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|a Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Preface -- PART ONE: INTRODUCTION -- 1: Introduction -- 1.1 Examples -- 1.2 Notation -- 1.3 Review of objectives and different approaches -- 1.4 Some general comments -- 1.5 Review of books on multivariate analysis -- 1.6 Some matrix algebra revision -- 1.7 The general linear model -- Exercises -- 2: Multivariate distributions -- 2.1 Multivariate, marginal and conditional distributions -- 2.2 Means, variances, covariances and correlations -- 2.3 The multivariate normal distribution -- 2.4 The bivariate normal distribution -- 2.5 Other multivariate distributions -- 2.5.1 Multivariate discrete distributions -- 2.5.2 Multivariate continuous distributions -- Exercises -- 3: Preliminary data analysis -- 3.1 Processing the data -- 3.1.1 Data editing -- 3.2 Calculating summary statistics -- 3.2.1 Interpreting the sample correlation matrix -- 3.2.2 The rank of R -- 3.3 Plotting the data -- 3.4 The analysis of discrete data -- Exercises -- PART TWO: FINDING NEW UNDERLYING VARIABLES -- 4: Principal component analysis -- 4.1 Introduction -- 4.2 Derivation of principal components -- 4.2.1 Principal components from the correlation matrix -- 4.2.2 Estimating the principal components -- 4.3 Further results on PCA -- 4.3.1 Mean-corrected component scores -- 4.3.2 The inverse transformation -- 4.3.3 Zero eigenvalues -- 4.3.4 Small eigenvalues -- 4.3.5 Repeated roots -- 4.3.6 Orthogonality -- 4.3.7 Component loadings/component correlations -- 4.3.8 Off-diagonal structure -- 4.3.9 Uncorrelated variables -- 4.4 The problem of scaling in PCA -- 4.5 Discussion -- 4.5.1 The identification o f important components -- 4.5.2 The use o f components in subsequent analyses -- 4.6 PCA for multivariate normal data -- 4.7 Summary -- Exercises -- 5: Factor analysis -- 5.1 Introduction
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|a 5.2 The factor-analysis model -- 5.3 Estimating the factor loadings -- 5.4 Discussion -- PART THREE: PROCEDURES BASED ON THE MULTIVARIATE NORMAL DISTRIBUTION -- 6: The multivariate normal distribution -- 6.1 Introduction -- 6.2 Definition of the multivariate normal distribution -- 6.3 Properties of the multivariate normal distribution -- 6.4 Linear compounds and linear combinations -- 6.5 Estimation of the parameters of the distribution -- 6.6 The Wishart distribution -- 6.7 The joint distribution of the sample mean vector and the sample covariance matrix -- 6.8 The Hotelling T2-distribution -- Exercises -- 7: Procedures based on normal distribution theory -- 7.1 Introduction -- 7.2 One-sample procedures -- 7.3 Confidence intervals and further analysis -- 7.4 Tests of structural relations among the components of the mean -- 7.5 Two-sample procedures -- 7.6 Confidence intervals and further analysis -- 7.7 Tests of structural relations among the components of the means -- 7.8 Discriminant analysis -- Exercises -- 8: The multivariate analysis of variance -- 8.1 Introduction -- 8.2 MANOVA calculations -- 8.3 Testing hypotheses -- 8.3.1 The special case: The univariate procedure -- 8.3.2 The multivariate model for Example 8.1 -- 8.3.3 Multivariate test procedures -- 8.3.4 Distributional approximations -- 8.3.5 Applications o f the methodology -- 8.4 Further analysis -- 8.5 The dimensionality of the alternative hypothesis -- 8.6 Canonical variates analysis -- 8.7 Linear functional relationships -- 8.8 Discriminant analysis -- Exercises -- 9: The multivariate analysis of covariance and related topics -- 9.1 Introduction -- 9.2 Multivariate regression -- 9.2.1 The special case: Univariate multiple regression -- 9.2.2 The general case: Multivariate regression -- 9.3 Canonical correlation -- 9.4 The multivariate analysis of covariance
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|a 9.4.1 The special case: Univariate analysis of covariance -- 9.4.2 The multivariate case: An example -- 9.4.3 The multivariate case: General results -- 9.5 The test for additional information -- 9.6 A test of an assigned subset of linear compounds -- Exercises -- PART FOUR: MULTIDIMENSIONAL SCALING AND CLUSTER ANALYSIS -- 10: Multidimensional scaling -- 10.1 Introduction -- 10.2 Measures of similarity and dissimilarity -- 10.2.1 Similarity coefficients for binary data -- 10.3 Classical scaling -- 10.3.1 The calculation of co-ordinate values from Euclidean distances -- 10.3.2 The relationship between classical scaling and principal component analysis -- 10.3.3 Classical scaling for a dissimilarity matrix -- 10.3.4 Interpretation of the results -- 10.3.5 Some related methods -- 10.4 Ordinal scaling -- 10.4.1 The iterative procedure -- 10.4.2 Interpreting the results -- 10.5 A comparison -- 10.6 Concluding remarks -- Exercises -- 11: Cluster analysis -- 11.1 Introduction -- 11.1.1 Objectives -- 11.1.2 Clumping, dissection and clustering variables -- 11.1.3 Some other preliminary points -- 11.2 Visual approaches to finding a partition -- 11.3 Hierarchical trees -- 11.4 Single-link clustering -- 11.5 Some other clustering procedures -- 11.5.1 Method or algorithm? -- 11.6 A comparison of procedures -- 11.6.1 Some desirable conditions for hierarchical clustering methods -- 11.6.2 A comparison -- Exercises -- References -- Answers to exercises -- Name Index -- Subject Index
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Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Preface -- PART ONE: INTRODUCTION -- 1: Introduction -- 1.1 Examples -- 1.2 Notation -- 1.3 Review of objectives and different approaches -- 1.4 Some general comments -- 1.5 Review of books on multivariate analysis -- 1.6 Some matrix algebra revision -- 1.7 The general linear model -- Exercises -- 2: Multivariate distributions -- 2.1 Multivariate, marginal and conditional distributions -- 2.2 Means, variances, covariances and correlations -- 2.3 The multivariate normal distribution -- 2.4 The bivariate normal distribution -- 2.5 Other multivariate distributions -- 2.5.1 Multivariate discrete distributions -- 2.5.2 Multivariate continuous distributions -- Exercises -- 3: Preliminary data analysis -- 3.1 Processing the data -- 3.1.1 Data editing -- 3.2 Calculating summary statistics -- 3.2.1 Interpreting the sample correlation matrix -- 3.2.2 The rank of R -- 3.3 Plotting the data -- 3.4 The analysis of discrete data -- Exercises -- PART TWO: FINDING NEW UNDERLYING VARIABLES -- 4: Principal component analysis -- 4.1 Introduction -- 4.2 Derivation of principal components -- 4.2.1 Principal components from the correlation matrix -- 4.2.2 Estimating the principal components -- 4.3 Further results on PCA -- 4.3.1 Mean-corrected component scores -- 4.3.2 The inverse transformation -- 4.3.3 Zero eigenvalues -- 4.3.4 Small eigenvalues -- 4.3.5 Repeated roots -- 4.3.6 Orthogonality -- 4.3.7 Component loadings/component correlations -- 4.3.8 Off-diagonal structure -- 4.3.9 Uncorrelated variables -- 4.4 The problem of scaling in PCA -- 4.5 Discussion -- 4.5.1 The identification o f important components -- 4.5.2 The use o f components in subsequent analyses -- 4.6 PCA for multivariate normal data -- 4.7 Summary -- Exercises -- 5: Factor analysis -- 5.1 Introduction, 5.2 The factor-analysis model -- 5.3 Estimating the factor loadings -- 5.4 Discussion -- PART THREE: PROCEDURES BASED ON THE MULTIVARIATE NORMAL DISTRIBUTION -- 6: The multivariate normal distribution -- 6.1 Introduction -- 6.2 Definition of the multivariate normal distribution -- 6.3 Properties of the multivariate normal distribution -- 6.4 Linear compounds and linear combinations -- 6.5 Estimation of the parameters of the distribution -- 6.6 The Wishart distribution -- 6.7 The joint distribution of the sample mean vector and the sample covariance matrix -- 6.8 The Hotelling T2-distribution -- Exercises -- 7: Procedures based on normal distribution theory -- 7.1 Introduction -- 7.2 One-sample procedures -- 7.3 Confidence intervals and further analysis -- 7.4 Tests of structural relations among the components of the mean -- 7.5 Two-sample procedures -- 7.6 Confidence intervals and further analysis -- 7.7 Tests of structural relations among the components of the means -- 7.8 Discriminant analysis -- Exercises -- 8: The multivariate analysis of variance -- 8.1 Introduction -- 8.2 MANOVA calculations -- 8.3 Testing hypotheses -- 8.3.1 The special case: The univariate procedure -- 8.3.2 The multivariate model for Example 8.1 -- 8.3.3 Multivariate test procedures -- 8.3.4 Distributional approximations -- 8.3.5 Applications o f the methodology -- 8.4 Further analysis -- 8.5 The dimensionality of the alternative hypothesis -- 8.6 Canonical variates analysis -- 8.7 Linear functional relationships -- 8.8 Discriminant analysis -- Exercises -- 9: The multivariate analysis of covariance and related topics -- 9.1 Introduction -- 9.2 Multivariate regression -- 9.2.1 The special case: Univariate multiple regression -- 9.2.2 The general case: Multivariate regression -- 9.3 Canonical correlation -- 9.4 The multivariate analysis of covariance, 9.4.1 The special case: Univariate analysis of covariance -- 9.4.2 The multivariate case: An example -- 9.4.3 The multivariate case: General results -- 9.5 The test for additional information -- 9.6 A test of an assigned subset of linear compounds -- Exercises -- PART FOUR: MULTIDIMENSIONAL SCALING AND CLUSTER ANALYSIS -- 10: Multidimensional scaling -- 10.1 Introduction -- 10.2 Measures of similarity and dissimilarity -- 10.2.1 Similarity coefficients for binary data -- 10.3 Classical scaling -- 10.3.1 The calculation of co-ordinate values from Euclidean distances -- 10.3.2 The relationship between classical scaling and principal component analysis -- 10.3.3 Classical scaling for a dissimilarity matrix -- 10.3.4 Interpretation of the results -- 10.3.5 Some related methods -- 10.4 Ordinal scaling -- 10.4.1 The iterative procedure -- 10.4.2 Interpreting the results -- 10.5 A comparison -- 10.6 Concluding remarks -- Exercises -- 11: Cluster analysis -- 11.1 Introduction -- 11.1.1 Objectives -- 11.1.2 Clumping, dissection and clustering variables -- 11.1.3 Some other preliminary points -- 11.2 Visual approaches to finding a partition -- 11.3 Hierarchical trees -- 11.4 Single-link clustering -- 11.5 Some other clustering procedures -- 11.5.1 Method or algorithm? 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Chatfield, Christopher 1941- VerfasserIn (DE-588)128358750 (DE-627)372613802 (DE-576)297097814 aut, Introduction to multivariate analysis Christopher Chatfield, Alexander J. Collins, School of Mathematics, University of Bath, United Kingdom, First edition, Boca Raton London New York Washington, D.C. Chapman and Hall/CRC 1980, 1 Online-Ressource (x, 246 Seiten), Text txt rdacontent, Computermedien c rdamedia, Online-Ressource cr rdacarrier, Chapman and Hall/CRC texts in statistical science, Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Preface -- PART ONE: INTRODUCTION -- 1: Introduction -- 1.1 Examples -- 1.2 Notation -- 1.3 Review of objectives and different approaches -- 1.4 Some general comments -- 1.5 Review of books on multivariate analysis -- 1.6 Some matrix algebra revision -- 1.7 The general linear model -- Exercises -- 2: Multivariate distributions -- 2.1 Multivariate, marginal and conditional distributions -- 2.2 Means, variances, covariances and correlations -- 2.3 The multivariate normal distribution -- 2.4 The bivariate normal distribution -- 2.5 Other multivariate distributions -- 2.5.1 Multivariate discrete distributions -- 2.5.2 Multivariate continuous distributions -- Exercises -- 3: Preliminary data analysis -- 3.1 Processing the data -- 3.1.1 Data editing -- 3.2 Calculating summary statistics -- 3.2.1 Interpreting the sample correlation matrix -- 3.2.2 The rank of R -- 3.3 Plotting the data -- 3.4 The analysis of discrete data -- Exercises -- PART TWO: FINDING NEW UNDERLYING VARIABLES -- 4: Principal component analysis -- 4.1 Introduction -- 4.2 Derivation of principal components -- 4.2.1 Principal components from the correlation matrix -- 4.2.2 Estimating the principal components -- 4.3 Further results on PCA -- 4.3.1 Mean-corrected component scores -- 4.3.2 The inverse transformation -- 4.3.3 Zero eigenvalues -- 4.3.4 Small eigenvalues -- 4.3.5 Repeated roots -- 4.3.6 Orthogonality -- 4.3.7 Component loadings/component correlations -- 4.3.8 Off-diagonal structure -- 4.3.9 Uncorrelated variables -- 4.4 The problem of scaling in PCA -- 4.5 Discussion -- 4.5.1 The identification o f important components -- 4.5.2 The use o f components in subsequent analyses -- 4.6 PCA for multivariate normal data -- 4.7 Summary -- Exercises -- 5: Factor analysis -- 5.1 Introduction, 5.2 The factor-analysis model -- 5.3 Estimating the factor loadings -- 5.4 Discussion -- PART THREE: PROCEDURES BASED ON THE MULTIVARIATE NORMAL DISTRIBUTION -- 6: The multivariate normal distribution -- 6.1 Introduction -- 6.2 Definition of the multivariate normal distribution -- 6.3 Properties of the multivariate normal distribution -- 6.4 Linear compounds and linear combinations -- 6.5 Estimation of the parameters of the distribution -- 6.6 The Wishart distribution -- 6.7 The joint distribution of the sample mean vector and the sample covariance matrix -- 6.8 The Hotelling T2-distribution -- Exercises -- 7: Procedures based on normal distribution theory -- 7.1 Introduction -- 7.2 One-sample procedures -- 7.3 Confidence intervals and further analysis -- 7.4 Tests of structural relations among the components of the mean -- 7.5 Two-sample procedures -- 7.6 Confidence intervals and further analysis -- 7.7 Tests of structural relations among the components of the means -- 7.8 Discriminant analysis -- Exercises -- 8: The multivariate analysis of variance -- 8.1 Introduction -- 8.2 MANOVA calculations -- 8.3 Testing hypotheses -- 8.3.1 The special case: The univariate procedure -- 8.3.2 The multivariate model for Example 8.1 -- 8.3.3 Multivariate test procedures -- 8.3.4 Distributional approximations -- 8.3.5 Applications o f the methodology -- 8.4 Further analysis -- 8.5 The dimensionality of the alternative hypothesis -- 8.6 Canonical variates analysis -- 8.7 Linear functional relationships -- 8.8 Discriminant analysis -- Exercises -- 9: The multivariate analysis of covariance and related topics -- 9.1 Introduction -- 9.2 Multivariate regression -- 9.2.1 The special case: Univariate multiple regression -- 9.2.2 The general case: Multivariate regression -- 9.3 Canonical correlation -- 9.4 The multivariate analysis of covariance, 9.4.1 The special case: Univariate analysis of covariance -- 9.4.2 The multivariate case: An example -- 9.4.3 The multivariate case: General results -- 9.5 The test for additional information -- 9.6 A test of an assigned subset of linear compounds -- Exercises -- PART FOUR: MULTIDIMENSIONAL SCALING AND CLUSTER ANALYSIS -- 10: Multidimensional scaling -- 10.1 Introduction -- 10.2 Measures of similarity and dissimilarity -- 10.2.1 Similarity coefficients for binary data -- 10.3 Classical scaling -- 10.3.1 The calculation of co-ordinate values from Euclidean distances -- 10.3.2 The relationship between classical scaling and principal component analysis -- 10.3.3 Classical scaling for a dissimilarity matrix -- 10.3.4 Interpretation of the results -- 10.3.5 Some related methods -- 10.4 Ordinal scaling -- 10.4.1 The iterative procedure -- 10.4.2 Interpreting the results -- 10.5 A comparison -- 10.6 Concluding remarks -- Exercises -- 11: Cluster analysis -- 11.1 Introduction -- 11.1.1 Objectives -- 11.1.2 Clumping, dissection and clustering variables -- 11.1.3 Some other preliminary points -- 11.2 Visual approaches to finding a partition -- 11.3 Hierarchical trees -- 11.4 Single-link clustering -- 11.5 Some other clustering procedures -- 11.5.1 Method or algorithm? -- 11.6 A comparison of procedures -- 11.6.1 Some desirable conditions for hierarchical clustering methods -- 11.6.2 A comparison -- Exercises -- References -- Answers to exercises -- Name Index -- Subject Index, 2018 |2018||||||||||, Collins, Alexander J. VerfasserIn aut, https://www.taylorfrancis.com/books/9780203749999 Verlag Volltext, https://doi.org/10.1201/9780203749999 Resolving-System Volltext, https://www.taylorfrancis.com/books/9780203749999 DE-Ch1, DE-Ch1 epn:3469259712 2019-05-06T11:30:58Z, https://doi.org/10.1201/9780203749999 Zum Online-Dokument DE-Zi4, DE-Zi4 epn:3519263831 2019-10-01T14:38:07Z |
| spellingShingle |
Chatfield, Christopher, Collins, Alexander J., Introduction to multivariate analysis, Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Preface -- PART ONE: INTRODUCTION -- 1: Introduction -- 1.1 Examples -- 1.2 Notation -- 1.3 Review of objectives and different approaches -- 1.4 Some general comments -- 1.5 Review of books on multivariate analysis -- 1.6 Some matrix algebra revision -- 1.7 The general linear model -- Exercises -- 2: Multivariate distributions -- 2.1 Multivariate, marginal and conditional distributions -- 2.2 Means, variances, covariances and correlations -- 2.3 The multivariate normal distribution -- 2.4 The bivariate normal distribution -- 2.5 Other multivariate distributions -- 2.5.1 Multivariate discrete distributions -- 2.5.2 Multivariate continuous distributions -- Exercises -- 3: Preliminary data analysis -- 3.1 Processing the data -- 3.1.1 Data editing -- 3.2 Calculating summary statistics -- 3.2.1 Interpreting the sample correlation matrix -- 3.2.2 The rank of R -- 3.3 Plotting the data -- 3.4 The analysis of discrete data -- Exercises -- PART TWO: FINDING NEW UNDERLYING VARIABLES -- 4: Principal component analysis -- 4.1 Introduction -- 4.2 Derivation of principal components -- 4.2.1 Principal components from the correlation matrix -- 4.2.2 Estimating the principal components -- 4.3 Further results on PCA -- 4.3.1 Mean-corrected component scores -- 4.3.2 The inverse transformation -- 4.3.3 Zero eigenvalues -- 4.3.4 Small eigenvalues -- 4.3.5 Repeated roots -- 4.3.6 Orthogonality -- 4.3.7 Component loadings/component correlations -- 4.3.8 Off-diagonal structure -- 4.3.9 Uncorrelated variables -- 4.4 The problem of scaling in PCA -- 4.5 Discussion -- 4.5.1 The identification o f important components -- 4.5.2 The use o f components in subsequent analyses -- 4.6 PCA for multivariate normal data -- 4.7 Summary -- Exercises -- 5: Factor analysis -- 5.1 Introduction, 5.2 The factor-analysis model -- 5.3 Estimating the factor loadings -- 5.4 Discussion -- PART THREE: PROCEDURES BASED ON THE MULTIVARIATE NORMAL DISTRIBUTION -- 6: The multivariate normal distribution -- 6.1 Introduction -- 6.2 Definition of the multivariate normal distribution -- 6.3 Properties of the multivariate normal distribution -- 6.4 Linear compounds and linear combinations -- 6.5 Estimation of the parameters of the distribution -- 6.6 The Wishart distribution -- 6.7 The joint distribution of the sample mean vector and the sample covariance matrix -- 6.8 The Hotelling T2-distribution -- Exercises -- 7: Procedures based on normal distribution theory -- 7.1 Introduction -- 7.2 One-sample procedures -- 7.3 Confidence intervals and further analysis -- 7.4 Tests of structural relations among the components of the mean -- 7.5 Two-sample procedures -- 7.6 Confidence intervals and further analysis -- 7.7 Tests of structural relations among the components of the means -- 7.8 Discriminant analysis -- Exercises -- 8: The multivariate analysis of variance -- 8.1 Introduction -- 8.2 MANOVA calculations -- 8.3 Testing hypotheses -- 8.3.1 The special case: The univariate procedure -- 8.3.2 The multivariate model for Example 8.1 -- 8.3.3 Multivariate test procedures -- 8.3.4 Distributional approximations -- 8.3.5 Applications o f the methodology -- 8.4 Further analysis -- 8.5 The dimensionality of the alternative hypothesis -- 8.6 Canonical variates analysis -- 8.7 Linear functional relationships -- 8.8 Discriminant analysis -- Exercises -- 9: The multivariate analysis of covariance and related topics -- 9.1 Introduction -- 9.2 Multivariate regression -- 9.2.1 The special case: Univariate multiple regression -- 9.2.2 The general case: Multivariate regression -- 9.3 Canonical correlation -- 9.4 The multivariate analysis of covariance, 9.4.1 The special case: Univariate analysis of covariance -- 9.4.2 The multivariate case: An example -- 9.4.3 The multivariate case: General results -- 9.5 The test for additional information -- 9.6 A test of an assigned subset of linear compounds -- Exercises -- PART FOUR: MULTIDIMENSIONAL SCALING AND CLUSTER ANALYSIS -- 10: Multidimensional scaling -- 10.1 Introduction -- 10.2 Measures of similarity and dissimilarity -- 10.2.1 Similarity coefficients for binary data -- 10.3 Classical scaling -- 10.3.1 The calculation of co-ordinate values from Euclidean distances -- 10.3.2 The relationship between classical scaling and principal component analysis -- 10.3.3 Classical scaling for a dissimilarity matrix -- 10.3.4 Interpretation of the results -- 10.3.5 Some related methods -- 10.4 Ordinal scaling -- 10.4.1 The iterative procedure -- 10.4.2 Interpreting the results -- 10.5 A comparison -- 10.6 Concluding remarks -- Exercises -- 11: Cluster analysis -- 11.1 Introduction -- 11.1.1 Objectives -- 11.1.2 Clumping, dissection and clustering variables -- 11.1.3 Some other preliminary points -- 11.2 Visual approaches to finding a partition -- 11.3 Hierarchical trees -- 11.4 Single-link clustering -- 11.5 Some other clustering procedures -- 11.5.1 Method or algorithm? -- 11.6 A comparison of procedures -- 11.6.1 Some desirable conditions for hierarchical clustering methods -- 11.6.2 A comparison -- Exercises -- References -- Answers to exercises -- Name Index -- Subject Index |
| title |
Introduction to multivariate analysis |
| title_auth |
Introduction to multivariate analysis |
| title_full |
Introduction to multivariate analysis Christopher Chatfield, Alexander J. Collins, School of Mathematics, University of Bath, United Kingdom |
| title_fullStr |
Introduction to multivariate analysis Christopher Chatfield, Alexander J. Collins, School of Mathematics, University of Bath, United Kingdom |
| title_full_unstemmed |
Introduction to multivariate analysis Christopher Chatfield, Alexander J. Collins, School of Mathematics, University of Bath, United Kingdom |
| title_short |
Introduction to multivariate analysis |
| title_sort |
introduction to multivariate analysis |
| title_unstemmed |
Introduction to multivariate analysis |
| url |
https://www.taylorfrancis.com/books/9780203749999, https://doi.org/10.1201/9780203749999 |
