Atnaujinkite slapukų nuostatas

Multiple Factor Analysis by Example Using R [Kietas viršelis]

(Agrocampus-Ouest, Rennes, France)
  • Formatas: Hardback, 272 pages, aukštis x plotis: 234x156 mm, weight: 514 g, 50 Tables, black and white; 94 Illustrations, black and white
  • Serija: Chapman & Hall/CRC The R Series
  • Išleidimo metai: 20-Nov-2014
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1482205475
  • ISBN-13: 9781482205473
Kitos knygos pagal šią temą:
Multiple Factor Analysis by Example Using RDidesnis paveikslėlis
  • Formatas: Hardback, 272 pages, aukštis x plotis: 234x156 mm, weight: 514 g, 50 Tables, black and white; 94 Illustrations, black and white
  • Serija: Chapman & Hall/CRC The R Series
  • Išleidimo metai: 20-Nov-2014
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1482205475
  • ISBN-13: 9781482205473
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781482205473.html
Raktažodžiai:

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.

Preface xi
1 Principal Component Analysis
1(38)
1.1 Data, Notations
1(1)
1.2 Why Analyse a Table with PCA?
2(1)
1.3 Clouds of individuals and Variables
3(4)
1.4 Centring and Reducing
7(1)
1.5 Fitting Clouds Ni and NK
7(9)
1.5.1 General Principles and Formalising Criteria
8(1)
1.5.2 Interpreting Criteria
9(1)
1.5.3 Solution
10(2)
1.5.4 Relationships Between the Analyses of the Two Clouds
12(2)
1.5.5 Representing the Variables
14(1)
1.5.6 Number of Axes
15(1)
1.5.7 Vocabulary: Axes and Factors
15(1)
1.6 interpretation Aids
16(2)
1.6.1 Percentage of Inertia Associated with an Axis
16(1)
1.6.2 Contribution of One Point to the Inertia of an Axis
17(1)
1.6.3 Quality of Representation of a Point by an Axis
17(1)
1.7 First Example: 909 Baccalaureate Candidates
18(5)
1.7.1 Projected Inertia (Eigenvalues)
18(1)
1.7.2 Interpreting the Axes
19(3)
1.7.3 Methodological Remarks
22(1)
1.8 Supplementary Elements
23(3)
1.9 Qualitative Variables in PCA
26(3)
1.10 Second Example: Six Orange Juices
29(2)
1.11 PCA in FactoMineR
31(8)
2 Multiple Correspondence Analysis
39(28)
2.1 Data
39(1)
2.2 Complete Disjunctive Table
40(1)
2.3 Questioning
41(1)
2.4 Clouds of Individuals and Variables
42(6)
2.4.1 Cloud of Individuals
43(2)
2.4.2 Cloud of Categories
45(1)
2.4.3 Qualitative Variables
46(2)
2.5 Fitting Clouds N, and NK
48(5)
2.5.1 Cloud of Individuals
48(2)
2.5.2 Cloud of Categories
50(1)
2.5.3 Relationships Between the Two Analyses
51(2)
2.6 Representing Individuals, Categories and Variables
53(1)
2.7 Interpretation Aids
54(1)
2.8 Example: Five Educational Tools Evaluated by 25 Students
55(6)
2.8.1 Data
55(2)
2.8.2 Analyses and Representations
57(2)
2.8.3 MCA/PCA Comparison for Ordinal Variables
59(2)
2.9 MCA in FactoMineR
61(6)
3 Factorial Analysis of Mixed Data
67(12)
3.1 Data, Notations
67(1)
3.2 Representing Variables
68(1)
3.3 Representing Individuals
69(1)
3.4 Transition Relations
70(2)
3.5 Implementation
72(1)
3.6 Example: Biometry of Six Individuals
72(2)
3.7 FAMD in FactoMineR
74(5)
4 Weighting Groups of Variables
79(22)
4.1 Objectives
79(2)
4.2 introductory Numerical Example
81(1)
4.3 Weighting Variables in MFA
82(4)
4.4 Application to the Six Orange Juices
86(2)
4.5 Relationships with Separate Analyses
88(3)
4.6 Conclusion
91(1)
4.7 MFA in FactoMineR (First Results)
92(9)
5 Comparing Clouds of Partial Individuals
101(20)
5.1 Objectives
101(2)
5.2 Method
103(3)
5.3 Application to the Six Orange Juices
106(1)
5.4 Interpretation Aids
107(3)
5.5 Distortions in Superimposed Representations
110(6)
5.5.1 Example (Trapeziums Data)
110(2)
5.5.2 Geometric Interpretation
112(2)
5.5.3 Algebra Approach
114(2)
5.6 Superimposed Representation: Conclusion
116(1)
5.7 MFA Partial Clouds in FactoMineR
116(5)
6 Factors Common to Different Groups of Variables
121(12)
6.1 Objectives
121(5)
6.1.1 Measuring the Relationship between a Variable and a Group
122(1)
6.1.2 Factors Common to Several Groups of Variables
123(1)
6.1.3 Back to the Six Orange Juices
123(2)
6.1.4 Canonical Analysis
125(1)
6.2 Relationship Between a Variable and Groups of Variables
126(1)
6.3 Searching for Common Factors
127(1)
6.4 Searching for Canonical Variables
128(1)
6.5 Interpretation Aids
129(4)
6.5.1 Lg Relationship Measurement
129(1)
6.5.2 Canonical Correlation Coefficients
130(3)
7 Comparing Groups of Variables and Indscal Model
133(26)
7.1 Cloud NJ of Groups of Variables
133(2)
7.2 Scalar Product and Relationship Between Groups of Variables
135(4)
7.3 Norm in the Groups' Space
139(1)
7.4 Representation of Cloud N;
139(3)
7.4.1 Principle
139(3)
7.4.2 Criterion
142(1)
7.5 Interpretation Aids
142(2)
7.6 The Indscal Model
144(12)
7.6.1 Model
144(2)
7.6.2 Estimating Parameters and Properties
146(2)
7.6.3 Example of an Indscal model via MFA (cards)
148(3)
7.6.4 Ten Touraine White Wines
151(5)
7.7 MFA in FactoMineR (groups)
156(3)
8 Qualitative and Mixed Data
159(30)
8.1 Weighted MCA
159(3)
8.1.1 Cloud of Categories in Weighted MCA
160(1)
8.1.2 Transition Relations in Weighted MCA
160(2)
8.2 MFA of Qualitative Variables
162(6)
8.2.1 From the Perspective of Factorial Analysis
162(1)
8.2.2 From the Perspective of Multicanonical Analysis
163(2)
8.2.3 Representing Partial Individuals
165(1)
8.2.4 Representing Partial Categories
166(1)
8.2.5 Analysing in Space of Groups of Variables (R12)
166(2)
8.3 Mixed Data
168(4)
8.3.1 Weighting the Variables
168(1)
8.3.2 Properties
169(3)
8.4 Application (Biometry2)
172(11)
8.4.1 Separate Analyses
172(2)
8.4.2 Inertias in the Overall Analysis
174(1)
8.4.3 Coordinates of the Factors of the Separate Analyses
175(1)
8.4.4 First Factor
176(4)
8.4.5 Second Factor
180(1)
8.4.6 Third Factor
180(1)
8.4.7 Representing Groups of Variables
181(2)
8.4.8 Conclusion
183(1)
8.5 MFA of Mixed Data in FactoMineR
183(6)
9 Multiple Factor Analysis and Procrustes Analysis
189(22)
9.1 Procrustes Analysis
189(3)
9.1.1 Data, Notations
189(1)
9.1.2 Objectives
190(1)
9.1.3 Methods and Variations
190(2)
9.2 Comparing MFA and GPA
192(7)
9.2.1 Representing NjI
192(1)
9.2.2 Mean Cloud
193(1)
9.2.3 Objective, Criterion, Algorithm
193(2)
9.2.4 Properties of the Representations of NjI
195(1)
9.2.5 A First Appraisal
195(1)
9.2.6 Harmonising the Inertia of NjI
196(1)
9.2.7 Relationships Between Homologous Factors
196(1)
9.2.8 Representing Individuals
197(1)
9.2.9 Interpretation Aids
198(1)
9.2.10 Representing the Variables
199(1)
9.3 Application (Data 23--1)
199(7)
9.3.1 Data 23--1
199(2)
9.3.2 Results of the MFA
201(2)
9.3.3 Results of the GPA
203(3)
9.4 Application to the Ten Touraine Wines
206(1)
9.5 Conclusion
207(1)
9.6 GPA in FactoMineR
208(3)
10 Hierarchical Multiple Factor Analysis
211(28)
10.1 Data, Examples
211(1)
10.2 Hierarchy and Partitions
212(2)
10.3 Weighting the Variables
214(1)
10.4 Representing Partial Individuals
215(4)
10.4.1 Method
215(2)
10.4.2 Application to the Six Orange Juices
217(2)
10.5 Canonical Correlation Coefficients
219(1)
10.6 Representing the Nodes
220(1)
10.7 Application to Mixed Data: Sorted Napping®
221(10)
10.7.1 Data and Methodology
221(2)
10.7.2 Intermediary Analysis: MFA on a Sorted Nappe
223(2)
10.7.3 Decompositions of Inertia
225(1)
10.7.4 Representing Partial and Mean Individuals
226(5)
10.8 HMFA in FactoMineR
231(8)
11 Matrix Calculus and Euclidean Vector Space
239(10)
11.1 Matrix Calculus
239(4)
11.2 Euclidean Vector Space
243(6)
11.2.1 Vector Space Endowed with the Usual Distance
243(2)
11.2.2 Euclidean Space Endowed with a Diagonal Metric
245(1)
11.2.3 Visualising a Cloud in a Space Endowed with a Metric Different from the Identity
246(3)
Bibliography 249(4)
Index 253
Jérōme Pagčs is a professor of statistics at Agrocampus (Rennes, France), where he heads the Laboratory of Applied Mathematics (LMA²).