| Description |
1 online resource (788 pages) |
| Contents |
Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Tables and Figures; Preface; 1. Introduction and Spearman Approach; 1.1 Introduction; 1.1.1 Interpretation of factors; 1.1.2 Example; Problem 1.1.2:1; 1.2 The Linear Model; Problem 1.2:1; 1.3 The Principles of Parsimony; 1.4 Spearman's Theory; 1.5 Elementary Theorems; 1.5.1 Factor pattern and correlation; 1.5.2 Sample and population; 1.5.3 Theorems on a single correlation coefficient; Problem 1.5.3:1; 1.5.4 Definition of triad; 1.5.5 Theorems on triads; Problem 1.5.5:1; 1.5.6 Tests of significance for triads |
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1.5.7 The tetradsProblem 1.5.7:1; 1.5.8 Negative triads; Heywood case; Problem 1.5.8:1; 1.5.9 Limiting conditions; 1.5.10 Theorem on group factors; Problem 1.5.10:1; 1.6 Tetrad-Triad Analysis; 1.6.1 Standard error of a tetrad; Problem 1.6.1:1; 1.6.2 Tetrad analysis; 1.6.3 The factor pattern; 1.6.4 Triad analysis; 1.6.5 The residuals; 1.6.6 Estimation of group-factor loadings; 1.6.7 The numerical factor pattern; Problem 1.6.7:1; 1.6.8 Interpretation; Exercise 1:1; 2. Centroid Method; Rotation in Two Dimensions; 2.1 Introduction; 2.1.1 The two-step procedure; 2.1.2 The transformation |
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2.2 Elementary Theory of Initial Factoring2.3 The Centroid Method; 2.3.1 Centroid equations; 2.3.2 Reflection; 2.3.3 Residual matrices and later factors; 2.3.4 Effects of reflection; 2.4 Centroid Computations; 2.4.1 Computational accuracy and checks; 2.4.2 First-factor loadings; 2.4.3 Residuals; 2.4.4 Reflection; 2.4.5 Factor matrix; Exercise 2:1; 2.5 Rotation in Two Dimensions; 2.5.1 Geometric model; 2.5.2 Centroid vectors; 2.5.3 The transformation equations and the rotated factor matrix; 2.5.4 Alternative orthogonal rotation; 2.5.5 Oblique rotation; 2.5.6 Efficient computation; Exercise 2:2 |
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2.6 Further Problems2.6.1 Example; 3. Elements of Matrix Algebra; 3.1 Introduction; 3.2 Elementary Matrix Algebra; 3.2.1 Preliminary definitions and rules of addition and subtraction; 3.2.2 Transpose of a matrix; Problem 3.2.2:1; 3.2.3 Vectors; Problem 3.2.3:1; 3.2.4 Matrix multiplication; 3.2.5 Application to nonhomogeneous linear equations; 3.2.6 Application to linear transformations; Problem 3.2.6:1; Problem 3.2.6:2; Problem 3.2.6:3; 3.2.7 Symmetric matrices; Problem 3.2.7:1; 3.2.8 Diagonal matrices; Problem 3.2.8:1; 3.2.9 Scalar matrices and scalar multiplication |
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3.2.10 The identity matrix3.3 The Inverse of a Square Matrix; 3.3.1 Definition and properties of the inverse; 3.3.2 Matrix inversion; 3.4 Some Further Matrix Algebra; 3.4.1 Orthogonal and orthonormal matrices; Problem 3.4.1:1; 3.4.2 Rank of a matrix; Problem 3.4.2:1; 3.4.3 Gramian matrices; Problem 3.4.3:1; Problem 3.4.3:2; 3.5 Notes; 3.5.1 Matrix multiplication is associative; 3.5.2 Matrix multiplication is distributive over matrix addition and subtraction; 4. Linear Computations; 4.1 Introduction; 4.2 Elimination Procedure; 4.2.1 Algebra of elimination; 4.2.2 Numerical example |
| Summary |
First published in 1993. Routledge is an imprint of Taylor & Francis, an informa company |
| Notes |
Problem 4.2.2:1 |
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Print version record |
| Form |
Electronic book
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| Author |
D'Agostino, Ralph B
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| ISBN |
9781317759652 |
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1317759656 |
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