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.
Author(s): Shizuhiko Nishisato
Edition: 1
Publisher: Chapman & Hall/CRC
Year: 2007
Language: English
Pages: 301
City: Boca Raton, FL
Tags: Информатика и вычислительная техника;Искусственный интеллект;Интеллектуальный анализ данных;
MULTIDIMENSIONAL NONLINEAR DESCRIPTIVE ANALYSIS......Page 1
Preface......Page 5
Contents......Page 9
PART I: Background......Page 14
CHAPTER 1: Motivation......Page 16
1.1.1 Traditional Unidimensional Analysis......Page 17
1.1.2 Multidimensional Analysis......Page 22
1.2 Why Nonlinear Analysis?......Page 25
1.2.1 Traditional Linear Analysis......Page 27
1.2.2 Nonlinear Analysis......Page 30
1.3 Why Descriptive Analysis?......Page 33
References......Page 276
2.1 Is Likert-Type Scoring Appropriate?......Page 36
2.2 Method of Reciprocal Averages (MRA)......Page 40
2.3 One-Way Analysis of Variance Approach......Page 44
2.4 Bivariate Correlation Approach......Page 50
2.5 Geometric Approach......Page 52
2.6 Other Approaches......Page 55
2.6.1 The Least-Squares Approach......Page 56
2.6.2 Approach by Cramer’s and Tchuproff ’s Coefficients......Page 57
2.7 Multidimensional Decomposition......Page 58
CHAPTER 3: Historical Overview......Page 61
3.1 Mathematical Foundations in Early Days......Page 62
3.2 Pioneers of MUNDA in the 20th Century......Page 63
3.3 Rediscovery and Further Developments......Page 65
3.3.1 Distinct Groups......Page 66
3.3.2 Books and Papers......Page 70
3.3.3 A Plethora of Aliases......Page 73
3.3.4 Notes on Dual Scaling......Page 76
3.4.1 Dedications......Page 77
4.1 Stevens’ Four Levels of Measurement......Page 79
4.2.1 Incidence Data......Page 81
4.2.2 Dominance Data......Page 84
4.3.2 The Cosine Law......Page 87
4.3.3 Young-Householder Theorem......Page 88
4.3.4 Chi-Square Distance......Page 89
4.4.2 Distance in Reduced Space......Page 91
4.4.3 Correlation in Reduced Space......Page 92
5.1 Linear Combination and Principal Space......Page 94
5.2 Eigenvalue and Singular Value Decompositions......Page 98
5.3.1 Some Basics......Page 101
5.3.2 MRA Revisited......Page 102
5.4 Dual Relations and Rectangular Coordinates......Page 103
5.5 Discrepancy Between Row Space and Column Space......Page 104
5.5.1 Geometrically Correct Joint Plots (Traditional)......Page 105
5.5.3 CGS Scaling......Page 106
5.5.4 Geometrically Correct Joint Plots (New)......Page 107
5.6 Information of Different Data Types......Page 108
PART II: Analysis of Incidence Data......Page 110
6.1 Example......Page 112
6.2 Early Work......Page 113
6.3.2 Total Information......Page 115
6.3.3 Information Accounted For By One Component......Page 116
6.4 Is My Pet a Flagrant Biter?......Page 117
6.5 Supplementary Notes......Page 123
7.1 Example......Page 125
7.2 Early Work......Page 126
7.3 Some Basics......Page 127
7.4 Future Use of English by Students in Hong Kong......Page 133
7.5 Blood Pressures, Migraines and Age Revisited......Page 142
7.6.1 Evaluation of alpha......Page 147
7.6.2 Standardized Quantification......Page 148
8.2 Early Work......Page 151
8.3 Sorting Familiar Animals into Clusters......Page 152
8.4 Some Notes......Page 158
9.1 Early Work......Page 161
9.2.1 Principles PEP and PIC......Page 162
9.2.2 Conditional Analysis......Page 165
9.2.3 Alternative Formulations......Page 167
9.2.4 Adjusted Correlation Ratio......Page 168
9.2.5 Value of Forcing Agent......Page 169
9.3 Age Effects on Blood Pressures and Migraines......Page 170
9.4 Ideal Sorter of Animals......Page 175
9.5 Generalized Forced Classification......Page 179
PART III: Analysis of Dominance Data......Page 182
10.1 Example......Page 184
10.2.1 Guttman’s Formulation......Page 185
10.2.2 Nishisato’s Formulation......Page 186
10.3 Some Basics......Page 187
10.4 Travel Destinations......Page 190
10.5 Criminal Acts......Page 196
11.1 Example......Page 202
11.2 Early Work......Page 203
11.3 Some Basics......Page 205
11.3.2 Tucker-Carroll’s Formulation......Page 207
11.5 Distribution of Information......Page 208
11.5.3 Coomb’s Unfolding and MUNDA......Page 209
11.5.4 Goodness of Fit......Page 211
11.6 Sales Points of Hot Springs......Page 212
12.2 Some Basics......Page 219
12.3 Seriousness of Criminal Acts......Page 221
12.4.1 Multidimensional Decomposition......Page 224
12.4.2 Rank Conversion without Category Boundaries......Page 226
12.4.3 Successive Categories Data as Multiple-Choice Data......Page 227
PART IV: Beyond the Basics......Page 230
13.1.1 Forced Classification of Paired Comparisons: Travel Destinations......Page 232
13.1.2 Forced Classification of Rank-Order Data: Hot Springs......Page 234
13.2 Order Constraints on Ordered Categories......Page 235
13.3 Stability, Robustness and Missing Responses......Page 238
13.4 Multiway Data......Page 239
13.5 Contingency Tables and Multiple-Choice Data......Page 240
13.5.1 General Case of Two Variables......Page 242
13.5.2 Statistic…......Page 243
13.5.3 Extensions from Two to Many Variables......Page 244
13.6 Permutations of Categories and Scaling......Page 245
14.1 Geometry of Multiple-Choice Items......Page 246
14.2 A Concept of Correlation......Page 247
14.3 A Statistic Related to Singular Values......Page 249
14.4.1 A New Measure ν......Page 253
14.4.2 Cramer’s Coefficient V......Page 257
14.4.3 Tchuproff ’s Coefficient T......Page 258
14.5 Properties of Squared Item-Total Correlation......Page 259
14.6 Decomposition of Nonlinear Correlation......Page 260
14.7 Interpreting Data in Reduced Dimension......Page 265
14.8.1 Why an Absolute Measure?......Page 268
14.8.2 Union of Sets, Joint Entropy and Covariation......Page 269
14.9 Final Word......Page 272
