Eintrag weiter verarbeiten
Introduction to multivariate analysis
Gespeichert in:
| Personen und Körperschaften: | , |
|---|---|
| Titel: | Introduction to multivariate analysis/ Christopher Chatfield, Alexander J. Collins, School of Mathematics, University of Bath, United Kingdom |
| Ausgabe: | First edition |
| Format: | E-Book |
| Sprache: | Englisch |
| veröffentlicht: |
Boca Raton, London, New York, Washington, D.C.
Chapman and Hall/CRC
1980
2018 |
| Gesamtaufnahme: |
Chapman and Hall/CRC texts in statistical science |
| Quelle: | Verbunddaten SWB |
| Zugangsinformationen: | Elektronischer Volltext - Campuslizenz |
| Zusammenfassung: |
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 |
|---|---|
| Umfang: | 1 Online-Ressource (x, 246 Seiten) |
| ISBN: |
9780203749999
|
| DOI: | 10.1201/9780203749999 |