Statistical factor analysis and related methods [[electronic resource] ] : theory and applications / / Alexander Basilevsky

• Autore: Basilevsky Alexander
• Pubblicazione: New York, : Wiley, c1994
• Descrizione fisica: 1 online resource (770 p.)
• Disciplina: 519.5; 519.5354
• Soggetto topico: Factor analysis; Multivariate analysis
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references (p. 690-731) and index.
• Nota di contenuto: Statistical Factor Analysis and Related Methods; Contents; 1. Preliminaries; 1.1. Introduction; 1.2. Rules for Univariate Distributions; 1.2.1. The Chi-Squared Distribution; 1.2.2. The F Distribution; 1.2.3. The t Distribution; 1.3. Estimation; 1.3.1. Point Estimation: Maximum Likelihood; 1.3.2. The Likelihood Ratio Criterion; 1.4. Notions of Multivariate Distributions; 1.5. Statistics and the Theory of Measurement; 1.5.1. The Algebraic Theory of Measurement; 1.5.2. Admissiblc Transformations and the Classification of Scales; 1.5.3. Scale Classification and Meaningful Statistics ; 1.5.4. Units of Measurc and Dimensional Analysis for Ratio Scales1.6. Statistical Entropy; 1.7. Complex Random Variables; Exercises; 2. Matrixes, Vector Spaces; 2.1. Introduction; 2.2. Linear, Quadratic Forms; 2.3. Multivariate Differentiation; 2.3.1. Derivative Vectors; 2.3.2. Derivative Matrices; 2.4. Grammian Association Matrices; 2.4.1. The inner Product Matrix; 2.4.2. The Cosine Matrix; 2.4.3. The Covariance Matrix; 2.4.4. The Correlation Matrix; 2.5. Transformation of Coordinates; 2.5.1. Orthogonal Rotations; 2.5.2. Oblique Rotations; 2.6. Latent Roots and Vectors of Grammian Matrices ; 2.7. Rotation of Quadratic Forms2.8. Elements of Multivariate Normal Theory; 2.8.1. The Multivariate Normal Distribution; 2.8.2. Sampling from the Multivariatc Normal; 2.9. Thc Kronecker Product; 2.10. Simultaneous Decomposition of Two Grammian Matrices; 2.11. The Complex Muitivariate Normal Distribution; 2.11.1. Complex Matrices, Hermitian Forms; 2.11.2. The Complex Multivariate Normat; Exercises; 3. The Ordinary Principal Components Model; 3.1. Introduction; 3.2. Principal Components in the Population; 3.3. Isotropic Variation; 3.4. Principal Components in the Sample; 3.4.1. Introduction ; 3.4.2. The General Model3.4.3. The Effect of Mean and Variances on PCs; 3.5. Principal Components and Projections; 3.6. Principal Components by Least Squares; 3.7. Nonlinearity in the Variables; 3.8. Alternative Scaling Criteria; 3.8.1. Introduction; 3.8.2. Standardized Regression Loadings; 3.8.3. Ratio Index Loadings; 3.8.4. Probability Index Loadings; Exercises; 4. Statistical Testing of the Ordinary Principal Components Model; 4.1. Introduction; 4.2. Testing Covariance and Correlation Matrices; 4.2.1. Testing for CompIete Independence; 4.2.2. Testing Sphericity ; 4.2.3. Other lests for Covariance Matrices4.3. Testing Principal Components by Maximum Likelihood; 4.3.1. Testing Equality of all Latent Roots; 4.3.2. Testing Subsets of Principal Components; 4.3.3. Testing Residuals; 4.3.4. Testing Individual Principal Components; 4.3.5. Information Criteria of Maximum Likelihood Estimation of the Number of Components; 4.4. Other Methods of Choosing Principal Components; 4.4.1. Estirnatcs Bascd on Resampling; 4.4.2. Residual Correlations Test; 4.4.3. Informal Rules of Thumb; 4.5. Discarding Redundant Variables; 4.6. Assessing Normality ; 4.6.1. Assessing for Univariate Normality
• Sommario/riassunto: Statistical Factor Analysis and Related Methods Theory and Applications In bridging the gap between the mathematical and statistical theory of factor analysis, this new work represents the first unified treatment of the theory and practice of factor analysis and latent variable models. It focuses on such areas as:* The classical principal components model and sample-population inference* Several extensions and modifications of principal components, including Q and three-mode analysis and principal components in the complex domain* Maximum likelihood and weighted factor models, fact
• Titolo autorizzato: Statistical factor analysis and related methods
• ISBN: 1-282-30742-8; 9786612307423; 0-470-31689-6; 0-470-31773-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910841321603321
• Lo trovi qui: Univ. Federico II
• Serie: Wiley Series in Probability and Statistics