Multivariate statistical analysis for geographers:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Upper Saddle River, NJ
Prentice Hall
1997
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 345 S. graph. Darst., Kt. |
| ISBN: | 013605692X |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE xiii
Acknowledgments xv
References xv
About the authors xvii
LIST OF ABBREVIATIONS xix
FART I: INTRODUCTION AND REVIE
CHAPTER 1. ELEMENTARY STATISTICS BACKGROUND 2
Data preview 2
1.0. Introduction 4
1.1. A review of the basics 5
1.2. Statistical inference versus statistical description 10
1.2.1. The concept of estimation: points and intervals 13
1.2.2. The meaning of a confidence region 14
1.2.3. The role of the sampling distribution in statistical estimation 15
1.2.4. Large-versus small-sample theory 16
1.2.5. Hypotheses and hypothesis testing 16
1.2.6. Errors in hypothesis testing 17
1.2.7. Critical values and test statistics 18
1.3. Variable transformations 19
1.3.1. The Shapiro-Wilk statistic and symmetry 21
1.3.2. Bivariate linearity 23
1.3.3. Constant variance 26
1.3.4. Implications 32
1.4. One more viewpoint: special normality and constant variance assessments in
preparation for multivariate analyses 34
1.5. A brief excursion into nonparametric statistics 35
1.6. References 39
CHAPTER 2. INFORMATION CONTENT IN GEO-REFERENCED DATA 42
2.0. Introduction 42
2.1. Elementary and spatial statistics 43
2.2. Redundant attribute and locational information 46
2.3. Exploring residuals in spatial analysis 51
2.4. References 53
vn
Contents
CHAPTER 3. INTRODUCTION TO MATRIX ALGEBRA 55
3.0. Elementary concepts of matrices 55
3.0.1. Matrix operations 56
3.1. Eigenfunctions and their meanings 5 8
3.2. Illustrative eigenfunction uses in multivariate analysis 62
3.3. Illustrative eigenfunction uses in spatial statistical analysis 66
3.4. References 74
CHAPTER 4. MULTIPLE LINEAR REGRESSION AND CORRELATION
ANALYSIS (P 3) 79
Chapter preview 79
4.0. Introduction 79
4.1. Background 80
4.2. Variable selection and conventional diagnostics 85
4.2.1. Statistical distribution properties of b 87
4.2.2. Selection criteria for the matrix of predictor variables X 89
4.2.3. Calculation error diagnostics 97
4.2.4. Other useful diagnostics 101
4.3. Exploring nonlinearities: trend surface models and polynomial regression 108
4.4. Analysis of variance (ANOVA) as a regression problem 111
4.4.1. Basic experimental design 112
4.4.2. N-way balanced designs 118
4.5. Analysis of covariance (P 2 2, K 3) 126
4.6. Effects of spatial autocorrelation 128
4.7. Problems 130
4.8. References 130
FART II: INSTANCES OF THE GENERAL LINEAR MODEL
CHAPTER 5. MULTIVARIATE ANALYSIS OF VARIANCE 133
Chapter preview 133
5.0. Introduction 133
5.1. N-way unbalanced designs 136
5.1.1. A two-way unbalanced design: the fixed effects model 137
5.1.2. A two-way unbalanced design: the mixed effects model 141
5.1.3. Two-way ANOVA interpretation when interaction is significant 144
vin
Contents
5.2. Multicollinearity and simultaneous testing: Multivariate Analysis of Variance
(MANOVA) 145
5.2.1. The MANOVA format 147
5.2.2. Selected diagnostics for MANOVA 151
5.3. Two-way MANOVA 152
5.3.1. Fixed effects MANOVA 152
5.3.2. Mixed effects MANOVA 154
5.4. Problems 156
5.5. References 157
CHAPTER 6. PRINCIPAL COMPONENTS AND FACTOR ANALYSIS 158
Chapter preview 158
6.0. Introduction 158
6.1. Selected mathematical features of PCA 160
6.2. Multicollinearity 162
6.3. Moving from PCA to factor analysis: seeking parsimony 166
6.4. PCA/FA and hypothesis testing 167
6.5. PCA/FA and spatial autocorrelation 171
6.6. PCA and dimensional hypothesis testing 176
6.7. Artificial orthogonality: principal components regression 178
6.8. A multivariate normality diagnostic 180
6.9. Problems 183
6.10. References 184
CHAPTER 7. DISCRIMINANT FUNCTION ANALYSIS 185
Chapter preview 185
7.0. Introduction 185
7.1. Properties of the linear DF A model 187
7.1.1. Notable assumptions for the linear DFA model 187
7.1.2. The DFA eigenfunction problem 188
7.1.3. Significance testing in DFA 194
7.2. Interpretation of the dimensions of regional differences 196
7.3. Probabilities for regional membership classifications 200
7.4. DFA as a regression problem: Two-regions DFA 202
7.5. Problems 205
7.6. References 205
IX
Contents
CHAPTER 8. CLUSTER ANALYSIS 207
Chapter preview 207
8.0. Introduction 207
8.1. Principles of cluster analysis 208
8.2. A comparison of clustering algorithm solutions 213
8.3. Location-allocation (L-A) and cluster analysis 220
8.4. Natural groups of coterminous areal units 226
8.5. Using DFA to improve CA solutions 228
8.6. Aggregation effects 229
8.7. Problems 232
8.8. References 232
CHAPTER 9. CANONICAL CORRELATION ANALYSIS 234
Chapter preview 234
9.0. Introduction 235
9.1. Properties of the linear CCA model 237
9.1.1. The CCA eigenfunction problem 237
9.1.2. Mathematical features of canonical dimensions 239
9.1.3. Significance testing in CCA 245
9.2. Interpretation of the canonical dimensions spanning
geo-referenced data sets 246
9.2.1. Dimensions spanning geo-referenced coordinates and
areal unit attributes 250
9.2.2. Dimensions spanning geo-referenced coordinates and eigenvectors of the
connectivity matrix C 251
9.3. DFA as a CCA problem: multiple-regions DFA 254
9.4. The GLM and CCA 255
9.5. Problems 258
9.6. References 259
PART III: NONLINEAR AND CATEGORICAL DATA MODELING
CHAPTER 10. NONLINEAR REGRESSION ANALYSIS 261
Chapter preview 261
10.0. Introduction 261
10.1. Error structure options 262
10.2. Principles of nonlinear least squares 263
Contents
10.2.1. Methods for defining A (advanced material) 265
10.3. Some statistical theory for NLS estimation (advanced material) 267
10.4. A comparison of various models for estimating empirical probabilities 267
10.5. Problems 273
10.6. References 274
CHAPTER 11. SPATIAL AUTOREGRESSIVE ANALYSIS 275
Chapter preview 275
11.0. Introduction 275
11.1. Specifying the n-by-n matrix Lj(p) 276
11.2. Computing the normalizing constant 277
11.3. Estimating the parameters of an SAR model 285
11.4. Estimating the parameters of an AR model 289
11.5. A repeated regressions interpretation of the spatial statistical analysis 294
11.6. Problems 298
11.7. References 299
CHAPTER 12. SPECIAL NONLINEAR REGRESSION APPLICATIONS IN SPATIAL
ANALYSIS 301
Chapter preview 301
12.0. Introduction 301
12.1. The binomial distribution and logistic regression 302
12.2. The binomial distribution and measurement error 306
12.3. The multinomial distribution and polychotomous logistic regression 309
12.4. A case study of children s elevated blood lead levels in
Syracuse, New York 312
12.5. Poisson regression 315
12.6. Problems 320
12.7. References 320
EPILOGUE 322
APPENDICES 325
A: Puerto Rico (PR) agricultural data set 326
B: Puerto Rico connectivity matrix, C, data set 329
C: Samples drawn for use in examples PR-4.10 and PR-4.11 331
D: Supplemental PR milk production data set 332
xi
Contents
E: Puerto Rico urban population components data set 335
F: Syracuse pediatric blood lead levels data set 337
G: Metropolitan Toronto origin-destination data set 339
INDEX 340
xn
|
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| language | English |
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| physical | XIX, 345 S. graph. Darst., Kt. |
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| spelling | Griffith, Daniel A. 1948- Verfasser (DE-588)124843697 aut Multivariate statistical analysis for geographers Daniel A. Griffith ; Carl G. Amrhein Upper Saddle River, NJ Prentice Hall 1997 XIX, 345 S. graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Analyse multivariée Geografie gtt Géographie - Méthodes statistiques Multivariate analyse gtt Statistische methoden gtt Geografie Geography Statistical methods Multivariate analysis Geografie (DE-588)4020216-1 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Geografie (DE-588)4020216-1 s Multivariate Analyse (DE-588)4040708-1 s DE-604 Amrhein, Carl G. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007801696&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Griffith, Daniel A. 1948- Amrhein, Carl G. Multivariate statistical analysis for geographers Analyse multivariée Geografie gtt Géographie - Méthodes statistiques Multivariate analyse gtt Statistische methoden gtt Geografie Geography Statistical methods Multivariate analysis Geografie (DE-588)4020216-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| subject_GND | (DE-588)4020216-1 (DE-588)4040708-1 |
| title | Multivariate statistical analysis for geographers |
| title_auth | Multivariate statistical analysis for geographers |
| title_exact_search | Multivariate statistical analysis for geographers |
| title_full | Multivariate statistical analysis for geographers Daniel A. Griffith ; Carl G. Amrhein |
| title_fullStr | Multivariate statistical analysis for geographers Daniel A. Griffith ; Carl G. Amrhein |
| title_full_unstemmed | Multivariate statistical analysis for geographers Daniel A. Griffith ; Carl G. Amrhein |
| title_short | Multivariate statistical analysis for geographers |
| title_sort | multivariate statistical analysis for geographers |
| topic | Analyse multivariée Geografie gtt Géographie - Méthodes statistiques Multivariate analyse gtt Statistische methoden gtt Geografie Geography Statistical methods Multivariate analysis Geografie (DE-588)4020216-1 gnd Multivariate Analyse (DE-588)4040708-1 gnd |
| topic_facet | Analyse multivariée Geografie Géographie - Méthodes statistiques Multivariate analyse Statistische methoden Geography Statistical methods Multivariate analysis Multivariate Analyse |
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