Modern factor analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Chicago ; London
Univ. of Chicago Press
1970
|
| Edition: | 2. ed., rev., 3. impr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 439 - 465 |
| Physical Description: | XX, 474 S. graph. Darst. |
| ISBN: | 0226316513 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804123648265551872 |
|---|---|
| adam_text | Contents
List of Illustrations xix
Guide to Notation xx
Part I
Foundations of Factor Analysis
1. Introduction 3
1.1. Brief History of Factor Analysis 3
1.2. Applications of Factor Analysis 6
1.3. Scientific Explanation and Choice 8
2. Factor Analysis Model 11
2.1. Introduction 11
2.2. Basic Statistics 11
2.3. Linear Models 14
2.4. Composition of Variance 16
2.5. Factor Patterns and Structures 19
2.6. Statistical Fit of the Factor Model 21
2.7. Indeterminacy of Factor Solutions 23
2.8. The Factor Model in Matrix Notation 24
3. Matrix Concepts Essential to Factor Analysis 29
3.1. Introduction 29
3.2. Basic Concepts of Determinants and Matrices 30
3.3. Solution of Systems of Linear Equations:
Method of Substitution 37
3.4. Solution of Systems of Linear Equations:
Square Root Method 39
3.5. Calculation of the Inverse of a Matrix 42
xiii
CONTENTS
4. Geometric Concepts Essential to Factor Analysis 45
4.1. Introduction 45
4.2. Geometry of N Dimensions 46
4.3. Cartesian Coordinate System 47
4.4. Linear Dependence 47
4.5. Distance Formulas in Rectangular Coordinates 52
4.6. Orthogonal Transformations 54
4.7. Angular Separation between Two Lines 55
4.8. Distance and Angle in General Cartesian Coordinates 58 ¦
4.9. Geometric Interpretation of Correlation 60
4.10. Subspaces Employed in Factor Analysis 63
5. The Problem of Communality 68
5.1. Introduction 68
5.2. Determination of the Common-Factor Space 69
5.3. Conditions for Reduced Rank of Correlation Matrix 72
5.4. Determination of Communality from Approximate
Rank 77
5.5. Theoretical Solution for Communality 81
5.6. Arbitrary Approximations to Communality 83
5.7. Complete Approximations to Communality 84
5.8. Examples of Approximations to Communality 88
5.9. Direct Factor Solution 90
6. Properties of Different Types of Factor Solutions 93
6.1. Introduction 93
6.2. Criteria for Choice of Factor Solutions 94
6.3. Solutions Requiring Estimates of Communalities 99
6.4. Solutions Requiring Estimates of Number of Common
Factors 103
6.5. Multiple-Factor Solutions 106
6.6. Summary of Factor Solutions 107
Part II
Direct Solutions
7. Simple Factor Models 113
7.1. Introduction 113
7.2. Two-Factor Solution 114
7.3. The Hey wood Case 117
7.4. Grouping of Variables 118
7.5. Bi-Factor Solution 121
7.6. Illustrative Example 124
xiv
CONTENTS
8. Principal-Factor and Related Solutions 135
8.1. Introduction 135
8.2. Component Analysis 136
8.3. Principal-Factor Method 137
8.4. Additional Theory 143
8.5. Computing Procedures With Desk Calculator 146
8.6. Outline of Electronic Computer Program 155
8.7. Illustrative Examples 161
8.8. Canonical Form 169
8.9. Centroid Method 171
9. Minres Solution 187
9.1. Introduction 187
9.2. Formulation of the Minres Solution 188
9.3. Minres Method 190
9.4. Additional Theory 192
9.5. Test of Significance for the Number of Factors 196
9.6. Computing Procedures 199
9.7. Illustrative Examples 202
10. Maximum-Likelihood Solution 211
10.1. Introduction 211
10.2. Statistical Estimation 211
10.3. Maximum-Likelihood Estimates of Factor Loadings 214
10.4. Test of Significance for the Number of Factors 219
10.5. Computing Procedures 221
10.6. Numerical Illustrations 226
11. Multiple-Group Solution 233
11.1. Introduction 233
11.2. Concepts and Notation 233
11.3. The Oblique Solution 236
11.4. The Orthogonal Solution 239
11.5. Multiple-Group Factor Algorithm 241
11.6. Numerical Illustration 243
Part III
Derived Solutions
12. Different Solutions in Common-factor Space 249
12.1. Introduction 249
12.2. Relationship between Two Known Solutions 250
12.3. Graphical Procedures for Orthogonal Multiple-Factor
Solution 254
xv
CONTENTS
12.4. Numerical Illustrations of Orthogonal Multiple-Factor
Solutions 261
12.5. Other Problems of Relationships between Factor
Solutions 268
13. Oblique Multiple-factor Solutions 273
13.1. Introduction 273
13.2. Geometric Basis for an Oblique Solution 274
13.3. Computing Procedures for Oblique Primary-Factor
Solution 276
13.4. Oblique Reference Solution 285
13.5. Relationship between Two Types of Oblique Solutions 289
14. Analytical Methods for the Multiple-factor Solution: Orthogonal
Case 293
14.1. Introduction 293
14.2. Rationale for Analytical Methods 294
14.3. Quartimax Method 298
14.4. Varimax Method 304
15. Analytical Methods for the Multiple-factor Solution: Oblique
Case 314
15.1. Introduction 314
15.2. Oblimax Method 315
15.3. Quartimin Method 318
15.4. Oblimin Method 324
15.5. Direct Oblimin 334
Part IV
Factor Measurements
16. Measurement of Factors 345
16.1. Introduction 345
16.2. Direct Solution versus Estimation 346
16.3. Measurement of Principal Components 348
16.4. Complete Estimation Method 350
16.5. Numerical Illustrations of Complete Estimation
Method 354
16.6. Approximation Method 360
16.7. Short Method 362
16.8. Estimation by Minimizing Unique Factors 369
16.9. Factor Measurements by Ideal Variables 373
xvi
CONTENTS
Part V
Problems and Exercises
Problems 377
Answers 401
Appendix
Statistical Tables 433
Bibliography 439
Index to Illustrative Examples 466
General Index 467
xvii
|
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| isbn | 0226316513 |
| language | German |
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| spelling | Harman, Harry H. 1913- Verfasser (DE-588)172151643 aut Modern factor analysis Harry H. Harman 2. ed., rev., 3. impr. Chicago ; London Univ. of Chicago Press 1970 XX, 474 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 439 - 465 Faktorenanalyse (DE-588)4016338-6 gnd rswk-swf Psychologie (DE-588)4047704-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Faktorenanalyse (DE-588)4016338-6 s Psychologie (DE-588)4047704-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006119725&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
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| title | Modern factor analysis |
| title_auth | Modern factor analysis |
| title_exact_search | Modern factor analysis |
| title_full | Modern factor analysis Harry H. Harman |
| title_fullStr | Modern factor analysis Harry H. Harman |
| title_full_unstemmed | Modern factor analysis Harry H. Harman |
| title_short | Modern factor analysis |
| title_sort | modern factor analysis |
| topic | Faktorenanalyse (DE-588)4016338-6 gnd Psychologie (DE-588)4047704-6 gnd |
| topic_facet | Faktorenanalyse Psychologie Einführung |
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