"Comprehensive and comprehensible, this classic text 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 applying its use. This includes the theory as well as the empirical evaluations. The overall goal is to show readers how to use factor analysis in their substantive research by highlighting when the differences in mathematical procedures have a major impact on the substantive conclusions, when the differences are not relevant, and when factor analysis might not be the best procedure to use.
Although the original version was written years ago, the book maintains its relevance today by providing readers with a thorough understanding of the basic mathematical models so they can easily apply these models to their own research. Readers are presented with a very complete picture of the "inner workings" of these methods. The new Introduction highlights the remarkably few changes that the author would make if he were writing the book today.
An ideal text for courses on factor analysis or as a supplement for multivariate analysis, structural equation modeling, or advanced quantitative techniques taught in psychology, education, and other social and behavioral sciences, researchers who use these techniques also appreciate this book’s thorough review of the basic models. Prerequisites include a graduate level course on statistics and a basic understanding of algebra. Sections with an asterisk can be skipped entirely if preferred."
Author(s): Richard L. Gorsuch
Publisher: Taylor & Francis
Year: 2015
Language: English
Pages: 465
Tags: statistics, factor analysis, principal components analysis, maximum likelihood, matrix algebra, psychology, psychometrics, latent variables
Cover......Page 1
Title Page......Page 6
Copyright Page......Page 7
Dedication......Page 8
Table of Contents......Page 10
Preface......Page 14
Preface to the First Edition......Page 16
Introduction to the Classic Edition......Page 19
1.1 Science and factor analysis......Page 22
1.2 Elementary procedures for factoring......Page 26
1.3 Examples......Page 30
2.1 Multivariate linear models and factor analysis......Page 36
2.2 The full component model......Page 42
2.3 The common factor model......Page 48
2.4 Correlated and uncorrelated factor models......Page 55
2.5 Which factor-analytic model?......Page 57
3.1 Matrix definitions and notation......Page 60
3.2 Matrix operations......Page 65
3.3 Definitional equations in matrix algebra form......Page 72
3.4 The full component model expressed in matrix algebra......Page 74
3.5 The common factor model in matrix algebra......Page 76
3.6 Uncorrelated factor models and matrix algebra......Page 79
4 Geometric Representation of Factor Models......Page 81
4.1 Representing variables and factors geometrically......Page 82
4.2 The uncorrelated (orthogonal) component model......Page 91
4.3 The correlated (oblique) component model......Page 94
4.4 Common factor models......Page 97
5 Diagonal and Multiple-group Analysis......Page 98
5.1 Diagonal analysis......Page 99
5.2 Multiple-group factor analysis......Page 106
5.3 Applications of diagonal and multiple-group factor analysis......Page 114
6 Principal Factor Solutions......Page 121
6.1 Characteristics of principal factor methods......Page 122
6.2 Principal components......Page 126
6.3 Communality estimation and principal axes......Page 130
6.4 Image analysis......Page 140
6.5 Other related procedures......Page 144
6.6 Nonlinear and nonmetric factor analysis......Page 147
6.7 Applications for principal factors......Page 149
6.8 A comparison of factor extraction procedures......Page 150
7.1 The maximum likelihood concept......Page 156
7.2 Confirmatory maximum likelihood factor analysis......Page 158
7.3 Applications......Page 162
7.4 Hypothesis testing by maximum likelihood and multiple-group procedures......Page 170
8 Determining the Number of Factors......Page 172
8.1 Adequacy of the fit of the model to the data......Page 173
8.2 Statistical approaches to the number of factors......Page 177
8.3 Mathematical approaches to the number of factors......Page 186
8.4 Extracting the nontrivial factors......Page 195
8.5 The search for the proper number of factors......Page 201
9 Rotation and Interpretation of Factors......Page 207
9.1 Principles for guiding the rotation of factors......Page 208
9.2 Orthogonal rotation for simple structure......Page 214
9.3 Oblique analytic rotation for simple structure......Page 220
9.4 Comparing alternative solutions......Page 229
9.5 Interpreting factors......Page 238
10 Rotation......Page 246
10.1 Algebraic principles of rotation......Page 247
10.2 Rotating visually......Page 251
10.3 Orthoblique solutions......Page 261
10.4 Nonsimple structure rotation......Page 266
10.5 Extension analysis......Page 271
11 Higher-order Factors......Page 274
11.1 Interpretation of higher-order factors......Page 275
11.2 Extracting higher-order factors......Page 277
11.3 Relationship of variables to higher-order factors......Page 281
11.4 Usefulness of higher-order factors......Page 290
12 Factor Scores......Page 293
12.1 Procedures for computing factor scores......Page 294
12.2 Approximation procedures for factor scores......Page 302
12.3 Cluster analysis of individuals: typological scoring......Page 306
12.4 Evaluating the factor scores......Page 308
12.5 Selecting among procedures......Page 312
13 Relating Factors Across Studies......Page 314
13.1 Information useful in relating factors......Page 315
13.2 Same individuals and variables but different procedures......Page 317
13.3 Same individuals but different variables......Page 318
13.4 Same variables but different individuals (Rvv, Svf, and Wvf available)......Page 319
13.5 Same variables but different individuals ( Rvv, Svf, and Wvf unavailable)......Page 321
13.7 Matching factors......Page 326
14.1 Noncontinuous data......Page 328
14.2 Effects of transformations......Page 334
14.3 Indices of association......Page 341
15 Two- and Three-mode Factor Analysis......Page 348
15.1 Two-mode factor analysis......Page 349
15.2 Three-mode factor analysis......Page 357
16.1 The replication of factors across random samples of individuals......Page 367
16.2 The invariance of factors......Page 373
17.1 Operationalization of constructs......Page 390
17.2 Factor analysis of independent and dependent variables......Page 399
17.3 Using factor analysis to suggest new leads for future research......Page 406
17.4 Other uses of factor analysis......Page 408
17.5 Concluding note......Page 409
18.1 Criticisms of present factor-analytic practices......Page 410
18.2 Recommended procedures for selected research designs......Page 413
18.3 The future of factor analysis......Page 420
Appendix A Data for Examples......Page 423
Appendix B.1 Computer Programs for Factor Analysis......Page 426
Appendix B.2 Accuracy of Computer Processing......Page 428
References......Page 433
Author Index......Page 453
Subject Index......Page 458
