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Introduction to Applied Multivariate Analysis

ISBN-10: 0805863753
ISBN-13: 9780805863758
Edition: 2008
List price: $115.00 Buy it from $75.98
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Book details

List price: $115.00
Copyright year: 2008
Publisher: Taylor & Francis Group
Publication date: 3/10/2008
Binding: Hardcover
Pages: 496
Size: 6.00" wide x 9.25" long x 1.50" tall
Weight: 1.760
Language: English

Preface
Introduction to Multivariate Statistics
Definition of Multivariate Statistics
Relationship of Multivariate Statistics to Univariate Statistics
Choice of Variables and Multivariate Method, and the Concept of Optimal Linear Combination
Data for Multivariate Analyses
Three Fundamental Matrices in Multivariate Statistics
Covariance Matrix
Correlation Matrix
Sums-of-Squares and Cross-Products Matrix
Illustration Using Statistical Software
Elements of Matrix Theory
Matrix Definition
Matrix Operations, Determinant, and Trace
Using SPSS and SAS for Matrix Operations
General Form of Matrix Multiplications With Vector, and Representation of the Covariance, Correlation, and Sum-of-Squares and Cross-Product Matrices
Linear Modeling and Matrix Multiplication
Three Fundamental Matrices of Multivariate Statistics in Compact Form
Raw Data Points in Higher Dimensions, and Distance Between Them
Data Screening and Preliminary Analyses
Initial Data Exploration
Outliers and the Search for Them
Univariate Outliers
Multivariate Outliers
Handling Outliers: A Revisit
Checking of Variable Distribution Assumptions
Variable Transformations
Multivariate Analysis of Group Differences
A Start-Up Example
A Definition of the Multivariate Normal Distribution
Testing Hypotheses About a Multivariate Mean
The Case of Known Covariance Matrix
The Case of Unknown Covariance Matrix
Testing Hypotheses About Multivariate Means of Two Groups
Two Related or Matched Samples (Change Over Time)
Two Unrelated (Independent) Samples
Testing Hypotheses About Multivariate Means in One-Way and Higher Order Designs (Multivariate Analysis of Variance, MANOVA)
Statistical Significance Versus Practical Importance
Higher Order MANOVA Designs
Other Test Criteria
MANOVA Follow-Up Analyses
Limitations and Assumptions of MANOVA
Repeated Measure Analysis of Variance
Between-Subject and Within-Subject Factors and Designs
Univariate Approach to Repeated Measure Analysis
Multivariate Approach to Repeated Measure Analysis
Comparison of Univariate and Multivariate Approaches to Repeated Measure Analysis
Analysis of Covariance
Logic of Analysis of Covariance
Multivariate Analysis of Covariance
Step-Down Analysis (Roy-Bargmann Analysis)
Assumptions of Analysis of Covariance
Principal Component Analysis
Introduction
Beginnings of Principal Component Analysis
How Does Principal Component Analysis Proceed?
Illustrations of Principal Component Analysis
Analysis of the Covariance Matrix [Sigma] (S) of the Original Variables
Analysis of the Correlation Matrix P (R) of the Original Variables
Using Principal Component Analysis in Empirical Research
Multicollinearity Detection
PCA With Nearly Uncorrelated Variables Is Meaningless
Can PCA Be Used as a Method for Observed Variable Elimination?
Which Matrix Should Be Analyzed?
PCA as a Helpful Aid in Assessing Multinormality
PCA as "Orthogonal" Regression
PCA Is Conducted via Factor Analysis Routines in Some Software
PCA as a Rotation of Original Coordinate Axes
PCA as a Data Exploratory Technique
Exploratory Factor Analysis
Introduction
Model of Factor Analysis
How Does Factor Analysis Proceed?
Factor Extraction
Principal Component Method
Maximum Likelihood Factor Analysis
Factor Rotation
Orthogonal Rotation
Oblique Rotation
Heywood Cases
Factor Score Estimation
Weighted Least Squares Method (Generalized Least Squares Method)
Regression Method
Comparison of Factor Analysis and Principal Component Analysis
Confirmatory Factor Analysis
Introduction
A Start-Up Example
Confirmatory Factor Analysis Model
Fitting Confirmatory Factor Analysis Models
A Brief Introduction to Mplus, and Fitting the Example Model
Testing Parameter Restrictions in Confirmatory Factor Analysis Models
Specification Search and Model Fit Improvement
Fitting Confirmatory Factor Analysis Models to the Mean and Covariance Structure
Examining Group Differences on Latent Variables
Discriminant Function Analysis
Introduction
What Is Discriminant Function Analysis?
Relationship of Discriminant Function Analysis to Other Multivariate Statistical Methods
Discriminant Function Analysis With Two Groups
Relationship Between Discriminant Function and Regression Analysis With Two Groups
Discriminant Function Analysis With More Than Two Groups
Tests in Discriminant Function Analysis
Limitations of Discriminant Function Analysis
Canonical Correlation Analysis
Introduction
How Does Canonical Correlation Analysis Proceed?
Tests and Interpretation of Canonical Variates
Canonical Correlation Approach to Discriminant Analysis
Generality of Canonical Correlation Analysis
An Introduction to the Analysis of Missing Data
Goals of Missing Data Analysis
Patterns of Missing Data
Mechanisms of Missing Data
Missing Completely at Random
Missing at Random
Ignorable Missingness and Nonignorable Missingness Mechanisms
Traditional Ways of Dealing With Missing Data
Listwise Deletion
Pairwise Deletion
Dummy Variable Adjustment
Simple Imputation Methods
Weighting Methods
Full Information Maximum Likelihood and Multiple Imputation
Examining Group Differences and Similarities in the Presence of Missing Data
Examining Group Mean Differences With Incomplete Data
Testing for Group Differences in the Covariance and Correlation Matrices With Missing Data
Multivariate Analysis of Change Processes
Introduction
Modeling Change Over Time With Time-Invariant and Time-Varying Covariates
Intercept-and-Slope Model
Inclusion of Time-Varying and Time-Invariant Covariates
An Example Application
Testing Parameter Restrictions
Modeling General Forms of Change Over Time
Level-and-Shape Model
Empirical Illustration
Testing Special Patterns of Growth or Decline
Possible Causes of Inadmissible Solutions
Modeling Change Over Time With Incomplete Data
Variable Naming and Order for Data Files
References
Author Index
Subject Index

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