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E-grāmata: Applied Multivariate Analysis

  • Formāts: PDF+DRM
  • Sērija : Springer Texts in Statistics
  • Izdošanas datums: 21-Jun-2007
  • Izdevniecība: Springer-Verlag New York Inc.
  • Valoda: eng
  • ISBN-13: 9780387227719
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Applied Multivariate AnalysisPalielināt
  • Formāts: PDF+DRM
  • Sērija : Springer Texts in Statistics
  • Izdošanas datums: 21-Jun-2007
  • Izdevniecība: Springer-Verlag New York Inc.
  • Valoda: eng
  • ISBN-13: 9780387227719
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Univariate statistical analysis is concerned with techniques for the analysis of a single random variable. This book is about applied multivariate analysis. It was written to p- vide students and researchers with an introduction to statistical techniques for the ana- sis of continuous quantitative measurements on several random variables simultaneously. While quantitative measurements may be obtained from any population, the material in this text is primarily concerned with techniques useful for the analysis of continuous obser- tions from multivariate normal populations with linear structure. While several multivariate methods are extensions of univariate procedures, a unique feature of multivariate data an- ysis techniques is their ability to control experimental error at an exact nominal level and to provide information on the covariance structure of the data. These features tend to enhance statistical inference, making multivariate data analysis superior to univariate analysis. While in a previous edition of my textbook on multivariate analysis, I tried to precede a multivariate method with a corresponding univariate procedure when applicable, I have not taken this approach here. Instead, it is assumed that the reader has taken basic courses in multiple linear regression, analysis of variance, and experimental design. While students may be familiar with vector spaces and matrices, important results essential to multivariate analysis are reviewed in Chapter 2. I have avoided the use of calculus in this text.

Recenzijas

From the reviews:



"This book is more than an up-to-date textbook on multivariate analysis. It could enable SAS users to take full and informed advantage of the many options offered in the SAS procedures. For non-SAS users, the clear statement of the models should enable them to fit and interpret them with other software."



ISI Short Book Reviews, Vol. 23/2, August 2003



"This textbook is another comprehensive work on applied multivariate analysis. Basic theory and methods are reviewed and illustrated by a number of examples and practices. The author has written a useful textbook combining most of general theory and practice of multivariate data analysis. The book is suitable to familiarize students at graduate level with main concepts and principles of multivariate analysis." (Dr. ir. M. H. J. de Bruijne, Kwantitatieve Methoden, Vol. 70B37, 2003)



"This text is on the analysis of structured data . The author has managed to encapsulate so much in this book by giving a clear statement of each model . This book is more than an up-to date textbook on multivariate analysis. It could enable SAS users to take full and informed advantage of the many options offered in the SAS procedures. For non-SAS users, the clear statement of the models should enable them to fit and interpret them with other software." (J. M. Juritz, Short Book Reviews, Vol. 23 (2), 2003)



"I was extremely pleased to see this book arrive. For each subject, all important equations and distributional results are very clearly stated. I found this book exciting, interesting and informative. The exercises are quite well chosen . In summary, Applied Multivariate Analysis is an excellent book. If you want only one book on multivariate analysis, I would suggest this as a strong candidate. I am extremely glad that I own this book ." (David E. Booth, Technometrics, Vol. 45 (2), May, 2003)



"This textbook provides a broad overview of the basic theory and methods of applied multivariate analysis. The presentation integrates theory and practice including both the analysis of formal linear multivariate models and exploratory date analysis techniques. The techniques and examples discussed in the book should be helpful in the analysis of multivariate data using SAS. All programs and data sets used may be downloaded from a Web site. The book appeals to practitioners, researchers, and applied statisticians." (T. Postelnicu, Zentralblatt MATH, Vol. 1002 (2), 2003)

Papildus informācija

Springer Book Archives
Preface vii
Acknowledgments ix
List of Tables
xix
List of Figures
xxiii
1 Introduction
1(6)
1.1 Overview
1(1)
1.2 Multivariate Models and Methods
1(2)
1.3 Scope of the Book
3(4)
2 Vectors and Matrices
7(72)
2.1 Introduction
7(1)
2.2 Vectors, Vector Spaces, and Vector Subspaces
7(5)
a Vectors
7(1)
b Vector Spaces
8(1)
c Vector Subspaces
9(3)
2.3 Bases, Vector Norms, and the Algebra of Vector Spaces
12(13)
a Bases
13(1)
b Lengths, Distances, and Angles
13(2)
c Gram-Schmidt Orthogonalization Process
15(2)
d Orthogonal Spaces
17(4)
e Vector Inequalities, Vector Norms, and Statistical Distance
21(4)
2.4 Basic Matrix Operations
25(16)
a Equality, Addition, and Multiplication of Matrices
26(2)
b Matrix Transposition
28(1)
c Some Special Matrices
29(1)
d Trace and the Euclidean Matrix Norm
30(2)
e Kronecker and Hadamard Products
32(3)
f Direct Sums
35(1)
g The Vec(·) and Vech(·) Operators
35(6)
2.5 Rank, Inverse, and Determinant
41(14)
a Rank and Inverse
41(6)
b Generalized Inverses
47(3)
c Determinants
50(5)
2.6 Systems of Equations, Transformations, and Quadratic Forms
55(21)
a Systems of Equations
55(6)
b Linear Transformations
61(2)
c Projection Transformations
63(4)
d Eigenvalues and Eigenvectors
67(4)
e Matrix Norms
71(1)
f Quadratic Forms and Extrema
72(1)
g Generalized Projectors
73(3)
2.7 Limits and Asymptotics
76(3)
3 Multivariate Distributions and the Linear Model
79(106)
3.1 Introduction
79(1)
3.2 Random Vectors and Matrices
79(5)
3.3 The Multivariate Normal (MVN) Distribution
84(9)
a Properties of the Multivariate Normal Distribution
86(2)
b Estimating μ and Σ
88(2)
c The Matrix Normal Distribution
90(3)
3.4 The Chi-Square and Wishart Distributions
93(6)
a Chi-Square Distribution
93(3)
b The Wishart Distribution
96(3)
3.5 Other Multivariate Distributions
99(7)
a The Univariate t and F Distributions
99(1)
b Hotelling's T2 Distribution
99(2)
c The Beta Distribution
101(3)
d Multivariate t, F, and X2 Distributions
104(2)
3.6 The General Linear Model
106(12)
a Regression, ANOVA, and ANCOVA Models
107(3)
b Multivariate Regression, MANOVA, and MANCOVA Models
110(4)
c The Seemingly Unrelated Regression (SUR) Model
114(1)
d The General MANOVA Model (GMANOVA)
115(3)
3.7 Evaluating Normality
118(15)
3.8 Tests of Covariance Matrices
133(16)
a Tests of Covariance Matrices
133(1)
b Equality of Covariance Matrices
133(4)
c Testing for a Specific Covariance Matrix
137(1)
d Testing for Compound Symmetry
138(1)
e Tests of Sphericity
139(4)
f Tests of Independence
143(2)
g Tests for Linear Structure
145(4)
3.9 Tests of Location
149(32)
a Two-Sample Case, Σ1 = Σ2 = Σ
149(7)
b Two-Sample Case, Σ1 ≠ Σ2
156(4)
c Two-Sample Case, Nonnormality
160(1)
d Profile Analysis, One Group
160(5)
e Profile Analysis, Two Groups
165(10)
f Profile Analysis, Σ1 ≠ Σ2
175(6)
3.10 Univariate Profile Analysis
181(1)
a Univariate One-Group Profile Analysis
182(1)
b Univariate Two-Group Profile Analysis
182(1)
3.11 Power Calculations
182(3)
4 Multivariate Regression Models
185(126)
4.1 Introduction
185(1)
4.2 Multivariate Regression
186(26)
a Multiple Linear Regression
186(1)
b Multivariate Regression Estimation and Testing Hypotheses
187(6)
c Multivariate Influence Measures
193(4)
d Measures of Association, Variable Selection and Lack-of-Fit Tests
197(7)
e Simultaneous Confidence Sets for a New Observation ynew and the Elements of B
204(2)
f Random X Matrix and Model Validation: Mean Squared Error of Prediction in Multivariate Regression
206(5)
g Exogeniety in Regression
211(1)
4.3 Multivariate Regression Example
212(6)
4.4 One-Way MANOVA and MANCOVA
218(16)
a One-Way MANOVA
218(7)
b One-Way MANCOVA
225(5)
c Simultaneous Test Procedures (STP) for One-Way MANOVA/MANCOVA
230(4)
4.5 One-Way MANOVA/MANCOVA Examples
234(11)
a MANOVA (Example 4.5.1)
234(5)
b MANCOVA (Example 4.5.2)
239(6)
4.6 MANOVA/MANCOVA with Unequal Σi or Nonnormal Data
245(1)
4.7 One-Way MANOVA with Unequal Σi Example
246(1)
4.8 Two-Way MANOVA/MANCOVA
246(11)
a Two-Way MANOVA with Interaction
246(6)
b Additive Two-Way MANOVA
252(4)
c Two-Way MANCOVA
256(1)
d Tests of Nonadditivity
256(1)
4.9 Two-Way MANOVA/MANCOVA Example
257(7)
a Two-Way MANOVA (Example 4.9.1)
257(4)
b Two-Way MANCOVA (Example 4.9.2)
261(3)
4.10 Nonorthogonal Two-Way MANOVA Designs
264(6)
a Nonorthogonal Two-Way MANOVA Designs with and Without Empty Cells, and Interaction
265(3)
b Additive Two-Way MANOVA Designs With Empty Cells
268(2)
4.11 Unbalance, Nonorthogonal Designs Example
270(3)
4.12 Higher Ordered Fixed Effect, Nested and Other Designs
273(3)
4.13 Complex Design Examples
276(6)
a Nested Design (Example 4.13.1)
276(3)
b Latin Square Design (Example 4.13.2)
279(3)
4.14 Repeated Measurement Designs
282(12)
a One-Way Repeated Measures Design
282(4)
b Extended Linear Hypotheses
286(8)
4.15 Repeated Measurements and Extended Linear Hypotheses Example
294(7)
a Repeated Measures (Example 4.15.1)
294(4)
b Extended Linear Hypotheses (Example 4.15.2)
298(3)
4.16 Robustness and Power Analysis for MR Models
301(3)
4.17 Power Calculations---Power.sas
304(3)
4.18 Testing for Mean Differences with Unequal Covariance Matrices
307(4)
5 Seemingly Unrelated Regression Models
311(40)
5.1 Introduction
311(1)
5.2 The SUR Model
312(4)
a Estimation and Hypothesis Testing
312(2)
b Prediction
314(2)
5.3 Seeming Unrelated Regression Example
316(2)
5.4 The CGMANOVA Model
318(1)
5.5 CGMANOVA Example
319(1)
5.6 The GMANOVA Model
320(7)
a Overview
320(1)
b Estimation and Hypothesis Testing
321(3)
c Test of Fit
324(1)
d Subsets of Covariates
324(2)
e GMANOVA vs SUR
326(1)
f Missing Data
326(1)
5.7 GMANOVA Example
327(6)
a One Group Design (Example 5.7.1)
328(2)
b Two Group Design (Example 5.7.2)
330(3)
5.8 Tests of Nonadditivity
333(2)
5.9 Testing for Nonadditivity Example
335(2)
5.10 Lack of Fit Test
337(1)
5.11 Sum of Profile Designs
338(1)
5.12 The Multivariate SUR (MSUR) Model
339(2)
5.13 Sum of Profile Example
341(3)
5.14 Testing Model Specification in SUR Models
344(4)
5.15 Miscellanea
348(3)
6 Multivariate Random and Mixed Models
351(68)
6.1 Introduction
351(1)
6.2 Random Coefficient Regression Models
352(5)
a Model Specification
352(1)
b Estimating the Parameters
353(2)
c Hypothesis Testing
355(2)
6.3 Univariate General Linear Mixed Models
357(12)
a Model Specification
357(2)
b Covariance Structures and Model Fit
359(2)
c Model Checking
361(5)
d Balanced Variance Component Experimental Design Models
366(1)
e Multilevel Hierarchical Models
367(1)
f Prediction
368(1)
6.4 Mixed Model Examples
369(16)
a Random Coefficient Regression (Example 6.4.1)
371(5)
b Generalized Randomized Block Design (Example 6.4.2)
376(4)
c Repeated Measurements (Example 6.4.3)
380(1)
d HLM Model (Example 6.4.4)
381(4)
6.5 Mixed Multivariate Models
385(9)
a Model Specification
386(2)
b Hypothesis Testing
388(3)
c Evaluating Expected Mean Square
391(1)
d Estimating the Mean
392(1)
e Repeated Measurements Model
392(2)
6.6 Balanced Mixed Multivariate Models Examples
394(6)
a Two-way Mixed MANOVA
395(1)
b Multivariate Split-Plot Design
395(5)
6.7 Double Multivariate Model (DMM)
400(3)
6.8 Double Multivariate Model Examples
403(12)
a Double Multivariate MANOVA (Example 6.8.1)
404(3)
b Split-Plot Design (Example 6.8.2)
407(8)
6.9 Multivariate Hierarchical Linear Models
415(2)
6.10 Tests of Means with Unequal Covariance Matrices
417(2)
7 Discriminant and Classification Analysis
419(26)
7.1 Introduction
419(1)
7.2 Two Group Discrimination and Classification
420(9)
a Fisher's Linear Discriminant Function
421(1)
b Testing Discriminant Function Coefficients
422(2)
c Classification Rules
424(3)
d Evaluating Classification Rules
427(2)
7.3 Two Group Discriminant Analysis Example
429(5)
a Egyptian Skull Data (Example 7.3.1)
429(3)
b Brain Size (Example 7.3.2)
432(2)
7.4 Multiple Group Discrimination and Classification
434(6)
a Fisher's Linear Discriminant Function
434(1)
b Testing Discriminant Functions for Significance
435(2)
c Variable Selection
437(1)
d Classification Rules
438(1)
e Logistic Discrimination and Other Topics
439(1)
7.5 Multiple Group Discriminant Analysis Example
440(5)
8 Principal Component, Canonical Correlation, and Exploratory Factor Analysis
445(70)
8.1 Introduction
445(1)
8.2 Principal Component Analysis
445(15)
a Population Model for PCA
446(3)
b Number of Components and Component Structure
449(4)
c Principal Components with Covariates
453(2)
d Sample PCA
455(3)
e Plotting Components
458(1)
f Additional Comments
458(1)
g Outlier Detection
458(2)
8.3 Principal Component Analysis Examples
460(8)
a Test Battery (Example 8.3.1)
460(1)
b Semantic Differential Ratings (Example 8.3.2)
461(4)
c Performance Assessment Program (Example 8.3.3)
465(3)
8.4 Statistical Tests in Principal Component Analysis
468(6)
a Tests Using the Covariance Matrix
468(4)
b Tests Using a Correlation Matrix
472(2)
8.5 Regression on Principal Components
474(2)
a GMANOVA Model
475(1)
b The PCA Model
475(1)
8.6 Multivariate Regression on Principal Components Example
476(1)
8.7 Canonical Correlation Analysis
477(15)
a Population Model for CCA
477(5)
b Sample CCA
482(1)
c Tests of Significance
483(2)
d Association and Redundancy
485(2)
e Partial, Part and Bipartial Canonical Correlation
487(3)
f Predictive Validity in Multivariate Regression using CCA
490(1)
g Variable Selection and Generalized Constrained CCA
491(1)
8.8 Canonical Correlation Analysis Examples
492(4)
a Rohwer CCA (Example 8.8.1)
492(2)
b Partial and Part CCA (Example 8.8.2)
494(2)
8.9 Exploratory Factor Analysis
496(15)
a Population Model for EFA
497(5)
b Estimating Model Parameters
502(4)
c Determining Model Fit
506(1)
d Factor Rotation
507(2)
e Estimating Factor Scores
509(1)
f Additional Comments
510(1)
8.10 Exploratory Factor Analysis Examples
511(4)
a Performance Assessment Program (PAP---Example 8.10.1)
511(1)
b Di Vesta and Walls (Example 8.10.2)
512(1)
c Shin (Example 8.10.3)
512(3)
9 Cluster Analysis and Multidimensional Scaling
515(42)
9.1 Introduction
515(1)
9.2 Proximity Measures
516(6)
a Dissimilarity Measures
516(3)
b Similarity Measures
519(3)
c Clustering Variables
522(1)
9.3 Cluster Analysis
522(11)
a Agglomerative Hierarchical Clustering Methods
523(7)
b Nonhierarchical Clustering Methods
530(1)
c Number of Clusters
531(2)
d Additional Comments
533(1)
9.4 Cluster Analysis Examples
533(8)
a Protein Consumption (Example 9.4.1)
534(2)
b Nonhierarchical Method (Example 9.4.2)
536(2)
c Teacher Perception (Example 9.4.3)
538(3)
d Cedar Project (Example 9.4.4)
541(1)
9.5 Multidimensional Scaling
541(7)
a Classical Metric Scaling
542(2)
b Nonmetric Scaling
544(3)
c Additional Comments
547(1)
9.6 Multidimensional Scaling Examples
548(9)
a Classical Metric Scaling (Example 9.6.1)
549(1)
b Teacher Perception (Example 9.6.2)
550(3)
c Nation (Example 9.6.3)
553(4)
10 Structural Equation Models
557(52)
10.1 Introduction
557(1)
10.2 Path Diagrams, Basic Notation, and the General Approach
558(9)
10.3 Confirmatory Factor Analysis
567(8)
10.4 Confirmatory Factor Analysis Examples
575(5)
a Performance Assessment 3 -- Factor Model (Example 10.4.1)
575(3)
b Performance Assessment 5-Factor Model (Example 10.4.2)
578(2)
10.5 Path Analysis
580(6)
10.6 Path Analysis Examples
586(8)
a Community Structure and Industrial Conflict (Example 10.6.1)
586(4)
b Nonrecursive Model (Example 10.6.2)
590(4)
10.7 Structural Equations with Manifest and Latent Variables
594(1)
10.8 Structural Equations with Manifest and Latent Variables Example
595(5)
10.9 Longitudinal Analysis with Latent Variables
600(4)
10.10 Exogeniety in Structural Equation Models
604(5)
Appendix 609(16)
References 625(42)
Author Index 667(8)
Subject Index 675
"This book is more than an up-to-date textbook on multivariate analysis. It could enable SAS users to take full and informed advantage of the many options offered in the SAS procedures. For non-SAS users, the clear statement of the models should enable them to fit and interpret them with other software."



ISI Short Book Reviews, Vol. 23/2, August 2003
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