Computational methods of multivariate analysis in physical geography:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Wiley
1976
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 532 S. graph. Darst. |
| ISBN: | 0471576263 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction.................... I
0.0 Exploratory Data Analysis............. 1
0.1 Structure of this Book............... 3
0.2 Computer Programs................ f
PART ONE ESSENTIALS OF MATRIX ALGEBRA
1 Mathematical Background............... 9
1.0 Introduction.................. 9
1.1 Basic Definitions................. 10
1.2 Further Definitions................ 14
1.3 Vectors.................... 16
1.4 The Inverse Matrix................ 23
1.5 Eigenvalues and Eigenvectors............ 28
1.6 Error in Matrix Computations............ 32
Appendix Summary of Matrix Theory.......... 35
PART TWO ANALYSIS OF DEPENDENCE
2 Regression Analysis: the Linear Model.......... 39
2.0 Introduction.................. 39
2.1 The Linear Regression Model............ 40
2.2 Estimation in the Linear Regression Model....... 45
2.3 Computational Aspects of Multiple Regression..... 52
2.4 Problems in Regression.............. 73
(i) Multicollinearity and Ridge Regression...... 73
(ii) Heteroscedasticity.............. 77
(iii) Autocorrelation.............. 82
X
3 Further Aspects of Least-squares Methods.........94
3.0 Introduction..................94
3.1 Least Squares Curve-fitting.............95
3.1.0 Introduction...............95
3.1.1 Gram-Schmidt Method: Computation.....96
3.1.2 Examples.................101
3.1.3 Confidence Intervals for Least-squares Coefficients . 109
3.2 Trend Surface Analysis..............116
3.2.0 Introduction...............116
3.2.1 Trend Surface Model............117
(A) Specification Phase...........119
(B) Data Point Distributions.........120
(C) Computational Aspects.........130
(D) Inferential Problems..........142
3.2.2 Comparison of Trend Surfaces.........147
3.2.3 Examples.................150
3.3 Selection of Explanatory Variables in Multiple Regression . 172
3.3.0 Introduction...............172
3.3.1 The Selection Approach...........173
3.3.2 The Combinational Approach.........178
3.4 Use of Binary Explanatory Variables.........193
3.4.0 Introduction...............193
3.4.1 Method and Example............194
3.5 Nonlinear Least Squares Methods..........198
3.5.0 Introduction...............198
3.5.1 Methods.................198
3.5.2 Example.................207
PART THREE ANALYSIS OF INTERDEPENDENCE
4 Principal Components Analysis.............215
4.0 Introduction..................215
4.1 Mathematical Foundations.............220
4.2 Computation..................226
4.3 Example....................232
4.4 Conclusions...................239
5 Factor Analysis...................240
5.0 Introduction..................240
5.1 Definitions...................241
5.2 Statistical Model.................243
5.3 Estimation...................245
5.3.0 Nonstatistical Factor Analysis.........247
5.3.1 Statistical Factor Analysis..........261
XI
5.3.2 Image Analysis...............272
5.4 Rotation of Factors................275
5.5 Factor Scores..................294
5.6 Summary....................304
PART FOUR CLASSIFICATION
6 Classification....................309
6.0 Introduction..................309
6.1 Cluster Analysis.................310
6.1.0 Types of Cluster Analysis..........310
6.1.1 Measurement of Similarity..........311
6.1.2 Hierarchical Clustering Methods........316
6.1.3 Display of Hierarchical Relationships......321
6.1.4 Comparison of Hierarchical Clustering Strategies . . 324
6.1.5 Nonhierarchical Clustering Methods......327
6.2 Ordination...................329
6.2.0 Principal Coordinates Analysis.........330
6.2.1 Nonmetric Multidimensional Scaling..... 331
6.2.2 Nonlinear Mapping.............339
6.2.3 Quadratic Loss Functions..........340
6.3 Examples....................341
6.3.0 Hierarchical Clustering............342
6.3.1 Nonhierarchical Cluster Analysis; Nonlinear
Mapping................343
6.3.2 Nonmetric Multidimensional Scaling......351
6.3.3 Principal Coordinates Analysis.........370
6.4 Computer Programs................371
7 Discriminant Analysis.................420
7.0 Introduction..................420
7.1 Two-group Discriminant Analysis ..........420
7.2 Multiple Discriminant Analysis...........432
7.2.0 Multivariate Analysis of Variance (MANOVA) . . 432
7.2.1 Multiple Discriminant Analysis........437
7.3 Discriminant Analysis based on Binary Attributes .... 453
Appendix A Fortran Subroutine Library..........460
Bibliography.....................504
Author Index.....................521
Subject Index.....................527
|
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| callnumber-subject | GB - Physical Geography |
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| discipline | Geographie |
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| id | DE-604.BV003242725 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:56:46Z |
| institution | BVB |
| isbn | 0471576263 |
| language | English |
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| physical | XI, 532 S. graph. Darst. |
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| publisher | Wiley |
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| spelling | Mather, Paul M. 1944-2021 Verfasser (DE-588)1049155378 aut Computational methods of multivariate analysis in physical geography P. M. Mather London [u.a.] Wiley 1976 XI, 532 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Géographie physique analyse donnée inriac analyse plurivalente inriac géographie inriac Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Physische Geografie (DE-588)4174629-6 gnd rswk-swf Physische Geografie (DE-588)4174629-6 s Datenverarbeitung (DE-588)4011152-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002039952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mather, Paul M. 1944-2021 Computational methods of multivariate analysis in physical geography Géographie physique analyse donnée inriac analyse plurivalente inriac géographie inriac Datenverarbeitung (DE-588)4011152-0 gnd Physische Geografie (DE-588)4174629-6 gnd |
| subject_GND | (DE-588)4011152-0 (DE-588)4174629-6 |
| title | Computational methods of multivariate analysis in physical geography |
| title_auth | Computational methods of multivariate analysis in physical geography |
| title_exact_search | Computational methods of multivariate analysis in physical geography |
| title_full | Computational methods of multivariate analysis in physical geography P. M. Mather |
| title_fullStr | Computational methods of multivariate analysis in physical geography P. M. Mather |
| title_full_unstemmed | Computational methods of multivariate analysis in physical geography P. M. Mather |
| title_short | Computational methods of multivariate analysis in physical geography |
| title_sort | computational methods of multivariate analysis in physical geography |
| topic | Géographie physique analyse donnée inriac analyse plurivalente inriac géographie inriac Datenverarbeitung (DE-588)4011152-0 gnd Physische Geografie (DE-588)4174629-6 gnd |
| topic_facet | Géographie physique analyse donnée analyse plurivalente géographie Datenverarbeitung Physische Geografie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002039952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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