Geological factor analysis:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier
1976
|
| Series: | Methods in geomathematics
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 178 S. zahlr. graph. Darst. |
| ISBN: | 0444413677 |
Staff View
MARC
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| 245 | 1 | 0 | |a Geological factor analysis |c K. G. Jöreskog ; J. E. Klovan ; R. A. Reyment |
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 1976 | |
| 300 | |a XI, 178 S. |b zahlr. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Methods in geomathematics |v 1 | |
| 650 | 7 | |a Analise Multivariada |2 larpcal | |
| 650 | 4 | |a Analyse factorielle | |
| 650 | 7 | |a Geologia Geral |2 larpcal | |
| 650 | 4 | |a Géologie - Mathématiques | |
| 650 | 4 | |a Géologie - Méthodes statistiques | |
| 650 | 4 | |a Geologie | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Factor analysis | |
| 650 | 4 | |a Geology |x Mathematics | |
| 650 | 4 | |a Geology |x Statistical methods | |
| 650 | 4 | |a Multivariate analysis | |
| 700 | 1 | |a Klovan, John E. |e Verfasser |4 aut | |
| 700 | 1 | |a Reyment, Richard A. |d 1926-2016 |e Verfasser |0 (DE-588)116458348 |4 aut | |
| 830 | 0 | |a Methods in geomathematics |v 1 |w (DE-604)BV001892262 |9 1 | |
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Record in the Search Index
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|---|---|
| adam_text |
CONTENTS
Preface . V
Glowury of the moil commonly used symbols. XII
C'hapU-r 1 Introduction . 1
11 Structure in multivariate data. ]
1 2 An example of factor analysis. 2
Chapter 2 Basic mathematical and statistical concepts. 8
2.1 Some definitions . 8
Data matrix. 8
Matrix . 8
Transpose matrix . 9
Vector. 10
Scalar. 10
Objects. 10
Variables. 10
2.2 Geometrical interpretation of data matrices. 11
Variables and objects as vectors. 11
Variable space . 11
Object space . 12
2 3 Elementary vector operations. 13
Equality of vectors. 13
Addition of vectors. 13
Subtraction of vectors. 13
Multiplication of vectors . 13
Minor product of vectors. 13
Major product of vectors. 14
Minor and major product moments. 14
Unit vector and null vector. 15
2 4 The geometry of vectors . 15
Resultant vector. 15
Difference vector. 15
Scalar multiples of vectors. 15
Vector length. 16
The angle between two vectors. 16
Distance. 17
2 r Types of matrices. 17
Rectangular matrices. 17
Square matrices. 17
Symmetrical matrices . 18
Diagonal matrices. 18
Null matrix. 18
2.6 Elementary matrix arithmetic. 18
Equality of matrice*. 18
Addition and subtraction of matrices. 18
Multiplication of matrice» . 19
Major and minor product moment«. 21
Products of matrice« »nd vector». 22
Determinant . 23
VIII
Minor. 23
Matrix inversion. 23
2.7 Normal and orthonormal vectors and matrices. 24
Normalized vectors. 24
Orthogonal vectors. 25
Orthogonal matrices. 25
2.8 Descriptive statistics in matrix notation . 26
The mean. 26
Deviate scores. 26
Variance. 26
Covariance . 27
Standard deviation. 27
Standardized scores. 27
Correlation. 28
Regression, multiple and partial correlation. 31
2.9 Rotation of coordinate systems. 32
Algebra of rotation. 33
Interpretation of rotation. 35
2.10 The structure of a matrix. 35
Matrices as products. 35
Rank of a matrix . 36
Linear independence and rank. 37
Geometry of linearly dependent and independent vectors. 38
The infinity of basis vectors. 39
The rank of product moment matrices. 40
2.11 Eigenvalues and eigenvectors. 41
Algebraic review. 42
Geometrical interpretation of eigenvalues and eigenvectors. 45
2.12 Basic structure of a matrix and the Eckart-Young theorem. 47
2.13 Least-squares properties of eigenvalues and eigenvectors. 50
Chapter 3 Aims, ideas and models of factor analysis. 53
3.1 Introduction. 53
3.2 Fixed and random cases. 54
Fixed case. 54
Random case. 54
3.3 Discussion of models. 54
Model for the observed variables. 54
3.4 Mode] for the variances and covariances . 57
3.5 Components versus true factor analysis. 59
3.6 Transformational indeterminancy of factors . 60
3.7 Factor pattern and factor structure . 61
3.8 Example. 61
True factor analysis. 62
3.9 Representation of results. 65
3.10 Summary . 66
Chapter 4 i?-mode methods. 68
4.1 Introduction. 68
4.2 Component analysis. 68
Fixed case. 68
Random case. 74
How many components?. 75
Scores for principal components. 76
Scale dependence. 76
Confidence intervals for eigenvalues of the covariance matrix. 77
Equality of eigenvalues of a covariance matrix. 77
Test that an eigenvector equals a specified vector. 77
IX
4.3 True factor analysis. 78
Scale-free estimation of A and ^. 79
More efficient methods of estimation. 82
Assessing the fit of the model. 82
Chapter 5 Q-mode methods . 86
5.1 Introduction. 86
5.2 Imbrie Q-mode method. 86
Geological interpretation. 87
Similarity coefficient. 88
Mathematical derivation. 90
Factor scores. 91
Number of end-members. 92
Geometrical representation. 92
Rotation of Q-mode factor axes . 97
Interpretation . 98
Oblique projection. 98
5.3 Principal coordinates. 100
Description of the method. 101
Distances between objects. 101
Q-mode development . 102
Principal coordinates versus Q-mode factor analysis. 105
Example. 105
5.4 Correspondence analysis . 107
Scaling procedure. 108
The similarity measure. 108
Derivation of factor-loadings matrices. 110
Example. Ill
5.5 Comparison of the three methods. 113
The biplot method. 115
Horseshoe plots. 115
Chapter 6 Steps in the analysis. 116
6.1 Introduction. 116
6.2 Specification of objectives. 116
6.3 Categories of data. 117
6.4 The data matrix. 118
Choice of variables. 119
Mixed populations. 119
Dimensions of the data cube. 120
Data collection. 120
Transformations of data. 121
The choice of transformation. 122
Normalization. 122
Range restriction. 122
Centring. 123
Standardizing. 123
Multivariate normality. 123
6.5 Selection of the measure of association. 123
Ä-mode coefficients . 124
Q-mode coefficients. 124
Major product moment. 124
The cosine association measure. 124
Euclidean distance measures. 124
6.6 Choice of the factor method. 125
6.7 Selection of the number of factors. 125
6.8 Rotation of factor axes. 127
X
Simple structure. 129
Analytical rotation. 130
The varimax procedure . 130
Example of varimax rotation . 132
Oblique rotation. 133
Geometrical considerations of oblique rotation . 134
The promax method. 137
Example of the promax method . 138
Oblique-projection method. 139
Mathematical derivation. 139
6.9 Factor scores. 142
Direct factor scores. 142
Regression estimation. 143
Interpretation of factor scores. 144
Chapter 7 Examples. 147
7.1 Introduction. 147
7.2 Ä-mode principal components in mineral chemistry. 147
Statement of the problem. 147
Material. 147
Methods. 147
Results. 148
7.3 Ä-mode factor analysis in sedimentology. 150
Statement of the problem . 150
Materials. 150
Methods. 150
Results. 151
7.4 R- and Q-mode analyses in subsurface brine geochemistry . 154
Statement of the problem . 154
Materials. 154
Methods. 154
Results. 155
Imbrie Q-mode analysis. 155
fi-mode principal components analysis. 156
7.5 Imbrie Q-mode factor analysis in sedimentology. 157
Statement of the problem . 157
Method. 159
Results. 159
Analysis of results. 159
7.6 Imbrie Q-mode factor analysis in foraminiferal palaeoecology. 160
Statement of the problem . 160
Materials. 161
Method. 161
Results. 163
7.7 Principal coordinates analysis of soils. 165
Statement of the problem . 165
Materials. 166
Method. 166
Results. 167
7.8 Correspondence analysis of metamorphic rocks. 167
Statement of the problem . 167
Materials. 167
Method. 168
Results. 168
7.9 True factor analysis in actuo-palaeoecology. 169
Statement of the problem . 169
Materials. 169
Method. 170
Results. 170
XI
7.10 Overview of types of geological problems amenable to treatment by factor
analysis. 171
Relationships between organisms and sedimentary facies. 171
Petrology . 171
Sedimentary petrology . 172
Mineralogy. 172
Stratigraphy . 172
Biofacies relationships. 172
Intertidal environment. 172
Heavy minerals. 172
Vertebrate palaeontology. 173
Geochemistry of magmas. 173
Palynology . 173
Geochemistry of Cambrian alum shale. 173
Palaeoecology . 174
References . 175 |
| any_adam_object | 1 |
| author | Jöreskog, Karl G. 1935- Klovan, John E. Reyment, Richard A. 1926-2016 |
| author_GND | (DE-588)170170578 (DE-588)116458348 |
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| ctrlnum | (OCoLC)832450423 (DE-599)BVBBV001982797 |
| dewey-full | 551.028 519.5/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 551 - Geology, hydrology, meteorology 519 - Probabilities and applied mathematics |
| dewey-raw | 551.028 519.5/3 |
| dewey-search | 551.028 519.5/3 |
| dewey-sort | 3551.028 |
| dewey-tens | 550 - Earth sciences 510 - Mathematics |
| discipline | Geologie / Paläontologie Mathematik Geographie |
| format | Book |
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| id | DE-604.BV001982797 |
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| indexdate | 2024-07-20T07:50:15Z |
| institution | BVB |
| isbn | 0444413677 |
| language | English |
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| spelling | Jöreskog, Karl G. 1935- Verfasser (DE-588)170170578 aut Geological factor analysis K. G. Jöreskog ; J. E. Klovan ; R. A. Reyment Amsterdam [u.a.] Elsevier 1976 XI, 178 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Methods in geomathematics 1 Analise Multivariada larpcal Analyse factorielle Geologia Geral larpcal Géologie - Mathématiques Géologie - Méthodes statistiques Geologie Mathematik Factor analysis Geology Mathematics Geology Statistical methods Multivariate analysis Klovan, John E. Verfasser aut Reyment, Richard A. 1926-2016 Verfasser (DE-588)116458348 aut Methods in geomathematics 1 (DE-604)BV001892262 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001293280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jöreskog, Karl G. 1935- Klovan, John E. Reyment, Richard A. 1926-2016 Geological factor analysis Methods in geomathematics Analise Multivariada larpcal Analyse factorielle Geologia Geral larpcal Géologie - Mathématiques Géologie - Méthodes statistiques Geologie Mathematik Factor analysis Geology Mathematics Geology Statistical methods Multivariate analysis |
| title | Geological factor analysis |
| title_auth | Geological factor analysis |
| title_exact_search | Geological factor analysis |
| title_full | Geological factor analysis K. G. Jöreskog ; J. E. Klovan ; R. A. Reyment |
| title_fullStr | Geological factor analysis K. G. Jöreskog ; J. E. Klovan ; R. A. Reyment |
| title_full_unstemmed | Geological factor analysis K. G. Jöreskog ; J. E. Klovan ; R. A. Reyment |
| title_short | Geological factor analysis |
| title_sort | geological factor analysis |
| topic | Analise Multivariada larpcal Analyse factorielle Geologia Geral larpcal Géologie - Mathématiques Géologie - Méthodes statistiques Geologie Mathematik Factor analysis Geology Mathematics Geology Statistical methods Multivariate analysis |
| topic_facet | Analise Multivariada Analyse factorielle Geologia Geral Géologie - Mathématiques Géologie - Méthodes statistiques Geologie Mathematik Factor analysis Geology Mathematics Geology Statistical methods Multivariate analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001293280&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001892262 |
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