[下载] Multidimensional Nonlinear Descriptive Analysis

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收藏 2009-03-26

pdf格式，高清文字版，1.4MAuthors: Shizuhiko NishisatoHardcover: 328 pages Publisher: Chapman & Hall/CRC; 1 edition (June 26, 2006) Language: English Product Description: Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for future progress. Covering both the early and later years of MUNDA research in the social sciences, psychology, ecology, biology, and statistics, this book provides a framework for potential developments in even more areas of study. Contents: I Background 1 1 Motivation 5 1.1 Why Multidimensional Analysis? 6 1.1.1 Traditional Unidimensional Analysis 6 1.1.2 Multidimensional Analysis 11 1.2 Why Nonlinear Analysis? 14 1.2.1 Traditional Linear Analysis 16 1.2.2 Nonlinear Analysis 19 1.3 Why Descriptive Analysis? 22 2 Quantification with Different Perspectives 25 2.1 Is Likert-Type Scoring Appropriate? 25 2.2 Method of Reciprocal Averages (MRA) 29 2.3 One-Way Analysis of Variance Approach 33 2.4 Bivariate Correlation Approach 39 2.5 Geometric Approach 41 2.6 Other Approaches 44 2.6.1 The Least-Squares Approach 45 2.6.2 Approach by Cram′er’s and Tchuproff’s Coefficients46 2.7 Multidimensional Decomposition 47 3 Historical Overview 51 3.1 Mathematical Foundations in Early Days 52 3.2 Pioneers of MUNDA in the 20th Century 53 3.3 Rediscovery and Further Developments 55 3.3.1 Distinct Groups 56 3.3.2 Books and Papers 60 3.3.3 A Plethora of Aliases 63 3.3.4 Notes on Dual Scaling 66 ix x CONTENTS 3.4 Additional Notes 67 3.4.1 Dedications 67 4 Conceptual Preliminaries 69 4.1 Stevens’ Four Levels of Measurement 69 4.2 Classification of Categorical Data 71 4.2.1 Incidence Data 71 4.2.2 Dominance Data 74 4.3 Euclidean Space 77 4.3.1 Pythagorean Theorem 77 4.3.2 The Cosine Law 77 4.3.3 Young-Householder Theorem 78 4.3.4 Chi-Square Distance 79 4.4 Multidimensional Space 81 4.4.1 Pierce’s Concept 81 4.4.2 Distance in Reduced Space 81 4.4.3 Correlation in Reduced Space 82 5 Technical Preliminaries 85 5.1 Linear Combination and Principal Space 85 5.2 Eigenvalue and Singular Value Decompositions 89 5.3 Finding the Largest Eigenvalue 92 5.3.1 Some Basics 92 5.3.2 MRA Revisited 93 5.4 Dual Relations and Rectangular Coordinates 94 5.5 Discrepancy Between Row Space and Column Space 95 5.5.1 Geometrically Correct Joint Plots (Traditional) 96 5.5.2 Symmetric Scaling 97 5.5.3 CGS Scaling 97 5.5.4 Geometrically Correct Joint Plots (New) 98 5.6 Information of Different Data Types 99 II Analysis of Incidence Data 101 6 Contingency Tables 105 6.1 Example 105 6.2 Early Work 106 6.3 Some Basics 108 6.3.1 Number of Components 108 6.3.2 Total Information 108 6.3.3 Information Accounted For By One Component 109 CONTENTS xi 6.4 Is My Pet a Flagrant Biter? 110 6.5 Supplementary Notes 116 7 Multiple-Choice Data 119 7.1 Example 119 7.2 Early Work 120 7.3 Some Basics 121 7.4 Future Use of English by Students in Hong Kong 127 7.5 Blood Pressures, Migraines and Age Revisited 136 7.6 Further Discussion 141 7.6.1 Evaluation of alpha 141 7.6.2 Standardized Quantification 142 8 Sorting Data 145 8.1 Example 145 8.2 Early Work 145 8.3 Sorting Familiar Animals into Clusters 146 8.4 Some Notes 152 9 Forced Classification of Incidence Data 155 9.1 Early Work 155 9.2 Some Basics 156 9.2.1 Principles PEP and PIC 156 9.2.2 Conditional Analysis 159 9.2.3 Alternative Formulations 161 9.2.4 Adjusted Correlation Ratio 162 9.2.5 Value of Forcing Agent 163 9.3 Age Effects on Blood Pressures and Migraines 164 9.4 Ideal Sorter of Animals 169 9.5 Generalized Forced Classification 173 III Analysis of Dominance Data 177 10 Paired Comparison Data 181 10.1 Example 181 10.2 Early Work 182 10.2.1 Guttman’s Formulation 182 10.2.2 Nishisato’s Formulation 183 10.3 Some Basics 184 10.4 Travel Destinations 187 10.5 Criminal Acts 193 xii CONTENTS 11 Rank-Order Data 199 11.1 Example 199 11.2 Early Work 200 11.3 Some Basics 202 11.3.1 Slater’s Formulation 204 11.3.2 Tucker-Carroll’s Formulation 204 11.4 Total Information and Number of Components 205 11.5 Distribution of Information 205 11.5.1 The Case of One Judge 206 11.5.2 One-Dimensional Rank Order Data 206 11.5.3 Coomb’s Unfolding and MUNDA 206 11.5.4 Goodness of Fit 208 11.6 Sales Points of Hot Springs 209 12 Successive Categories Data 217 12.1 Example 217 12.2 Some Basics 217 12.3 Seriousness of Criminal Acts 219 12.4 Multidimensionality 222 12.4.1 Multidimensional Decomposition 222 12.4.2 Rank Conversion without Category Boundaries 224 12.4.3 Successive Categories Data as Multiple-Choice Data 225 IV Beyond the Basics 229 13 Further Topics of Interest 233 13.1 Forced Classification of Dominance Data 233 13.1.1 Forced Classification of Paired Comparisons: Travel Destinations 233 13.1.2 Forced Classification of Rank-Order Data: Hot Springs 235 13.2 Order Constraints on Ordered Categories 236 13.3 Stability, Robustness and Missing Responses 239 13.4 Multiway Data 240 13.5 Contingency Tables and Multiple-Choice Data 241 13.5.1 General Case of Two Variables 243 13.5.2 Statistic δ 244 13.5.3 Extensions from Two to Many Variables 245 13.6 Permutations of Categories and Scaling 246 CONTENTS xiii 14 Further Perspectives 247 14.1 Geometry of Multiple-Choice Items 247 14.2 A Concept of Correlation 248 14.3 A Statistic Related to Singular Values 250 14.4 Correlation for Categorical Variables 254 14.4.1 A New Measure ν 254 14.4.2 Cram′er’s Coefficient V 258 14.4.3 Tchuproff’s Coefficient T 259 14.5 Properties of Squared Item-Total Correlation 260 14.6 Decomposition of Nonlinear Correlation 261 14.7 Interpreting Data in Reduced Dimension 266 14.8 Towards an Absolute Measure of Information 269 14.8.1 Why an Absolute Measure? 269 14.8.2 Union of Sets, Joint Entropy and Covariation 270 14.9 FinalWord 273 References 277 Author index 303 Subject index 309