groups of Variables
1. 6.1 Objectives
2. 6.2 Relationship Between a Variable and Groups of Variables
3. 6.3 Searching for Common Factors
4. 6.4 Searching for Canonical Variables
5. 6.5 Interpretation Aids
9. Chapter 7 Comparing Groups of Variables and Indscal Model
1. 7.1 Cloud NJ of Groups of Variables
2. 7.2 Scalar Product and Relationship Between Groups of Variables
3. 7.3 Norm in the Groups’ Space
4. 7.4 Representation of Cloud NJ
1. 7.4.1 Principle
2. 7.4.2 Criterion
5. 7.5 Interpretation Aids
6. 7.6 The Indscal Model
1. 7.6.1 Model
2. 7.6.2 Estimating Parameters and Properties
3. 7.6.3 Example of an Indscal model via MFA (cards)
4. 7.6.4 Ten Touraine White Wines
7. 7.7 MFA in FactoMineR (groups)
10. Chapter 8 Qualitative and Mixed Data
1. 8.1 Weighted MCA
2. 8.2 MFA of Qualitative Variables
1. 8.2.1 From the Perspective of Factorial Analysis
2. 8.2.2 From the Perspective of Multicanonical Analysis
3. 8.2.3 Representing Partial Individuals
4. 8.2.4 Representing Partial Categories
5. 8.2.5 Analysing in Space of Groups of Variables (ℝI2)
3. 8.3 Mixed Data
1. 8.3.1 Weighting the Variables
2. 8.3.2 Properties
4. 8.4 Application (Biometry2)
1. 8.4.1 Separate Analyses
2. 8.4.2 Inertias in the Overall Analysis
3. 8.4.3 Coordinates of the Factors of the Separate Analyses
4. 8.4.4 First Factor
5. 8.4.5 Second Factor
6. 8.4.6 Third Factor
7. 8.4.7 Representing Groups of Variables
8. 8.4.8 Conclusion
5. 8.5 MFA of Mixed Data in FactoMineR
11. Chapter 9 Multiple Factor Analysis and Procrustes Analysis
1. 9.1 Procrustes Analysis
1. 9.1.1 Data, Notations
2. 9.1.2 Objectives
3. 9.1.3 Methods and Variations
2. 9.2 Comparing MFA and GPA
1. 9.2.1 Representing NjI
2. 9.2.2 Mean Cloud
3. 9.2.3 Objective, Criterion, Algorithm
4. 9.2.4 Properties of the Representations of NjI
5. 9.2.5 A First Appraisal
6. 9.2.6 Harmonising the Inertia of NjI
7. 9.2.7 Relationships Between Homologous Factors
8. 9.2.8 Representing Individuals
9. 9.2.9 Interpretation Aids
10. 9.2.10 Representing the Variables
3. 9.3 Application (Data 23−1)
1. 9.3.1 Data 23−1
2. 9.3.2 Results of the MFA
3. 9.3.3 Results of the GPA
4. 9.4 Application to the Ten Touraine Wines
5. 9.5 Conclusion
6. 9.6 GPA in FactoMineR
12. Chapter 10 Hierarchical Multiple Factor Analysis
1. 10.1 Data, Examples
2. 10.2 Hierarchy and Partitions
3. 10.3 Weighting the Variables
4. 10.4 Representing Partial Individuals
5. 10.5 Canonical Correlation Coefficients
6. 10.6 Representing the Nodes
7. 10.7 Application to Mixed Data: Sorted Napping®
8. 10.8 HMFA in FactoMineR
13. Chapter 11 Matrix Calculus and Euclidean Vector Space
1. 11.1 Matrix Calculus
2. 11.2 Euclidean Vector Space
1. 11.2.1 Vector Space Endowed with the Usual Distance
2. 11.2.2 Euclidean Space Endowed with a Diagonal Metric
3. 11.2.3 Visualising a Cloud in a Space Endowed with a Metric Different from the Identity
14. Bibliography