This is a very good book. Springer Texts in Statistics Everitt - An R and SPLUS Companion to Multivariate Analysis.pdf The first Four chapters
.... . . . . . . . . . . . . vii 1 Multivariate Data and Multivariate Analysis. . . . . . . . 1 1.1 Introduction... . . 1 1.2 Types of Data... . 1 1.3 Summary Statistics for Multivariate Data. . . . . . . . . 4 1.3.1 Means... . 4 1.3.2 Variances..5 1.3.3 Covariances.. . . . . . . . . . . . 5 1.3.4 Correlations.. . . . . . . . . . . . 6 1.3.5 Distances.. . . . . . . . . . . . . . 7 1.4 The Multivariate Normal Distribution. . . . . . . . . . . . 9 1.5 The Aims of Multivariate Analysis. . . . . . . . . . . . . . 13 1.6 Summary... . . . . 15
1.2 Types of Data... . 1 1.3 Summary Statistics for Multivariate Data. . . . . . . . . 4 1.3.1 Means... . 4 1.3.2 Variances..5 1.3.3 Covariances.. . . . . . . . . . . . 5 1.3.4 Correlations.. . . . . . . . . . . . 6 1.3.5 Distances.. . . . . . . . . . . . . . 7 1.4 The Multivariate Normal Distribution. . . . . . . . . . . . 9 1.5 The Aims of Multivariate Analysis. . . . . . . . . . . . . . 13 1.6 Summary... . . . . 15
1.2 Types of Data... . 1 1.3 Summary Statistics for Multivariate Data. . . . . . . . . 4 1.3.1 Means... . 4 1.3.2 Variances..5 1.3.3 Covariances.. . . . . . . . . . . . 5 1.3.4 Correlations.. . . . . . . . . . . . 6 1.3.5 Distances.. . . . . . . . . . . . . . 7 1.4 The Multivariate Normal Distribution. . . . . . . . . . . . 9 1.5 The Aims of Multivariate Analysis. . . . . . . . . . . . . . 13 1.6 Summary... . . . . 15
1.1 Introduction... . . 1 1.2 Types of Data... . 1 1.3 Summary Statistics for Multivariate Data. . . . . . . . . 4 1.3.1 Means... . 4 1.3.2 Variances..5 1.3.3 Covariances.. . . . . . . . . . . . 5 1.3.4 Correlations.. . . . . . . . . . . . 6 1.3.5 Distances.. . . . . . . . . . . . . . 7 1.4 The Multivariate Normal Distribution. . . . . . . . . . . . 9 1.5 The Aims of Multivariate Analysis. . . . . . . . . . . . . . 13 1.6 Summary... . . . . 15
1.1 Introduction... . . 1 1.2 Types of Data... . 1 1.3 Summary Statistics for Multivariate Data. . . . . . . . . 4 1.3.1 Means... . 4 1.3.2 Variances..5 1.3.3 Covariances.. . . . . . . . . . . . 5 1.3.4 Correlations.. . . . . . . . . . . . 6 1.3.5 Distances.. . . . . . . . . . . . . . 7 1.4 The Multivariate Normal Distribution. . . . . . . . . . . . 9 1.5 The Aims of Multivariate Analysis. . . . . . . . . . . . . . 13 1.6 Summary... . . . . 15
1.2 Types of Data... . 1 1.3 Summary Statistics for Multivariate Data. . . . . . . . . 4 1.3.1 Means... . 4 1.3.2 Variances..5 1.3.3 Covariances.. . . . . . . . . . . . 5 1.3.4 Correlations.. . . . . . . . . . . . 6 1.3.5 Distances.. . . . . . . . . . . . . . 7 1.4 The Multivariate Normal Distribution. . . . . . . . . . . . 9 1.5 The Aims of Multivariate Analysis. . . . . . . . . . . . . . 13 1.6 Summary... . . . . 15
1.2 Types of Data... . 1 1.3 Summary Statistics for Multivariate Data. . . . . . . . . 4 1.3.1 Means... . 4 1.3.2 Variances..5 1.3.3 Covariances.. . . . . . . . . . . . 5 1.3.4 Correlations.. . . . . . . . . . . . 6 1.3.5 Distances.. . . . . . . . . . . . . . 7 1.4 The Multivariate Normal Distribution. . . . . . . . . . . . 9 1.5 The Aims of Multivariate Analysis. . . . . . . . . . . . . . 13 1.6 Summary... . . . . 15
1.1 Introduction... . . 1 1.2 Types of Data... . 1 1.3 Summary Statistics for Multivariate Data. . . . . . . . . 4 1.3.1 Means... . 4 1.3.2 Variances..5 1.3.3 Covariances.. . . . . . . . . . . . 5 1.3.4 Correlations.. . . . . . . . . . . . 6 1.3.5 Distances.. . . . . . . . . . . . . . 7 1.4 The Multivariate Normal Distribution. . . . . . . . . . . . 9 1.5 The Aims of Multivariate Analysis. . . . . . . . . . . . . . 13 1.6 Summary... . . . . 15
1.2 Types of Data... . 1 1.3 Summary Statistics for Multivariate Data. . . . . . . . . 4 1.3.1 Means... . 4 1.3.2 Variances..5 1.3.3 Covariances.. . . . . . . . . . . . 5 1.3.4 Correlations.. . . . . . . . . . . . 6 1.3.5 Distances.. . . . . . . . . . . . . . 7 1.4 The Multivariate Normal Distribution. . . . . . . . . . . . 9 1.5 The Aims of Multivariate Analysis. . . . . . . . . . . . . . 13 1.6 Summary... . . . . 15 2 Looking at Multivariate Data.. . . . . . . 16 2.1 Introduction... . . 16 2.2 Scatterplots and Beyond.. . . . . . . . 17 2.2.1 The Convex Hull of Bivariate Data. . . . . . . . 22 2.2.2 The Chiplot.. . . . . . . . . . . . . 23 2.2.3 The Bivariate Boxplot.. . . . 25 2.3 Estimating Bivariate Densities.. . . 29 2.4 Representing Other Variables on a Scatterplot. . . . . 32 2.5 The Scatterplot Matrix.. . . . . . . . . 33 2.6 Three-Dimensional Plots.. . . . . . . 35 2.7 Conditioning Plots and Trellis Graphics. . . . . . . . . . 37 2.8 Summary... . . . . 40 Exercises... . . . . . . . . . 40
2.2 Scatterplots and Beyond.. . . . . . . . 17 2.2.1 The Convex Hull of Bivariate Data. . . . . . . . 22 2.2.2 The Chiplot.. . . . . . . . . . . . . 23 2.2.3 The Bivariate Boxplot.. . . . 25 2.3 Estimating Bivariate Densities.. . . 29 2.4 Representing Other Variables on a Scatterplot. . . . . 32 2.5 The Scatterplot Matrix.. . . . . . . . . 33 2.6 Three-Dimensional Plots.. . . . . . . 35 2.7 Conditioning Plots and Trellis Graphics. . . . . . . . . . 37 2.8 Summary... . . . . 40 Exercises... . . . . . . . . . 40
2.2 Scatterplots and Beyond.. . . . . . . . 17 2.2.1 The Convex Hull of Bivariate Data. . . . . . . . 22 2.2.2 The Chiplot.. . . . . . . . . . . . . 23 2.2.3 The Bivariate Boxplot.. . . . 25 2.3 Estimating Bivariate Densities.. . . 29 2.4 Representing Other Variables on a Scatterplot. . . . . 32 2.5 The Scatterplot Matrix.. . . . . . . . . 33 2.6 Three-Dimensional Plots.. . . . . . . 35 2.7 Conditioning Plots and Trellis Graphics. . . . . . . . . . 37 2.8 Summary... . . . . 40 Exercises... . . . . . . . . . 40
2.1 Introduction... . . 16 2.2 Scatterplots and Beyond.. . . . . . . . 17 2.2.1 The Convex Hull of Bivariate Data. . . . . . . . 22 2.2.2 The Chiplot.. . . . . . . . . . . . . 23 2.2.3 The Bivariate Boxplot.. . . . 25 2.3 Estimating Bivariate Densities.. . . 29 2.4 Representing Other Variables on a Scatterplot. . . . . 32 2.5 The Scatterplot Matrix.. . . . . . . . . 33 2.6 Three-Dimensional Plots.. . . . . . . 35 2.7 Conditioning Plots and Trellis Graphics. . . . . . . . . . 37 2.8 Summary... . . . . 40 Exercises... . . . . . . . . . 40
2.2 Scatterplots and Beyond.. . . . . . . . 17 2.2.1 The Convex Hull of Bivariate Data. . . . . . . . 22 2.2.2 The Chiplot.. . . . . . . . . . . . . 23 2.2.3 The Bivariate Boxplot.. . . . 25 2.3 Estimating Bivariate Densities.. . . 29 2.4 Representing Other Variables on a Scatterplot. . . . . 32 2.5 The Scatterplot Matrix.. . . . . . . . . 33 2.6 Three-Dimensional Plots.. . . . . . . 35 2.7 Conditioning Plots and Trellis Graphics. . . . . . . . . . 37 2.8 Summary... . . . . 40 Exercises... . . . . . . . . . 40 3 Principal Components Analysis.. . . . . 41 3.1 Introduction... . . 41 3.2 Algebraic Basics of Principal Components. . . . . . . 42
3.2 Algebraic Basics of Principal Components. . . . . . . 42
3.2 Algebraic Basics of Principal Components. . . . . . . 42
3.1 Introduction... . . 41 3.2 Algebraic Basics of Principal Components. . . . . . . 42
3.2 Algebraic Basics of Principal Components. . . . . . . 42 xi xii Contents 3.2.1 Rescaling Principal Components. . . . . . . . . . 45 3.2.2 Choosing the Number of Components. . . . . 46 3.2.3 Calculating Principal Component Scores. . . 47 3.2.4 Principal Components of Bivariate Data with Correlation Coefficient r.. . . . . . . . . . . . 48 3.3 An Example of Principal Components Analysis: Air Pollution in U.S. Cities... . . . 49 3.4 Summary... . . . . 61 Exercises... . . . . . . . . . 62
U.S. Cities... . . . 49 3.4 Summary... . . . . 61 Exercises... . . . . . . . . . 62
U.S. Cities... . . . 49 3.4 Summary... . . . . 61 Exercises... . . . . . . . . . 62
3.3 An Example of Principal Components Analysis: Air Pollution in U.S. Cities... . . . 49 3.4 Summary... . . . . 61 Exercises... . . . . . . . . . 62
U.S. Cities... . . . 49 3.4 Summary... . . . . 61 Exercises... . . . . . . . . . 62 4 Exploratory Factor Analysis.. . . . . . . . 65 4.1 Introduction... . . 65 4.2 The Factor Analysis Model.. . . . . 65 4.2.1 Principal Factor Analysis.. 68 4.2.2 Maximum Likelihood Factor Analysis. . . . . 69 4.3 Estimating the Numbers of Factors. . . . . . . . . . . . . . 69 4.4 A Simple Example of Factor Analysis. . . . . . . . . . . 70 4.5 Factor Rotation..71 4.6 Estimating Factor Scores.. . . . . . . 76 4.7 Two Examples of Exploratory Factor Analysis. . . . 77 4.7.1 Expectations of Life.. . . . . 77 4.7.2 Drug Usage by American College Students. 82 4.8 Comparison of Factor Analysis and Principal Components Analysis.. . . . . . . . . . 85 4.9 Confirmatory Factor Analysis.. . . 88 4.10 Summary... . . . . 88 Exercises... . . . . . . . . . 89
4.2 The Factor Analysis Model.. . . . . 65 4.2.1 Principal Factor Analysis.. 68 4.2.2 Maximum Likelihood Factor Analysis. . . . . 69 4.3 Estimating the Numbers of Factors. . . . . . . . . . . . . . 69 4.4 A Simple Example of Factor Analysis. . . . . . . . . . . 70 4.5 Factor Rotation..71 4.6 Estimating Factor Scores.. . . . . . . 76 4.7 Two Examples of Exploratory Factor Analysis. . . . 77 4.7.1 Expectations of Life.. . . . . 77 4.7.2 Drug Usage by American College Students. 82 4.8 Comparison of Factor Analysis and Principal Components Analysis.. . . . . . . . . . 85 4.9 Confirmatory Factor Analysis.. . . 88 4.10 Summary... . . . . 88 Exercises... . . . . . . . . . 89
4.2 The Factor Analysis Model.. . . . . 65 4.2.1 Principal Factor Analysis.. 68 4.2.2 Maximum Likelihood Factor Analysis. . . . . 69 4.3 Estimating the Numbers of Factors. . . . . . . . . . . . . . 69 4.4 A Simple Example of Factor Analysis. . . . . . . . . . . 70 4.5 Factor Rotation..71 4.6 Estimating Factor Scores.. . . . . . . 76 4.7 Two Examples of Exploratory Factor Analysis. . . . 77 4.7.1 Expectations of Life.. . . . . 77 4.7.2 Drug Usage by American College Students. 82 4.8 Comparison of Factor Analysis and Principal Components Analysis.. . . . . . . . . . 85 4.9 Confirmatory Factor Analysis.. . . 88 4.10 Summary... . . . . 88 Exercises... . . . . . . . . . 89
4.1 Introduction... . . 65 4.2 The Factor Analysis Model.. . . . . 65 4.2.1 Principal Factor Analysis.. 68 4.2.2 Maximum Likelihood Factor Analysis. . . . . 69 4.3 Estimating the Numbers of Factors. . . . . . . . . . . . . . 69 4.4 A Simple Example of Factor Analysis. . . . . . . . . . . 70 4.5 Factor Rotation..71 4.6 Estimating Factor Scores.. . . . . . . 76 4.7 Two Examples of Exploratory Factor Analysis. . . . 77 4.7.1 Expectations of Life.. . . . . 77 4.7.2 Drug Usage by American College Students. 82 4.8 Comparison of Factor Analysis and Principal Components Analysis.. . . . . . . . . . 85 4.9 Confirmatory Factor Analysis.. . . 88 4.10 Summary... . . . . 88 Exercises... . . . . . . . . . 89
4.2 The Factor Analysis Model.. . . . . 65 4.2.1 Principal Factor Analysis.. 68 4.2.2 Maximum Likelihood Factor Analysis. . . . . 69 4.3 Estimating the Numbers of Factors. . . . . . . . . . . . . . 69 4.4 A Simple Example of Factor Analysis. . . . . . . . . . . 70 4.5 Factor Rotation..71 4.6 Estimating Factor Scores.. . . . . . . 76 4.7 Two Examples of Exploratory Factor Analysis. . . . 77 4.7.1 Expectations of Life.. . . . . 77 4.7.2 Drug Usage by American College Students. 82 4.8 Comparison of Factor Analysis and Principal Components Analysis.. . . . . . . . . . 85 4.9 Confirmatory Factor Analysis.. . . 88 4.10 Summary... . . . . 88 Exercises... . . . . . . . . . 89
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