MULTIDIMENSIONAL NONLINEAR DESCRIPTIVE ANALYSIS
CONTENTS I BACKGROUND MOTIVATION WHY MULTIDIMENSIONAL ANALYSIS? TRADITIONAL UNIDIMENSIONAL ANALYSIS MULTIDIMENSIONAL ANALYSIS WHY NONLINEAR ANALYSIS? TRADITIONAL LINEAR ANALYSIS NONLINEAR ANALYSIS WHY DESCRIPTIVE ANALYSIS? QUANTI?CATION WITH DIFFERENT PERSPECTIVES IS LIKERT-TYPE SCORING APPROPRIATE? METHOD OF RECIPROCAL AVERAGES (MRA) ONE-WAY ANALYSIS OF VARIANCE APPROACH BIVARIATE CORRELATION APPROACH GEOMETRIC APPROACH OTHER APPROACHES THE LEAST-SQUARES APPROACH APPROACH BY CRAM´ER’S AND TCHUPROFF’S COEF?- CIENTS MULTIDIMENSIONAL DECOMPOSITION HISTORICAL OVERVIEW MATHEMATICAL FOUNDATIONS IN EARLY DAYS PIONEERS OF MUNDA IN THE 20TH CENTURY REDISCOVERY AND FURTHER DEVELOPMENTS DISTINCT GROUPS BOOKS AND PAPERS A PLETHORA OF ALIASES NOTES ON DUAL SCALING ADDITIONAL NOTES DEDICATIONS CONCEPTUAL PRELIMINARIES STEVENS’ FOUR LEVELS OF MEASUREMENT CLASSI?CATION OF CATEGORICAL DATA INCIDENCE DATA DOMINANCE DATA EUCLIDEAN SPACE PYTHAGOREAN THEOREM THE COSINE LAW YOUNG-HOUSEHOLDER THEOREM CHI-SQUARE DISTANCE MULTIDIMENSIONAL SPACE PIERCE’S CONCEPT DISTANCE IN REDUCED SPACE CORRELATION IN REDUCED SPACE TECHNICAL PRELIMINARIES LINEAR COMBINATION AND PRINCIPAL SPACE EIGENVALUE AND SINGULAR VALUE DECOMPOSITIONS FINDING THE LARGEST EIGENVALUE SOME BASICS MRA REVISITED DUAL RELATIONS AND RECTANGULAR COORDINATES DISCREPANCY BETWEEN ROW SPACE AND COLUMN SPACE GEOMETRICALLY CORRECT JOINT PLOTS (TRADITIONAL) SYMMETRIC SCALING CGS SCALING GEOMETRICALLY CORRECT JOINT PLOTS (NEW) INFORMATION OF DIFFERENT DATA TYPES II ANALYSIS OF INCIDENCE DATA CONTINGENCY TABLES EXAMPLE EARLY WORK NUMBER OF COMPONENTS TOTAL INFORMATION INFORMATION ACCOUNTED FOR BY ONE COMPONENT IS MY PET A FLAGRANT BITER? SUPPLEMENTARY NOTES MULTIPLE-CHOICE DATA FUTURE USE OF ENGLISH BY STUDENTS IN HONG KONG BLOOD PRESSURES, MIGRAINES AND AGE REVISITED FURTHER DISCUSSION EVALUATION OF ALPHA STANDARDIZED QUANTI?CATION SORTING DATA SORTING FAMILIAR ANIMALS INTO CLUSTERS SOME NOTES FORCED CLASSI?CATION OF INCIDENCE DATA PRINCIPLES PEP AND PIC CONDITIONAL ANALYSIS ALTERNATIVE FORMULATIONS ADJUSTED CORRELATION RATIO VALUE OF FORCING AGENT AGE EFFECTS ON BLOOD PRESSURES AND MIGRAINES IDEAL SORTER OF ANIMALS GENERALIZED FORCED CLASSI?CATION III ANALYSIS OF DOMINANCE DATA 10 PAIRED COMPARISON DATA 10 1 EXAMPLE 10 2 EARLY WORK 10 2 1 GUTTMAN’S FORMULATION 10 2 2 NISHISATO’S FORMULATION 10 3 SOME BASICS 10 4 TRAVEL DESTINATIONS 10 5 CRIMINAL ACTS 11 RANK-ORDER DATA 11 1 EXAMPLE 11 2 EARLY WORK 11 3 SOME BASICS 11 3 1 SLATER’S FORMULATION 11 3 2 TUCKER-CARROLL’S FORMULATION 11 4 TOTAL INFORMATION AND NUMBER OF COMPONENTS 11 5 DISTRIBUTION OF INFORMATION 11 5 1 THE CASE OF ONE JUDGE 11 5 2 ONE-DIMENSIONAL RANK ORDER DATA 11 5 3 COOMB’S UNFOLDING AND MUNDA 11 5 4 GOODNESS OF FIT 11 6 SALES POINTS OF HOT SPRINGS 12 SUCCESSIVE CATEGORIES DATA 12 1 EXAMPLE 12 2 SOME BASICS 12 3 SERIOUSNESS OF CRIMINAL ACTS 12 4 MULTIDIMENSIONALITY 12 4 1 MULTIDIMENSIONAL DECOMPOSITION 12 4 2 RANK CONVERSION WITHOUT CATEGORY BOUNDARIES 12 4 3 SUCCESSIVE CATEGORIES DATA AS MULTIPLE-CHOICE DATA IV BEYOND THE BASICS 13 FURTHER TOPICS OF INTEREST 13 1 FORCED CLASSI?CATION OF DOMINANCE DATA 13 1 1 FORCED CLASSI?CATION OF PAIRED COMPARISONS: TRAVEL DESTINATIONS 13 1 2 FORCED CLASSI?CATION OF RANK-ORDER DATA: HOT SPRINGS 13 2 ORDER CONSTRAINTS ON ORDERED CATEGORIES 13 3 STABILITY, ROBUSTNESS AND MISSING RESPONSES 13 4 MULTIWAY DATA 13 5 CONTINGENCY TABLES AND MULTIPLE-CHOICE DATA 13 5 1 GENERAL CASE OF TWO VARIABLES 13 5 2 STATISTIC ? 13 5 3 EXTENSIONS FROM TWO TO MANY VARIABLES 13 6 PERMUTATIONS OF CATEGORIES AND SCALING 14 FURTHER PERSPECTIVES 14 1 GEOMETRY OF MULTIPLE-CHOICE ITEMS 14 2 A CONCEPT OF CORRELATION 14 3 A STATISTIC RELATED TO SINGULAR VALUES 14 4 CORRELATION FOR CATEGORICAL VARIABLES 14 4 1 A NEW MEASURE ? 14 4 2 CRAM´ER’S COEF?CIENT V 14 4 3 TCHUPROFF’S COEF?CIENT T 14 5 PROPERTIES OF SQUARED ITEM-TOTAL CORRELATION 14 6 DECOMPOSITION OF NONLINEAR CORRELATION 14 7 INTERPRETING DATA IN REDUCED DIMENSION 14 8 TOWARDS AN ABSOLUTE MEASURE OF INFORMATION 14 8 1 WHY AN ABSOLUTE MEASURE? 14 8 2 UNION OF SETS, JOINT ENTROPY AND COVARIATION 14 9 FINAL WORD REFERENCES