Modern factor analysis:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Chicago ; London
Univ. of Chicago Press
1976
|
| Ausgabe: | 3. ed., rev. |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004830940&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XX, 487 S. graph. Darst. |
| ISBN: | 0226316521 |
Internformat
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| 264 | 1 | |a Chicago ; London |b Univ. of Chicago Press |c 1976 | |
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| 650 | 4 | |a Factor analysis | |
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Datensatz im Suchindex
| _version_ | 1819374192205758464 |
|---|---|
| adam_text | Contents
Preface to Third Edition xi
Preface to the First and Second Editions xv
List of Illustrations xix
Guide to Notation xx
Parti
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 18
2.5. Factor Patterns and Structures 20
2.6. Underlying Correlations 24
2.7. Statistical Fit of the Factor Model 25
2.8. Indeterminacy of Factor Solutions 27
2.9. Factor Model in Matrix Notation 28
3. Matrix Concepts Essential to Factor Analysis 33
3.1. Introduction 33
3.2. Basic Concepts of Determinants and Matrices 34
3.3. Solution of Systems of Linear Equations 41
3.4. Calculation of the Inverse of a Matrix 44
vii
Contents
4. Geometric Concepts Essential to Factor Analysis 47
4.1. Introduction 47
4.2. Geometry o/N Dimensions 47
4.3. Cartesian Coordinate System 48
4.4. Linear Dependence 49
4.5. Distance Formulas in Rectangular Coordinates 54
4.6. Orthogonal Transformations 55
4.7. Angular Separation between Two Lines 57
4.8. Distance and Angle in General Cartesian Coordinates 60
4.9. Geometric Interpretation of Correlation 62
4.10. Common Factor Space 64
5. The Problem of Communality 70
5.1. Introduction 70
5.2. Determination of the Common Factor Space 71
5.3. Conditions for Reduced Rank of Correlation Matrix 75
5.4. Determination of Communality from Approximate
Rank 79
5.5. Theoretical Solution for Communality 83
5.6. Estimation of Communality 84
5.7. Direct Factor Solution 90
6. Properties of Different Factor Methods 93
6.1. Introduction 93
6.2. Criteria for Choice of Factor Methods 94
6.3. Methods Requiring Estimates of Communalities 99
6.4. Methods Requiring Estimate of Number of Common
Factors 102
6.5. Derived Factor Solutions 105
6.6. Summary of Factor Methods 107
Part II
Direct Factor Analysis Methods
7. Early Factor Models and Methods 113
7.1. Introduction 113
7.2. Two Factor Method 114
7.3. The Heywood Case 116
7.4. Grouping of Variables 117
7.5. Bi Factor Method 120
7.6. Illustrative Example 123
8. Principal factor and Related Methods 133
8.1. Introduction 133
8.2. Component Analysis 134
8.3. Principal Factor Method 135
viii
Contents
8.4. Additional Theory 141
8.5. Outline of Computer Program 144
8.6. Illustrative Examples 148
8.7. Canonical Form 164
8.8. Centroid Method 166
9. Minres Method 174
9.1. Introduction 174
9.2. Formulation of the Minres Method 175
9.3. Minres Procedure 177
9.4. Additional Theory 179
9.5. 7e,stf of Significance for the Number of Factors 183
9.6. Computing Procedures 186
9.7. Illustrative Examples 189
10. Maximum likelihood Method 197
10.1. Introduction 197
10.2. Statistical Estimation 197
10.3. Maximum Likelihood Estimates of Factor Loadings 200
10.4. 7es/ of Significance for the Number of Factors 205
10.5. Computing Procedures 207
10.6. Numerical Illustrations 211
11. Other Direct Methods 217
11.1. Introduction 217
11.2. Canonical Factor Analysis 218
11.3. Image Factor Analysis 221
11.4. Alpha Factor Analysis 228
11.5. Multiple Group Method 234
Part HI
Derived Factor Solutions
12. Subjective Basis for Multiple Factor Solutions 247
12.1. Introduction 247
12.2. Orthogonal Multiple Factor Solution 248
12.3. Geometric Basis for an Oblique Solution 259
12.4. Oblique Primary Factor Solution 262
12.5. Oblique Reference Axes Solution 270
12.6. Relationship between Two Types of Oblique Solutions 21A
13. Objective Orthogonal Multiple Factor Solutions 278
13.1. Introduction 278
13.2. Rationale for Analytic Methods 219
13.3. Quartimax Criterion 283
13.4. Varimax Criterion 290
13.5. Orthomax Criteria 299
ix
Contents
14. Objective Oblique Multiple Factor Solution 300
14.1. Introduction 300
14.2. Oblimax Criterion 301
14.3. Quartimin Criterion 304
14.4. Oblimin Methods 310
14.5. Direct Oblimin 320
14.6. Orthoblique Method 327
15. Congruent and Prescribed Factor Solutions 336
15.1. Introduction 336
15.2. Relationship between Two Known Solutions 338
15.3. Measuring Factor Congruence 341
15.4. Matching Factor Solutions 347
15.5. Fitting a Prescribed Factor Model 353
Part IV
Factor Measurements
16. Measurement of Factors 363
16.1. Introduction 363
16.2. Direct Solution versus Estimation 365
16.3. Measurement of Principal Components 366
16.4. Estimation by Regression 368
16.5. Estimation by Theoretical Model 376
16.6. Estimation by Minimizing Unique Factors 379
16.7. Estimation by Ideal Variables 382
16.8. Comparison of Factor Estimation Methods 384
Part V
Problems and Exercises
Problems 391
Answers 413
Appendix
Statistical Tables 441
Bibliography 447
Author Index 475
Subject Index 478
Problem Index 486
x
|
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| discipline | Psychologie Mathematik |
| edition | 3. ed., rev. |
| format | Book |
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| id | DE-604.BV007447924 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T09:04:47Z |
| institution | BVB |
| isbn | 0226316521 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004830940 |
| oclc_num | 2352855 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XX, 487 S. graph. Darst. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Univ. of Chicago Press |
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| spellingShingle | Harman, Harry H. 1913- Modern factor analysis Analyse factorielle Factoranalyse gtt Factor Analysis, Statistical Factor analysis Faktorenanalyse (DE-588)4016338-6 gnd Psychologie (DE-588)4047704-6 gnd |
| subject_GND | (DE-588)4016338-6 (DE-588)4047704-6 (DE-588)4151278-9 |
| 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 | Analyse factorielle Factoranalyse gtt Factor Analysis, Statistical Factor analysis Faktorenanalyse (DE-588)4016338-6 gnd Psychologie (DE-588)4047704-6 gnd |
| topic_facet | Analyse factorielle Factoranalyse Factor Analysis, Statistical Factor analysis Faktorenanalyse Psychologie Einführung |
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