Geometric data analysis : from correspondence analysis to structured data analysis

Geometric Data Analysis (gda) Is The Name Suggested By P. Suppes (stanford University) To Designate The Approach To Multivariate Statistics Initiated By Benzécri As Correspondence Analysis, An Approach That Has Become More And More Used And Appreciated Over The Years. This Book Presents The Full Formalization Of Gda In Terms Of Linear Algebra - The Most Original And Far-reaching Consequential Feature Of The Approach - And Shows Also How To Integrate The Standard Statistical Tools Such As Analysis Of Variance, Including Bayesian Methods. Chapter 9, Research Case Studies, Is Nearly A Book In Itself; It Presents The Methodology In Action On Three Extensive Applications, One For Medicine, One From Political Science, And One From Education (data Borrowed From The Stanford Computer-based Educational Program For Gifted Youth ). Thus The Readership Of The Book Concerns Both Mathematicians Interested In The Applications Of Mathematics, And Researchers Willing To Master An Exceptionally Powerful Approach Of Statistical Data Analysis. Foreword / Patrick Suppes -- 1. Overview Of Geometric Data Analysis -- 2. Correspondence Analysis (ca) -- 3. Euclidean Cloud -- 4. Principal Component Analysis (pca) -- 5. Multiple Correspondence Analysis (mca) -- 6. Structured Data Analysis -- 7. Stability Of A Euclidean Cloud -- 8. Inductive Data Analysis -- 9. Research Case Studies -- 10. Mathematical Bases. Brigitte Le Roux And Henry Rouanet. Includes Bibliographical References (p. [451]-463) And Indexes. Contents Foreword Preface 1 Overview of Geometric Data Analysis 1.1 CA of a Historical Data Set 1.2 The Three Key Ideas of GDA 1.3 Three Paradigms of GDA 1.4 Historical Sketch 1.5 Methodological Strong Points 1.6 From Descriptive to Inductive Analysis 1.7 Organization of the Book 2 Correspondence Analysis (CA) 2.1 Measure vs Variable Duality 2.2 Measure over a Cartesian Product 2.3 Correspondence Analysis 2.4 Extensions and Concluding Comments Exercises 3 Euclidean Cloud 3.1 Basic Statistics 3.2 Projected Clouds 3.3 Principal Directions 3.4 Principal Hyperellipsoids 3.5 Between and Within Clouds 3.6 Euclidean Classification 3.7 Matrix Formulas 4 Principal Component Analysis (PCA) 4.1 Biweighted PCA 4.2 Simple PCA 4.3 Standard PCA 4.4 General PCA 4.5 PCA of a Table of Measures 4.6 Methodology of PCA 5 Multiple Correspondence Analysis (MCA) 5.1 Standard MCA 5.2 Specific MCA 5.3 Methodology of MCA 5.4 The Culture Example Exercises 6 Structured Data Analysis 6.1 Structuring Factors 6.2 Analysis of Comparisons 6.3 Additive and Interaction Clouds 6.4 Related Topics 7 Stability of a Euclidean Cloud 7.1 Stability and Grouping/Effect of Coding according to a Partition 7.2 Influence of a Group of Points 7.3 Change of Metric 7.4 Influence of a Variable 7.5 Basic Theorems 8 Inductive Data Analysis 8.1 Inference in Multivariate Statistics 8.2 Univariate Effects 8.3 Combinatorial Inference 8.4 Bayesian Data Analysis 8.5 Inductive GDA 8.6 Guidelines for Inductive Analysis 9 Research Case Studies 9.1 Parkinson Study 9.2 French Political Space 9.3 EPGY Study 9.4 About Software 10 Mathematical Bases 10.1 Matrix Operations 10.2 Finite–dimensional Vector Space 10.3 Euclidean Vector Space 10.4 Multidimensional Geometry 10.5 Spectral Theorem Bibliography Index Name Index A B C D E F G H J K L M N P Q R S T V W Y Symbol Index Subject Index A B C D E F G H I K L M N O P Q R S T V W X ""Geometric Data Analysis" (GDA) is the name suggested by P. Suppes (Stanford University) to designate the approach to Multivariate Statistics initiated by Benzecri as Correspondence Analysis, an approach that has become more and more used and appreciated over the years. This book presents the full formalization of GDA in terms of linear algebra - the most original and far-reaching consequential feature of the approach - and shows also how to integrate the standard statistical tools such as Analysis of Variance, including Bayesian methods. The readership of the book concerns both mathematicians interested in the applications of mathematics, and researchers willing to master an exceptionally powerful approach of statistical data analysis."--Jacket Geometric Data Analysis (GDA) is the name suggested by P. Suppes (Stanford University) to designate the approach to Multivariate Statistics initiated by Benz cri as Correspondence Analysis, an approach that has become more and more used and appreciated over the years. This book presents the full formalization of GDA in terms of linear algebra - the most original and far-reaching consequential feature of the approach - and shows also how to integrate the standard statistical tools such as Analysis of Variance, including ..