Factor Analysis

by Gorsuch; Richard L.

• ISBN13: 9780898592023
• ISBN10: 089859202X
• Edition: 2nd
• Format: Hardcover
• Copyright: 1983-11-01
• Publisher: Psychology Pres

Summary

Comprehensive and comprehensible, this classic covers the basic and advanced topics essential for using factor analysis as a scientific tool in psychology, education, sociology, and related areas. Emphasizing the usefulness of the techniques, it presents sufficient mathematical background for understanding and sufficient discussion of applications for effective use. This includes not only theory but also the empirical evaluations of the importance of mathematical distinctions for applied scientific analysis.

Table of Contents

Preface	xiii
Preface to the First Edition	xv
Introduction	1	(13)
Science and Factor Analysis	1	(4)
Elementary Procedures for Factoring	5	(4)
Examples	9	(5)
Basic Factor Models	14	(23)
Multivariate Linear Models and Factor Analysis	14	(6)
The Full Component Model	20	(6)
The Common Factor Model	26	(7)
Correlated and Uncorrelated Factor Models	33	(1)
Which Factor-Analytic Model?	34	(3)
Matrix Algebra and Factor Analysis	37	(20)
Matrix Definitions and Notation	37	(4)
Matrix Operations	41	(7)
Definitional Equations in Matrix Algebra Form	48	(3)
The Full Component Model Expressed in Matrix Algebra	51	(2)
The Common Factor Model in Matrix Algebra	53	(2)
Uncorrelated Factor Models and Matrix Algebra	55	(2)
Geometric Representation of Factor Models	57	(16)
Representing Variables and Factors Geometrically	58	(9)
The Uncorrelated (Orthogonal) Component Model	67	(2)
The Correlated (Oblique) Component Model	69	(3)
Common Factor Models	72	(1)
Diagonal and Multiple-Group Analysis	73	(21)
Diagonal Analysis	74	(6)
Multiple-Group Factor Analysis	80	(8)
Applications of Diagonal and Multiple-Group Factor Analysis	88	(6)
Principal Factor Solutions	94	(33)
Characteristics of Principal Factor Methods	95	(4)
Principal Components	99	(3)
Communality Estimation and Principal Axes	102	(10)
Image Analysis	112	(3)
Other Related Procedures	115	(3)
Nonlinear and Nonmetric Factor Analysis	118	(2)
Applications for Principal Factors	120	(1)
A Comparison of Factor Extraction Procedures	121	(6)
Confirmatory Maximum Likelihood Solutions	127	(15)
The Maximum Likelihood Concept	127	(2)
Confirmatory Maximum Likelihood Factor Analysis	129	(4)
Applications	133	(7)
Hypothesis Testing by Maximum Likelihood and Multiple-Group Procedures	140	(2)
Determining the Number of Factors	142	(33)
Adequacy of the Fit of the Model to the Data	143	(5)
Statistical Approaches to the Number of Factors	148	(8)
Mathematical Approaches to the Number of Factors	156	(8)
Extracting the Nontrivial Factors	164	(7)
The Search for the Proper Number of Factors	171	(4)
Rotation and Interpretation of Factors	175	(38)
Principles For Guiding the Rotation of Factors	176	(6)
Orthogonal Rotation for Simple Structure	182	(6)
Oblique Analytic Rotation for Simple Structure	188	(9)
Comparing Alternative Solutions	197	(9)
Interpreting Factors	206	(7)
Rotation	213	(26)
Algebraic Principles of Rotation	213	(5)
Rotating Visually	218	(9)
Orthoblique Solutions	227	(4)
Nonsimple Structure Rotation	231	(5)
Extension Analysis	236	(3)
Higher-Order Factors	239	(18)
Interpretation of Higher-Order Factors	240	(2)
Extracting Higher-Order Factors	242	(3)
Relationship of Variables to Higher-Order Factors	245	(9)
Usefulness of Higher-Order Factors	254	(3)
Factor Scores	257	(20)
Procedures For Computing Factor Scores	258	(8)
Approximation Procedures For Factor Scores	266	(4)
Cluster Analysis of Individuals: Typological Scoring	270	(2)
Evaluating the Factor Scores	272	(3)
Selecting Among Procedures	275	(2)
Relating Factors Across Studies	277	(14)
Information Useful in Relating Factors	278	(2)
Same Individuals and Variables but Different Procedures	280	(1)
Same Individuals but Different Variables	281	(1)
Same Variables but Different Individuals (Rvv, Svf, and Wvf Available)	282	(2)
Same Variables But Different Individuals (Rvv, Svf, and Wvf Unavailable)	284	(5)
Different Variables and Different Individuals	289	(1)
Matching Factors	289	(2)
Data Transformations and Indices of Association	291	(19)
Noncontinuous Data	291	(6)
Effects of Transformations	297	(6)
Indices of Association	303	(7)
Two- and Three-Mode Factor Analysis	310	(18)
Two-Mode Factor Analysis	311	(8)
Three-Mode Factor Analysis	319	(9)
The Replication and Invariance of Factors	328	(22)
The Replication of Factors Across Random Samples of Individuals	328	(6)
The Invariance of Factors	334	(16)
Factor Analysis as a Research Technique	350	(19)
Operationalization of Constructs	350	(9)
Factor Analysis of Independent and Dependent Variables	359	(6)
Using Factor Analysis to Suggest New Leads for Future Research	365	(2)
Other Uses of Factor Analysis	367	(1)
Concluding Note	368	(1)
Epilogue	369	(14)
Criticisms of Present Factor-Analytic Practices	369	(3)
Recommended Procedures for Selected Research Designs	372	(7)
The Future of Factor Analysis	379	(4)
Appendix A Data for Examples	383	(4)
Appendix B.1 Computer Programs for Factor Analysis	387	(2)
Appendix B.2 Accuracy of Computer Processing	389	(6)
References	395	(18)
Author Index	413	(6)
Subject Index	419