An Introduction to Applied Multivariate Analysis

by Raykov; Tenko

• ISBN13: 9780805863758
• ISBN10: 0805863753
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-03-10
• Publisher: Routledge/Psych

Summary

This comprehensive text introduces readers to the most commonly used multivariate techniques at an introductory, non-technical level. By focusing on the fundamentals, readers are better prepared for more advanced applied pursuits, particularly on topics that are most critical to the behavioral, social, and educational sciences. Analogies between the already familiar univariate statistics and multivariate statistics are emphasized throughout. The authors examine in detail how each multivariate technique can be implemented using SPSS and SAS and Mplus in the book's later chapters. Important assumptions are discussed along the way along with tips for how to deal with pitfalls the reader may encounter. Mathematical formulas are used only in their definitional meaning rather than as elements of formal proofs. A book specific website - www.psypress.com/applied-multivariate-analysis - provides files with all of the data used in the text so readers can replicate the results. The Appendix explains the data files and its variables. The software code (for SAS and Mplus) and the menu option selections for SPSS are also discussed in the book. The book is distinguished by its use of latent variable modeling to address multivariate questions specific to behavioral and social scientists including missing data analysis and longitudinal data modeling. Ideal for graduate and advanced undergraduate students in the behavioral, social, and educational sciences, this book will also appeal to researchers in these disciplines who have limited familiarity with multivariate statistics. Recommended prerequisites include an introductory statistics course with exposure to regression analysis and some familiarity with SPSS and SAS.

Author Biography

Tenko Raykov is a Professor of Measurement and Quantitative Methods at Michigan State University. He received his Ph.D. in Mathematical Psychology from Humboldt University in Berlin. He is an editorial board member of the British Journal of Mathematical and Statistical Psychology, Multivariate Behavioral Research, Psychological Methods, and Structural Equation Modeling George A. Marcoulides is a Professor of Research Methods and Statistics at the University of California, Riverside. He is the Editor of Structural Equation Modeling, the Quantitative Methodology Series, and an editorial board member of numerous other measurement and statistics journals

Table of Contents

Preface	p. ix
Introduction to Multivariate Statistics
Definition of Multivariate Statistics	p. 1
Relationship of Multivariate Statistics to Univariate Statistics	p. 5
Choice of Variables and Multivariate Method, and the Concept of Optimal Linear Combination	p. 7
Data for Multivariate Analyses	p. 8
Three Fundamental Matrices in Multivariate Statistics	p. 11
Covariance Matrix	p. 12
Correlation Matrix	p. 13
Sums-of-Squares and Cross-Products Matrix	p. 15
Illustration Using Statistical Software	p. 17
Elements of Matrix Theory
Matrix Definition	p. 31
Matrix Operations, Determinant, and Trace	p. 33
Using SPSS and SAS for Matrix Operations	p. 46
General Form of Matrix Multiplications With Vector, and Representation of the Covariance, Correlation, and Sum-of-Squares and Cross-Product Matrices	p. 50
Linear Modeling and Matrix Multiplication	p. 50
Three Fundamental Matrices of Multivariate Statistics in Compact Form	p. 51
Raw Data Points in Higher Dimensions, and Distance Between Them	p. 54
Data Screening and Preliminary Analyses
Initial Data Exploration	p. 61
Outliers and the Search for Them	p. 69
Univariate Outliers	p. 69
Multivariate Outliers	p. 71
Handling Outliers: A Revisit	p. 78
Checking of Variable Distribution Assumptions	p. 80
Variable Transformations	p. 83
Multivariate Analysis of Group Differences
A Start-Up Example	p. 99
A Definition of the Multivariate Normal Distribution	p. 101
Testing Hypotheses About a Multivariate Mean	p. 102
The Case of Known Covariance Matrix	p. 103
The Case of Unknown Covariance Matrix	p. 107
Testing Hypotheses About Multivariate Means of Two Groups	p. 110
Two Related or Matched Samples (Change Over Time)	p. 110
Two Unrelated (Independent) Samples	p. 113
Testing Hypotheses About Multivariate Means in One-Way and Higher Order Designs (Multivariate Analysis of Variance, MANOVA)	p. 116
Statistical Significance Versus Practical Importance	p. 129
Higher Order MANOVA Designs	p. 130
Other Test Criteria	p. 132
MANOVA Follow-Up Analyses	p. 143
Limitations and Assumptions of MANOVA	p. 145
Repeated Measure Analysis of Variance
Between-Subject and Within-Subject Factors and Designs	p. 148
Univariate Approach to Repeated Measure Analysis	p. 150
Multivariate Approach to Repeated Measure Analysis	p. 168
Comparison of Univariate and Multivariate Approaches to Repeated Measure Analysis	p. 179
Analysis of Covariance
Logic of Analysis of Covariance	p. 182
Multivariate Analysis of Covariance	p. 192
Step-Down Analysis (Roy-Bargmann Analysis)	p. 198
Assumptions of Analysis of Covariance	p. 203
Principal Component Analysis
Introduction	p. 211
Beginnings of Principal Component Analysis	p. 213
How Does Principal Component Analysis Proceed?	p. 220
Illustrations of Principal Component Analysis	p. 224
Analysis of the Covariance Matrix [Sigma] (S) of the Original Variables	p. 224
Analysis of the Correlation Matrix P (R) of the Original Variables	p. 224
Using Principal Component Analysis in Empirical Research	p. 234
Multicollinearity Detection	p. 234
PCA With Nearly Uncorrelated Variables Is Meaningless	p. 235
Can PCA Be Used as a Method for Observed Variable Elimination?	p. 236
Which Matrix Should Be Analyzed?	p. 236
PCA as a Helpful Aid in Assessing Multinormality	p. 237
PCA as "Orthogonal" Regression	p. 237
PCA Is Conducted via Factor Analysis Routines in Some Software	p. 237
PCA as a Rotation of Original Coordinate Axes	p. 238
PCA as a Data Exploratory Technique	p. 238
Exploratory Factor Analysis
Introduction	p. 241
Model of Factor Analysis	p. 242
How Does Factor Analysis Proceed?	p. 248
Factor Extraction	p. 248
Principal Component Method	p. 248
Maximum Likelihood Factor Analysis	p. 256
Factor Rotation	p. 262
Orthogonal Rotation	p. 266
Oblique Rotation	p. 267
Heywood Cases	p. 273
Factor Score Estimation	p. 273
Weighted Least Squares Method (Generalized Least Squares Method)	p. 274
Regression Method	p. 274
Comparison of Factor Analysis and Principal Component Analysis	p. 276
Confirmatory Factor Analysis
Introduction	p. 279
A Start-Up Example	p. 279
Confirmatory Factor Analysis Model	p. 281
Fitting Confirmatory Factor Analysis Models	p. 284
A Brief Introduction to Mplus, and Fitting the Example Model	p. 287
Testing Parameter Restrictions in Confirmatory Factor Analysis Models	p. 298
Specification Search and Model Fit Improvement	p. 300
Fitting Confirmatory Factor Analysis Models to the Mean and Covariance Structure	p. 307
Examining Group Differences on Latent Variables	p. 314
Discriminant Function Analysis
Introduction	p. 331
What Is Discriminant Function Analysis?	p. 332
Relationship of Discriminant Function Analysis to Other Multivariate Statistical Methods	p. 334
Discriminant Function Analysis With Two Groups	p. 336
Relationship Between Discriminant Function and Regression Analysis With Two Groups	p. 351
Discriminant Function Analysis With More Than Two Groups	p. 353
Tests in Discriminant Function Analysis	p. 355
Limitations of Discriminant Function Analysis	p. 364
Canonical Correlation Analysis
Introduction	p. 367
How Does Canonical Correlation Analysis Proceed?	p. 370
Tests and Interpretation of Canonical Variates	p. 372
Canonical Correlation Approach to Discriminant Analysis	p. 384
Generality of Canonical Correlation Analysis	p. 389
An Introduction to the Analysis of Missing Data
Goals of Missing Data Analysis	p. 391
Patterns of Missing Data	p. 392
Mechanisms of Missing Data	p. 394
Missing Completely at Random	p. 396
Missing at Random	p. 398
Ignorable Missingness and Nonignorable Missingness Mechanisms	p. 400
Traditional Ways of Dealing With Missing Data	p. 401
Listwise Deletion	p. 402
Pairwise Deletion	p. 402
Dummy Variable Adjustment	p. 403
Simple Imputation Methods	p. 403
Weighting Methods	p. 405
Full Information Maximum Likelihood and Multiple Imputation	p. 406
Examining Group Differences and Similarities in the Presence of Missing Data	p. 407
Examining Group Mean Differences With Incomplete Data	p. 410
Testing for Group Differences in the Covariance and Correlation Matrices With Missing Data	p. 427
Multivariate Analysis of Change Processes
Introduction	p. 433
Modeling Change Over Time With Time-Invariant and Time-Varying Covariates	p. 434
Intercept-and-Slope Model	p. 435
Inclusion of Time-Varying and Time-Invariant Covariates	p. 436
An Example Application	p. 437
Testing Parameter Restrictions	p. 442
Modeling General Forms of Change Over Time	p. 448
Level-and-Shape Model	p. 448
Empirical Illustration	p. 450
Testing Special Patterns of Growth or Decline	p. 455
Possible Causes of Inadmissible Solutions	p. 459
Modeling Change Over Time With Incomplete Data	p. 461
Variable Naming and Order for Data Files	p. 467
References	p. 469
Author Index	p. 473
Subject Index	p. 477
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