LEADER 05451nam 2200649Ia 450 001 9910831051403321 005 20170814174234.0 010 $a1-282-30742-8 010 $a9786612307423 010 $a0-470-31689-6 010 $a0-470-31773-6 035 $a(CKB)1000000000687544 035 $a(EBL)469210 035 $a(OCoLC)264615491 035 $a(SSID)ssj0000343229 035 $a(PQKBManifestationID)11304607 035 $a(PQKBTitleCode)TC0000343229 035 $a(PQKBWorkID)10288729 035 $a(PQKB)10469753 035 $a(MiAaPQ)EBC469210 035 $a(PPN)157931145 035 $a(EXLCZ)991000000000687544 100 $a19930520d1994 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStatistical factor analysis and related methods$b[electronic resource] $etheory and applications /$fAlexander Basilevsky 210 $aNew York $cWiley$dc1994 215 $a1 online resource (770 p.) 225 0 $aWiley series in probability and mathematical statistics. Probability and mathematical statistics 300 $aDescription based upon print version of record. 311 $a0-471-57082-6 320 $aIncludes bibliographical references (p. 690-731) and index. 327 $aStatistical 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 327 $a1.5.4. 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 327 $a2.7. 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 327 $a3.4.2. 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 327 $a4.2.3. 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 327 $a4.6.1. Assessing for Univariate Normality 330 $aStatistical Factor Analysis and Related Methods Theory and Applications In bridging the gap between the mathematical and statistical theory of factor analysis, this new work represents the first unified treatment of the theory and practice of factor analysis and latent variable models. It focuses on such areas as:* The classical principal components model and sample-population inference* Several extensions and modifications of principal components, including Q and three-mode analysis and principal components in the complex domain* Maximum likelihood and weighted factor models, fact 410 0$aWiley Series in Probability and Statistics 606 $aFactor analysis 606 $aMultivariate analysis 615 0$aFactor analysis. 615 0$aMultivariate analysis. 676 $a519.5 676 $a519.5354 700 $aBasilevsky$b Alexander$0447995 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910831051403321 996 $aStatistical factor analysis and related methods$9103604 997 $aUNINA