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Methods of Multivariate Analysis

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ISBN-10: 0470178965

ISBN-13: 9780470178966

Edition: 3rd 2012

Authors: Alvin C. Rencher, William F. Christensen

List price: $110.00
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Description:

This new edition, now with a co-author, offers a complete and up-to-date examination of the field. The authors have streamlined previously tedious topics, such as multivariate regression and MANOVA techniques, to add newer, more timely content. Each chapter contains exercises, providing readers with the opportunity to test and extend their understanding. The new edition also presents several expanded topics in Kronecker product; prediction errors; maximum likelihood estimation; and selective key, but accessible proofs. This resource meets the needs of both statistics majors and those of students and professionals in other fields.
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Book details

List price: $110.00
Edition: 3rd
Copyright year: 2012
Publisher: John Wiley & Sons, Limited
Publication date: 7/27/2012
Binding: Hardcover
Pages: 800
Size: 6.50" wide x 9.50" long x 2.00" tall
Weight: 3.014

Preface
Acknowledgments
Introduction
Why Multivariate Analysis?
Prerequisites
Objectives
Basic Types of Data And Analysis
Matrix Algebra
Introduction
Notation and Basic Definitions
Operations
Partitioned Matrices
Rank
Inverse
Positive Definite Matrices
Determinants
Trace
Orthogonal Vectors and Matrices
Eigenvalues and Eigenvectors
Kronecker and VEC Notation
Problems
Characterizing and Displaying Multivariate Data
Mean and Variance of a Univariate Random Variable
Covariance and Correlation Of Bivariate Random Variables
Scatter Plots of Bivariate Samples
Graphical Displays for Multivariate Samples
Dynamic Graphics
Mean Vectors
Covariance Matrices
Correlation Matrices
Mean Vectors and Covariance Matrices for Subsets of Variables
Two Subsets
Three or More Subsets
Linear Combinations of Variables
Sample Properties
Population Properties
Measures of Overall Variability
Estimation of Missing Values
Distance Between Vectors
Problems
The Multivariate Normal Distribution
Multivariate Normal Density Function
Properties of Multivariate Normal Random Variables
Estimation in the Multivariate Normal
Assessing Multivariate Normality
Transformations to Normality
Outliers
Problems
Tests on One or Two Mean Vectors
Multivariate Versus Univariate Tests
Tests on � With ??Known
Tests on � When ??is Unknown
Comparing two Mean Vectors
Tests on Individual Variables Conditional on Rejection of H0 by the T2-test
Computation of T2
Paired Observations Test
Test for Additional Information
Profile Analysis
Profile Analysis
Problems
Multivariate Analysis of Variance
One-way Models
Comparison of the Four Manova Test Statistics
Contrasts
Tests on Individual Variables Following Rejection of H0 by the Overall Manova Test
Two-Way Classification
Other Models
Checking on the Assumptions
Profile Analysis
Repeated Measures Designs
Growth Curves
Tests on a Subvector
Problems
Tests on Covariance Matrices
Introduction
Testing a Specified Pattern for ∑
Tests Comparing Covariance Matrices
Tests of Independence
Problems
Discriminant Analysis: Description of Group Separation
Introduction
The Discriminant Function for two Groups
Relationship Between two-group Discriminant Analysis and Multiple Regression
Discriminant Analysis for Several Groups
Standardized Discriminant Functions
Tests of Significance
Interpretation of Discriminant Functions
Scatter Plots
Stepwise Selection of Variables
Problems
Classification Analysis: Allocation of Observations to Groups
Introduction
Classification into two Groups
Classification into Several Groups
Estimating Misclassification Rates
Improved Estimates of Error Rates
Subset Selection
Nonparametric Procedures
Problems
Multivariate Regression
Introduction
Multiple Regression: Fixed X’s
Multiple Regression: Random X’s
Multivariate Multiple Regression: Estimation
Multivariate Multiple Regression: Hypothesis Tests
Multivariate Multiple Regression: Prediction
Measures of Association Between the Y’s and the X’s
Subset Selection
Multivariate Regression: Random X’s
Problems
Canonical Correlation
Introduction
Canonical Correlations and Canonical Variates
Properties of Canonical Correlations
Tests of Significance
Interpretation
Relationships of Canonical Correlation Analysis to Other Multivariate Problems
Principal Component Analysis
Introduction
Geometric and Algebraic Bases of Principal Components
Principal Components and Perpendicular Regression
Plotting of Principal Components
Principal Components from the Correlation Matrix
Deciding How Many Components to Retain
Information in the Last Few Principal Components
Interpretation of Principal Components
Selection of Variables
Problems
Exploratory Factor Analysis
Introduction
Orthogonal Factor Model
Estimation of Loadings and Communalities
Choosing the Number of Factors, m
Rotation
Factor Scores
Validity of the Factor Analysis Model
Relationship of Factor Analysis to Principal Component Analysis
Problems
Confirmatory Factor Analysis
Introduction
Model Specification and Identification
Parameter Estimation and Model Assessment
Inference for Model Parameters
Factor Scores
Problems
Cluster Analysis
Introduction
Measures of Similarity or Dissimilarity
Hierarchical Clustering
Nonhierarchical Methods
Choosing the Number of Clusters
Cluster Validity
Clustering Variables
Problems
Graphical Procedures
Multidimensional Scaling
Correspondence Analysis
Biplots
Problems
Tables
Answers and Hints to Problems
Data Sets and SAS Files
References
Index