Multivariate Exploratory Data Analysis

Dr. Yates is Senior Project Director at The Psychological Corporation.

"For anyone interested in human abilities, their organization, and how effectively to study them, this book is apt to be most engaging. Its foundational emphasis, clarity, consistency, and the appeal of an encompassing methodological system marries together some of the best of the new and old ideas about statistics and psychology." — Robert M. Pruzek, State University of New York at Albany

• TablesFiguresPrefaceProloguePART I. INTRODUCTORY ALGEBRA, GEOMETRY, AND TERMINOLOGY 1. The Factor Analysis Model Factor Analysis as a Special Case of Multivariate Multiple RegressionThe Geometry of Factor Analysis in the Case of an Ideal Simple StructurePART II. TRANSFORMATION OF PRIMARY FACTORS ON THE BASIS OF THURSTONE'S ORIGINAL MATHEMATICAL CRITERION FOR A BEST-FITTING SIMPLE STRUCTURE 2. Simple Structure Transformation Thurstone's Mathematical Criterion for a Best-Fitting Simple StructureDirect Geomin Transformation for Primary Factor Pattern SimplificationThe Geometry of Primary Factor RotationThe Algebra of Factor Pair RotationSolution for the Optimum Angle of Rotation 3. Practical Application of Direct Geomin Transformation A Comparison of Direct Geomin and Direct QuartiminHard vs. Soft Squeeze Direct Geomin Transformation StrategiesResistant Fitting Aspects of Direct Geomin TransformationSensitivity of Direct Geomin to Characteristics of the Starting Configuration PART III. BOUNDING THE TEST VECTOR CONFIGURATION WITH HYPERPLANES THROUGH SIMPLE STRUCTURE TRANSFORMATION 4. Simple Structure Reconsidered Beyond Factorial Purity and Ease of InterpretationThe Positive Manifold AssumptionA Source of Prior Information About Test Vector Configuration Location 5. Bounding Hyperplane Simple Structure Transformation Toward Bounding the Test Vector Configuration with Hyperplanes In the Identifications of Primary FactorsDistinguishability WeightingComplexity Weighting and the Associated Factor Contribution MatrixFactor Size ScalingDirect Geoplane Transformation 6. A Global Strategy for Bounding Hyperplane Simple Structure Transformation Locating the Central Axis of a Polyhedral Convex Cone of Test VectorsTransformation to Orthogonal BoundsIterative Recomputation of Distinguishability and Complexity WeightsIterative Reweighting and Factor Size ScalingAn Orthogonal Initial Configuration for Direct Geoplane Transformation 7. Factorial Invariance and the Global Direct Geoplane Transformation Strategy Analysis of Thurstone's Invariant 26-Variable Box ProblemAssessing Factorial Invariance Through Extended Vectors Projection of Direct Geoplane Factors PART IV. DISTINGUISHING INVARIANT MAJOR COMMON FACTORS FROM UNSTABLE MINOR FACTORS OF GROUP OVERLAP 8. Alternative Approaches to the Problem of Extracting Common Factors The Problem of Minor and Doublet Factors in Fitting the Common Factor ModelThe Classical Statistical Approach to Fitting the Factor Analysis ModelA Perspective on the Maximum Likelihood Method of Factor ExtractionConvergence of Simple Iterative Techniques for Maximum Likelihood Factor ExtractionAlternatives to the Classical Confirmatory Approach to Fitting the Unrestricted Common Factor ModelGauss-Seidel and Multidimensional Sectioning Methods of Fitting the Factor Analysis ModelCollinearity-Resistant Fitting of the Common Factor Model in the Presence of Local Dependency Outliers 9. Resistent Fitting and the Number of Factors Problem - Toward Fully Exploratory Factor Analysis Fitting Lord's Highly Clustered DataPractical Comparison of Collinearity-Resistant Fitting and Direct Geoplane Transformation with Available Approaches to Unrestricted Factor AnalysisAchieving Solution Invariance Through Dimensionality Reduction in Fully Exploratory Factor AnalysisAn Alternative to Second Order FactoringAccomodating Observed Data of High DimensionalityResolution of the Psychometric Vs. Statistical Conflict in Fitting the Factor Analysis Model PART V. FULLY EXPLORATORY FACTOR ANALYSIS 10. Historical Perspective, Practical Application, and Future Possibilities A Synthesis of the Classical Common Factor Theories of Spearman and Thurstone via Multivariate Exploratory Data AnalysisA Second Look at the Primary Mental AbilitiesToward an Understanding of Higher Integrative Mental Functioning Epilogue: Release From the Burden of Confirmation in Fully Exploratory Multivariate Data Analysis Appendix: Summary of Computational StepsBibliographyIndex