The scientific use of factor analysis in behavioral and life sciences

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The scientific use of factor analysis in behavioral and life sciences

Raymond B. Cattell

Plenum Press, c1978

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Bibliography: p. 573-599

Includes indexes

内容説明・目次

目次

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.

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