Introduction to Factor Analysis: What it is and How to do it

CONTENTS Editor's Introduction 5 1. Introduction 7 Basic Orientation 7 What Is Factor Analysis? 9 Doing Factor Analysis 10 General Outline of Presentation 11 11. Logical Foundations of Factor Analysis 12 Fundamental Concepts of Factor Analysis 12 Factors and Variables 12 Variance, Covariance, and Correlation 15 Linear Combinations and Derivations of Variance and Covariance 17 Recapitulation: Factor Loadings, Correlations, and Causal Diagrams 21 Correspondence Between Factor Models and Covariance Structures 23 Derivation of Covariance Structure from the Factor Structure 23 1. One-common factor with many variables 23 2. Two-common factors: The orthogonal case 25 3. Two.-common factors: The oblique case 28 Number of Common Factors and the Rank of the Adjusted Correlation Matiix 32 Uncertainties Inherent to Deriving Factors from Covariance Structures 38 1. One covariance structure: Different factor loadings 38 2. One covariance structure: Varying number of Factors 39 3. Competing causal structures 41 Fundamental Postulates of Factor Analysis: Recapitulation 43 111. Obtaining Factor Analysis Solutions 46 Major Steps in Actual Factor Analysis 46 Data Collection and Preparation of the Covariance Matrix 47 Extracting Initial Factors 48 Rotation to a Terminal Solution 49 Construction of Factor Scales and Their Use in Further Analysis 50 Illustration of Actual Analysis, as Applied to Known Error-Free Data 51 Obtaining Basic Factor Analysis Solutions through the Use of Computer Packages 60 Illustration with SPSS 60 Additional Illustrations with SPSS, BMD, OSIRIS, and SAS 62 Complications in Analyzing Real Data 64 Sampling Variability 64 Selection Bias 66 Measurement Errors 69 Minor Factors 70 Note 70 Questions Pertaining to Books, Journals, and Computer Programs 71 References 71 Glossary 75