The Scientific Use of Factor Analysis in Behavioral and Life Sciences

ISBN-13: 9781468422641 / Angielski / Miękka / 2012 / 618 str.

Raymond Cattell

Opis

It needs no great scientific insight to see that such multitudinously multi variate subjects as psychology, physiology, sociology, and history need multivariate methods. As this book may show, those methods-multivari ate analysis of variance, regression analysis, typal and discriminant func tion analysis, multidimensional scaling, and factor analysis-belong to a single structural arch which bears up conceptual and causal understanding in all these subjects. But factor analysis is the keystone of that arch. Since factor analysis has itself developed fantastically in thirty years my first small book (Cattell, 1952b) could almost cover the field in a few chap ters ], this book confines itself to that subject, with only brief connecting asides on the related areas. The purpose of a preface is to permit more personal comments and to explain why the design is what it is. Among the former the author often apologizes for writing in an already crowded library shelf, and, having con fessed the crime, thanks his friends for their connivance. The area already enjoys a truly excellent array of books, from extremely good elementary introductions by Child, Henrysson, Lawlis, and Chatfield, through the workbook emphasis of Fruchter, and the intermediates of Guertin and Bailey and Comrey, to the comprehensive technical works of Anderson, Ahmavaara, Gorsuch, Harman, Horst, Lawley and Maxwell, Mulaik, Rao, Rummel, and Van de Geer, not to mention the undating books by Burt, Thomson, and Thurstone.

Spis treści

I.- 1 The Position of Factor Analysis in Psychological Research.- 1.1. The ANOVA and CORAN Methods of Finding Significant Relations in Data.- 1.2. The Reason for the Salient Role of Statistics in the Biosocial Sciences.- 1.3. What Is an Experiment? Bivariate and Multivariate Designs.- 1.4. Dimensions of Experiment and Their Relation to Historic Areas of Research.- 1.5. The Relation of Experiment to the Inductive-Hypothetico-Deductive Method.- 1.6. The Relative Power and Economies and the Mutual Utilities of ANOVA and CORAN Methods.- 1.7. Summary.- 2 Extracting Factors: The Algebraic Picture.- 2.1. The Aims of Multivariate CORAN: Component Analysis, Cluster Analysis, and Factor Analysis.- 2.2. The Basic Factor Proposition: Correlation Size Related to Common Factor Size.- 2.3. The Centroid or Unweighted Summation Extraction of Factor Components.- 2.4. The Principal Components or Weighted Summation Extraction..- 2.5. Communality: Common (Broad) and Unique Variances.- 2.6. Checking Back from Factor Matrices to Correlation Matrices.- 2.7. The Specification and Estimation Equations Linking Factors and Variables.- 2.8. Summary.- 3 Rotating Factors: The Geometric Picture.- 3.1. The Correlation Coefficient Geometrically Represented.- 3.2. Plotting Variables in Hyperspace from the V0 Matrix.- 3.3. The Relation of Cluster Analysis to Factor Analysis.- 3.4. The Effect of Factor Rotation on Factor Patterns.- 3.5. The Possibility of a Unique Rotation and the Need to Find It ..- 3.6. Summary.- 4 Fixing the Number of Factors: TheScientific Model 52.- 4.1. A Return to the “Number of Factors” Issue.- 4.2. The Alternatives of Statistical and Psychometric Bases of Decision on Factor Number.- 4.3. Broader View of the Number of Factors Problem in the Light of the Scientific Model.- 4.4. Practical Decision by the Scree Test and Maximum Likelihood..- 4.5. The Contrasting Properties of the Principal Components and Factor Models.- 4.6. Summary.- 5 Fixing the Number of Factors: The Most Practicable Psychometric Procedures.- 5.1. Fixing the Number of Factors by Deciding the Communalities..- 5.2. Deciding Number of Factors by Latent Root Plots: The Scree and K-G Tests.- 5.3. The Empirical Support for the Scree Test from Plasmodes.- 5.4. The Empirical Support for the Scree Test from Internal Consistencies.- 5.5. Ensuring Objectivity of Evaluation Procedure in the Scree Test.- 5.6. Findings in the Use of the K-G Test.- 5.7. Proceeding from Factor Number to Sizes of Communalities.- 5.8. Summary.- 6 The Theory of Unique Rotational Resolution by Confactor, Procrustes, and Simple Structure Principles.- 6.1. The Properties and Limitations of the Unrotated Dimension Matrices, V0 and V0.- 6.2. The Rationale for Rotation by Hypothesis-Testing and Hypothesis-Creating Principles.- 6.3. Hypothesis-Creating Rotation: By the Confactor Principle.- 6.4. Hypothesis-Creating Rotation: By the Simple Structure Principle.- 6.5. Illustration of Simple Structure Properties in Real Data.- 6.6. Some Problems of Research Design and Interpretation in Simple Structures.- 6.7. Summary.- 7 The Techniques of Simple Structure Rotation.- 7.1. Transforming the Unrotated to a Rotated Matrix.- 7.2. The Definition of a Matrix and Matrix Multiplication.- 7.3. The Nature of the Transformation Matrix in Hyperspace.- 7.4. The Rationale for Oblique, Correlated Factors, and the Computation of Their Correlations.- 7.5. Rotation by Visual Inspection of Single Plane Plots.- 7.6. Analytical and Topological Automatic Rotation Programs....- 7.7. Comparative Studies of the Strengths and Weaknesses of Various Automatic Programs.- 7.8. The Tactics of Reaching Maximum Simple Structure.- 7.9. ROTOPLOT: The Calculations in Successive Shifts.- 7.10. Summary.- 8 More Refined Issues in Rotation and the Use of Oblique Factors.- 8.1. More Refined Tactics from Experience Necessary in SS (Simple Structure) Resolution.- 8.2. Three Tactical Principles in Controlled Rotation.- 8.3. Discussion of Matrix Inverses and Transposes in the Calculation of Correlations among Reference Vectors and Factors ...- 8.4. Reaching Correct Primary Factor Correlations in SS Rotation.- 8.5. Singular and Non-Gramian Matrices and the Collapse of Factors.- 8.6. Geometers’ Hyperplanes and the Use of Rotation as a Check on Factor Number.- 8.7. The Evaluation of a Simple Structure.- 8.8. Reference Vectors and Factors, Loadings and Correlations Distinguished.- 8.9. Which VD Matrix Should Direct the Simple Structure Search?.- 8.10. An Overview of SS Alongside Other Rotational Principles ….- 8.11. Summary.- 9 Higher-Order Factors: Models and Formulas.- 9.1. The Need to Recognize the Existence of Higher-Order Factor Influences.- 9.2. Extracting Factors from Rotated Primaries and from Correlations of Primary Scales and Batteries.- 9.3. Factor Interrelations: The Possibilities of Strata, Reticular, and Other Scientific Models.- 9.4. The Theory of Higher-Strata Factors: New Influences or Spiral Feedback Emergents?.- 9.5. Calculating Loadings of Higher-Strata Factors Directly on Variables: The C-W Formula.- 9.6. The Ultimate Factor Theory: The Stratified Uncorrelated Determiner Model.- 9.7. The Calculations for the SUD Model, Beginning with the Schmid-Leiman Formula.- 9.8. Some Bases of Decision among Alternative Models of Factor Action.- 9.9. Summary.- 10 The Identification and Interpretation of Factors.- 10.1. What Are the Bases of Identification and Interpretation?.- 10.2. Identification and Interpretation from Loading Patterns.- 10.3. The Nature of the Five Most Common Variable Dimension Relation Matrices with an Introduction to Factor Scores.- 10.4. Five More Esoteric Variable Dimension Relation Matrices.- 10.5. Discussion and Illustration of Relations of VD Matrices.- 10.6. Planning for Factor Identification by Matching: The Four Experimental Possibilities.- 10.7. Indices for Matching: The Congruence Coefficients rc.- 10.8. Indices for Matching: The Salient Variable Similarity Index s.- 10.9. Indices for Matching: The Configurative Method.- 10.10. Comparative Properties of Various Approaches to Matching, Including rp.- 10.11. Summary.- II.- 11 Factor Measures: Their Construction, Scoring, Psychometric Validity, and Consistency.- 11.1. Orientation of Factor Analysis to Psychometric Practice.- 11.2. The Initial, Common Form of Estimation of Scores for Primaries and Higher-Strata Factors.- 11.3. Specifics and the Practical-versus-Complete Theoretical Specification Equation.- 11.4. Is Estimation Necessarily a Circular Process?.- 11.5. Estimation Problems Peculiar to Higher-Strata Factors.- 11.6. Basic Concepts Regarding Types of Validity.- 11.7. Definitions of Homogeneity, Reliability, Factor Trueness, and Unitractic and Univocal Batteries.- 11.8. Relations among Homogeneity, Reliability, Transferability, and Validity.- 11.9. The Arguments for Low Item or Subtest Homogeneity in Constructing Tests for Factor Estimation.- 11.10. More Theoretical Issues in Factor Score Estimations.- 11.11. Approximate Estimation Procedures.- 11.12. Some Special Issues of Factor Estimation among Oblique Factors.- 11.13. Estimation of Factor Scores Required for Comparisons across Different Populations: The Equipotent and Isopodic Concepts.- 11.14. Summary.- 12 Broader Experimental Designs and Uses: The Data Box and the New Techniques.- 12.1. Perspective on Uses of Factor Analysis in General Experimental Work.- 12.2. The BDRM Initially Studied as the Covariation Chart.- 12.3. The Misspent Youth of Q Technique.- 12.4. Choice and Sampling Principles for Relatives and Referees...- 12.5. The Complete BDRM.- 12.6. The Five Signatures of a Psychological Event.- 12.7. The Factoring of Facets, Faces, Frames, and Grids.- 12.8. Sampling and Standardization of Measures across the Five Sets.- 12.9. The Nature of Factors from Each of the Ten Main Techniques.- 12.10. Differential R Technique (dR Technique).- 12.11. The Problem of Difference Scores and Their Scaling.- 12.12. The Experimental Design Called P Technique.- 12.13. Trend and Cycle Problems Peculiar to P Technique.- 12.14. P Technique with Manipulation, Lead and Lag, and Chain Designs.- 12.15. The Relation of dR-and P-Technique Factors.- 12.16. Manipulative and Causal-Analysis Designs in Learning and Other Factor Analytic Treatment Experiments.- 12.17. The Relation of Factors from Various BDRM Facets, Faces, Frames, and Grids: n-Way Factor Analysis.- 12.18. Comparison of n-Way (Disjunct and Conjoint) and n-Mode Factor Analysis.- 12.19. Summary.- 13 Varieties of Factor Models in Relation to Scientific Models.- 13.1. Scientific Aims in Modifying the Factor Model.- 13.2. Departures from Assumptions of Linearity and Additivity.- 13.3. Adjustments to Mixtures of Populations.- 13.4. Alpha and Image Methods of Analysis.- 13.5. Canonical Correlation and the Factor Concept.- 13.6. Canonical and Maximum Likelihood Factor Extraction, Ordinary and Proofing Forms.- 13.7. Other Developments and Comparison of Extraction Models..- 13.8. The Aim of Real-Base Factor Analysis.- 13.9. Covariance Factoring and the Law of Constancy of Factor Effect.- 13.10. The Conception of Standard Raw Scores at a Core Matrix Position.- 13.11. Relative Size, Potency, and Final Size of Factors.- 13.12. The Role of Modulation in Determining Factor Size.- 13.13. Broader Models: Nonmetric Analysis and Bentler’s Multistructure Model.- 13.14. Path Analytic Factor Analysis and the Quantifying of Causes..- 13.15. Brief View of Factor Analysis in Relation to Regression and Other Models.- 13.16. Summary.- 14 Distribution, Scaling, and Significance Problems.- 14.1. The Five Domains of Distribution and Sampling in Factor Analysis.- 14.2. Taxonomic Principles in Recognizing Homostats and Segregates.- 14.3. Within Type and Between Type Factor Dimensions.- 14.4. “Multidimensional Scaling” or “Dimensional Integration” Concepts.- 14.5. Equal Interval Scales and True-Zero Factor Scores.- 14.6. The Theory of a True Zero.- 14.7. Permissive, Staggered Onset, and ontinuous Action Factor Models.- 14.8. The Effects of Different Coefficients of core Relationships Including “Cross Products” in the R? Matrix.- 14.9. The Statistical Significance of Correlation Matrices and Factors.- 14.10. The Significance of Correlations and Loadings of Particular Variables on Particular Factors.- 14.11. Error of Measurement.- 14.12. Summary.- 15 Conducting a Factor Analytic Research: Strategy and Tactics.- 15.1. The Choice of Experimental Design.- 15.2. The Choice of Variables: Markers and Matching.- 15.3. The Choice of Variables: Numbers, Matrix Divisions, and Combinations.- 15.4. The Choice of Variables: Instrument Factors and Perturbation Theory.- 15.5. The Choice of Number of Referees in Relation to Relatives..- 15.6. Purposes in Manipulating the Selection of Referees.- 15.7. Correlating Variables and Extracting the Unrotated Factors..- 15.8. Rotating and Testing the Significance of a Rotational Resolution.- 15.9. Matching and Interpreting Factors: Programmatic Design and the Need for a Universal Index.- 15.10. The Use of Factor Scores and Taxonomic Type Classifications.- 15.11. Summary.- Appendixes.- A. 1. Proposed Standard Notation: Rationale and Outline.- A.2. An Indexing System for Psychological Factors.- A.3. Note on Utility of Confactor Resolutions with Oblique Factors.- A.4. Transformations among SUD, SSA, and IIA Strata Models: Reversion from the Schmid-Leiman Matrix (IIA).- A.5. A Practicable Minimum List of Computer Programs.- A.6. Tables for Statistical Significance of Simple Structure.- A. 7. Tables for Significance of Congruence Coefficients in Factor Matching.- A.8. Tables for Significance of Salient Variable Similarity Index s.- References.- Author Index.