Modern Factor Analysis
3d edition, revised
508 pages
|
© 1960, 1967, 1976
This thoroughly revised edition of Harry H. Harman's authoritative text incorporates the many new advances made in computer science and technology over the last ten years. The author gives full coverage to both theoretical and applied aspects of factor analysis from its foundations through the most advanced techniques. This highly readable text will be welcomed by researchers and students working in psychology, statistics, economics, and related disciplines.
Contents
Preface to Third Edition
Preface to the First and Second Editions
List of Illustrations
Guide to Notation
Part I - Foundations of Factor Analysis
1. Introduction
1.1. Brief History of Factor Analysis
1.2. Applications of Factor Analysis
1.3. Scientific Explanation and Choice
2. Factor Analysis Model
2.1. Introduction
2.2. Basic Statistics
2.3. Linear Models
2.4. Composition of Variance
2.5. Factor Patterns and Structures
2.6. Underlying Correlations
2.7. Statistical Fit of the Factor Model
2.8. Indeterminacy of Factor Solutions
2.9. Factor Model in Matrix Notation
3. Matrix Concepts Essential to Factor Analysis
3.1. Introduction
3.2. Basic Concepts of Determinants and Matrices
3.3. Solution of Systems of Linear Equations
3.4. Calculation of the Inverse of a Matrix
4. Geometric Concepts Essential to Factor Analysis
4.1. Introduction
4.2. Geometry of N Dimensions
4.3. Cartesian Coordinate System
4.4. Linear Dependence
4.5. Distance Formulas in Rectangular Coordinates
4.6. Orthogonal Transformations
4.7. Angular Separation between Two Lines
4.8. Distance and Angle in General Cartesian Coordinates
4.9. Geometric Interpretation of Correlation
4. 10. Common-Factor Space
5. The Problem of Communality
5.1. Introduction
5.2. Determination of the Common-Factor Space
5.3. Conditions for Reduced Rank of Correlation Matrix
5.4. Determination of Communality from Approximate Rank
5.5. Theoretical Solution for Communality
5.6. Estimation of Communality
5.7. Direct Factor Solution
6. Properties of Different Factor Methods
6.1. Introduction
6.2. Criteria for Choice of Factor Methods
6.3. Methods Requiring Estimates of Communalities
6.4. Methods Requiring Estimate of Number of Common Factors
6.5. Derived Factor Solutions
6.6. Summary of Factor Methods
Part II - Direct Factor Analysis Methods
7. Early Factor Models and Methods
7.1. Introduction
7.2. Two-Factor Method
7.3. The Heywood Case
7.4. Grouping of Variables
7.5. Bi-Factor Method
7.6. Illustrative Example
8. Principal-factor and Related Methods
8.1. Introduction
8.2. Component Analysis
8.3. Principal-Factor Methods
8.4. Additional Theory
8.5. Outline of Computer Program
8.6. Illustrative Examples
8.7. Canonical Form
8.8. Centroid Method
9. Minres Method
9.1. Introduction
9.2. Formulation of the Minres Method
9.3. Minres Procedure
9.4. Additional Theory
9.5. Test of Significance for the Number of Factors
9.6. Computing Procedures
9.7. Illustrative Examples
10. Maximum-likelihood Method
10.1. Introduction
10.2. Statistical Estimation
10.3. Maximum-Likelihood Estimates of Factor Loadings
10.4. Test of Significance for the Number of Factors
10.5. Computing Procedures
10.6. Numerical Illustrations
11. Other Direct Methods
11.1. Introduction
11.2. Canonical Factor Analysis
11.3. Image Factor Analysis
11.4. Alpha Factor Analysis
11.5. Multiple-Group Method
Part III - Derived Factors Solutions
12. Subjective Basis for Multiple-Factor Solutions
12.1. Introduction
12.2. Orthogonal Multiple-Factor Solution
12.3. Geometric Basis for an Oblique Solution
12.4. Oblique Primary-Factor Solution
12.5. Oblique Reference-Axes Solution
12.6. Relationship between Two Types of Oblique Solutions
13. Objective Orthogonal Multiple-Factor Solutions
13.1. Introduction
13.2. Rationale for Analytic Methods
13.3. Quartimax Criterion
13.4. Varimax Criterion
13.5. Orthomax Criteria
14. Objective Oblique Multiple-Factor Solution
14.1. Introduction
14.2. Oblimax Criterion
14.3. Quartimin Criterion
14.4. Oblimin Methods
14.5. Direct Oblimin
14.6. Orthoblique Method
15. Congruent and Prescribed Factor Solutions
15.1. Introduction
15.2. Relationship between Two Known Solutions
15.3. Measuring Factor Congruence
15.4. Matching Factor Solutions
15.5. Fitting a Prescribed Factor Model
Part IV - Factor Measurements
16. Measurement of Factors
16.1. Introduction
16.2. Direct Solution versus Estimation
16.3. Measurement of Principal Components
16.4. Estimation by Regression
16.5. Estimation by Theoretical Model
16.6. Estimation by Minimizing Unique Factors
16.7. Estimation by Ideal Variables
16.8. Comparison of Factor Estimation Methods
Part V - Problems and Exercises
Problems
Answers
Appendix
Statistical Tables
Bibliography
Author Index
Subject Index
Problem Index
Preface to the First and Second Editions
List of Illustrations
Guide to Notation
Part I - Foundations of Factor Analysis
1. Introduction
1.1. Brief History of Factor Analysis
1.2. Applications of Factor Analysis
1.3. Scientific Explanation and Choice
2. Factor Analysis Model
2.1. Introduction
2.2. Basic Statistics
2.3. Linear Models
2.4. Composition of Variance
2.5. Factor Patterns and Structures
2.6. Underlying Correlations
2.7. Statistical Fit of the Factor Model
2.8. Indeterminacy of Factor Solutions
2.9. Factor Model in Matrix Notation
3. Matrix Concepts Essential to Factor Analysis
3.1. Introduction
3.2. Basic Concepts of Determinants and Matrices
3.3. Solution of Systems of Linear Equations
3.4. Calculation of the Inverse of a Matrix
4. Geometric Concepts Essential to Factor Analysis
4.1. Introduction
4.2. Geometry of N Dimensions
4.3. Cartesian Coordinate System
4.4. Linear Dependence
4.5. Distance Formulas in Rectangular Coordinates
4.6. Orthogonal Transformations
4.7. Angular Separation between Two Lines
4.8. Distance and Angle in General Cartesian Coordinates
4.9. Geometric Interpretation of Correlation
4. 10. Common-Factor Space
5. The Problem of Communality
5.1. Introduction
5.2. Determination of the Common-Factor Space
5.3. Conditions for Reduced Rank of Correlation Matrix
5.4. Determination of Communality from Approximate Rank
5.5. Theoretical Solution for Communality
5.6. Estimation of Communality
5.7. Direct Factor Solution
6. Properties of Different Factor Methods
6.1. Introduction
6.2. Criteria for Choice of Factor Methods
6.3. Methods Requiring Estimates of Communalities
6.4. Methods Requiring Estimate of Number of Common Factors
6.5. Derived Factor Solutions
6.6. Summary of Factor Methods
Part II - Direct Factor Analysis Methods
7. Early Factor Models and Methods
7.1. Introduction
7.2. Two-Factor Method
7.3. The Heywood Case
7.4. Grouping of Variables
7.5. Bi-Factor Method
7.6. Illustrative Example
8. Principal-factor and Related Methods
8.1. Introduction
8.2. Component Analysis
8.3. Principal-Factor Methods
8.4. Additional Theory
8.5. Outline of Computer Program
8.6. Illustrative Examples
8.7. Canonical Form
8.8. Centroid Method
9. Minres Method
9.1. Introduction
9.2. Formulation of the Minres Method
9.3. Minres Procedure
9.4. Additional Theory
9.5. Test of Significance for the Number of Factors
9.6. Computing Procedures
9.7. Illustrative Examples
10. Maximum-likelihood Method
10.1. Introduction
10.2. Statistical Estimation
10.3. Maximum-Likelihood Estimates of Factor Loadings
10.4. Test of Significance for the Number of Factors
10.5. Computing Procedures
10.6. Numerical Illustrations
11. Other Direct Methods
11.1. Introduction
11.2. Canonical Factor Analysis
11.3. Image Factor Analysis
11.4. Alpha Factor Analysis
11.5. Multiple-Group Method
Part III - Derived Factors Solutions
12. Subjective Basis for Multiple-Factor Solutions
12.1. Introduction
12.2. Orthogonal Multiple-Factor Solution
12.3. Geometric Basis for an Oblique Solution
12.4. Oblique Primary-Factor Solution
12.5. Oblique Reference-Axes Solution
12.6. Relationship between Two Types of Oblique Solutions
13. Objective Orthogonal Multiple-Factor Solutions
13.1. Introduction
13.2. Rationale for Analytic Methods
13.3. Quartimax Criterion
13.4. Varimax Criterion
13.5. Orthomax Criteria
14. Objective Oblique Multiple-Factor Solution
14.1. Introduction
14.2. Oblimax Criterion
14.3. Quartimin Criterion
14.4. Oblimin Methods
14.5. Direct Oblimin
14.6. Orthoblique Method
15. Congruent and Prescribed Factor Solutions
15.1. Introduction
15.2. Relationship between Two Known Solutions
15.3. Measuring Factor Congruence
15.4. Matching Factor Solutions
15.5. Fitting a Prescribed Factor Model
Part IV - Factor Measurements
16. Measurement of Factors
16.1. Introduction
16.2. Direct Solution versus Estimation
16.3. Measurement of Principal Components
16.4. Estimation by Regression
16.5. Estimation by Theoretical Model
16.6. Estimation by Minimizing Unique Factors
16.7. Estimation by Ideal Variables
16.8. Comparison of Factor Estimation Methods
Part V - Problems and Exercises
Problems
Answers
Appendix
Statistical Tables
Bibliography
Author Index
Subject Index
Problem Index
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