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Modern Factor Analysis

by Harry Horace Harman

  • ISBN: 9780226316529
  • ISBN10: 0226316521

Modern Factor Analysis

by Harry Horace Harman

  • List Price: $70.00
  • Binding: Hardcover
  • Edition: 3
  • Publisher: Univ of Chicago Pr
  • Publish date: 08/01/1976
  • ISBN: 9780226316529
  • ISBN10: 0226316521
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Description: 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 Solutio
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