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Applied Multivariate Research

Applied Multivariate Research
Design and Interpretation

Third Edition
Additional resources:

November 2016 | 1 016 pages | SAGE Publications, Inc
Using a conceptual, non-mathematical approach, the updated Third Edition provides full coverage of the wide range of multivariate topics that graduate students across the social and behavioral sciences encounter. Authors Lawrence S. Meyers, Glenn Gamst, and A. J. Guarino integrate innovative multicultural topics in examples throughout the book, which include both conceptual and practical coverage of: statistical techniques of data screening; multiple regression; multilevel modeling; exploratory factor analysis; discriminant analysis; structural equation modeling; structural equation modeling invariance; survival analysis; multidimensional scaling; and cluster analysis. 

About the Authors
Chapter 1: An Introduction to Multivariate Design
1.1 The Use of Multivariate Designs  
1.2 The Definition of the Multivariate Domain  
1.3 The Importance of Multivariate Designs  
1.4 The General Form of a Variate  
1.5 The Type of Variables Combined to Form a Variate  
1.6 The General Organization of the Book  
Chapter 2: Some Fundamental Research Design Concepts
2.1 Populations and Samples  
2.2 Variables and Scales of Measurement  
2.3 Independent Variables, Dependent Variables, and Covariates  
2.4 Between Subjects and Within Subjects Independent Variables  
2.5 Latent Variables and Measured Variables  
2.6 Endogenous and Exogenous Variables  
2.7 Statistical Significance  
2.8 Statistical Power  
2.9 Recommended Readings  
Chapter 3A: Data Screening
3A.1 Overview  
3A.2 Value Cleaning  
3A.3 Patterns of Missing Values  
3A.4 Overview of Methods of Handling Missing Data  
3A.5 Deletion Methods of Handling Missing Data  
3A.6 Single Imputation Methods of Handling Missing Data  
3A.7 Modern Imputation Methods of Handling Missing Data  
3A.8 Recommendations for Handling Missing Data  
3A.9 Outliers  
3A.10 Using Descriptive Statistics in Data Screening  
3A.11 Using Pictorial Representations in Data Screening  
3A.12 Multivariate Statistical Assumptions Underlying the General Linear Model  
3A.13 Data Transformations  
3A.14 Recommended Readings  
Chapter 3B: Data Screening Using IBM SPSS
3B.1 The Look of IBM SPSS  
3B.2 Data Cleaning: All Variables  
3B.3 Screening Quantitative Variables  
3B.4 Missing Values: Overview  
3B.5 Missing Value Analysis  
3B.6 Multiple Imputation  
3B.7 Mean Substitution as a Single Imputation Approach  
3B.8 Univariate Outliers  
3B.9 Normality  
3B.10 Linearity  
3B.11 Multivariate Outliers  
3B.12 Screening Within Levels of Categorical Variables  
3B.13 Reporting the Data Screening Results  
Chapter 4A: Bivariate Correlation and Simple Linear Regression
4A.1 The Concept of Correlation  
4A.2 Different Types of Relationships  
4A.3 Statistical Significance of the Correlation Coefficient  
4A.4 Strength of Relationship  
4A.5 Pearson Correlation Using a Quantitative Variable and a Dichotomous Nominal Variable  
4A.6 Simple Linear Regression  
4A.7 Statistical Error in Prediction: Why Bother With Regression?  
4A.8 How Simple Linear Regression Is Used  
4A.9 Factors Affecting the Computed Pearson r and Regression Coefficients  
4A.10 Recommended Readings  
Chapter 4B: Bivariate Correlation and Simple Linear Regression Using IBM SPSS
4B.1 Bivariate Correlation: Analysis Setup  
4B.2 Simple Linear Regression  
4B.3 Reporting Simple Linear Regression Results  
Chapter 5A: Multiple Regression Analysis
5A.1 General Considerations  
5A.2 Statistical Regression Methods  
5A.3 The Two Classes of Variables in a Multiple Regression Analysis  
5A.4 Multiple Regression Research  
5A.5 The Regression Equations  
5A.6 The Variate in Multiple Regression  
5A.7 The Standard (Simultaneous) Regression Method  
5A.8 Partial Correlation  
5A.9 The Squared Multiple Correlation  
5A.10 The Squared Semipartial Correlation  
5A.11 Structure Coefficients  
5A.12 Statistical Summary of the Regression Solution  
5A.13 Evaluating the Overall Model  
5A.14 Evaluating the Individual Predictor Results  
5A.15 Step Methods of Building the Model  
5A.16 The Forward Method  
5A.17 The Backward Method  
5A.18 Backward Versus Forward Solutions  
5A.19 The Stepwise Method  
5A.20 Evaluation of the Statistical Methods  
5A.21 Collinearity and Multicollinearity  
5A.22 Recommended Readings  
Chapter 5B: Multiple Regression Analysis Using IBM SPSS
5B.1 Standard Multiple Regression  
5B.2 Stepwise Multiple Regression  
Chapter 6A: Beyond Statistical Regression
6A.1 A Larger World of Regression  
6A.2 Hierarchical Linear Regression  
6A.3 Suppressor Variables  
6A.4 Linear and Nonlinear Regression  
6A.5 Dummy and Effect Coding  
6A.6 Moderator Variables and Interactions  
6A.7 Simple Mediation: A Minimal Path Analysis  
6A.8 Recommended Readings  
Chapter 6B: Beyond Statistical Regression Using IBM SPSS
6B.1 Hierarchical Linear Regression  
6B.2 Polynomial Regression  
6B.3 Dummy and Effect Coding  
6B.4 Interaction Effects of Quantitative Variables in Regression  
6B.5 Mediation  
Chapter 7A: Canonical Correlation Analysis
7A.1 Overview  
7A.2 Canonical Functions or Roots  
7A.3 The Index of Shared Variance  
7A.4 The Dynamics of Extracting Canonical Functions  
7A.5 Accounting for Variance: Eigenvalues and Theta Values  
7A.6 The Multivariate Tests of Statistical Significance  
7A.7 Specifying the Amount of Variance Explained in Canonical Correlation Analysis  
7A.8 Coefficients Associated With the Canonical Functions  
7A.9 Interpreting the Canonical Functions  
7A.10 Recommended Readings  
Chapter 7B: Canonical Correlation Analysis Using IBM SPSS
7B.1 Canonical Correlation: Analysis Setup  
7B.2 Canonical Correlation: Overview of Output  
7B.3 Canonical Correlation: Multivariate Tests of Significance  
7B.4 Canonical Correlation: Eigenvalues and Canonical Correlations  
7B.5 Canonical Correlation: Dimension Reduction Analysis  
7B.6 Canonical Correlation: How Many Functions Should Be Interpreted?  
7B.7 Canonical Correlation: The Coefficients in the Output  
7B.8 Canonical Correlation: Interpreting the Dependent Variates  
7B.9 Canonical Correlation: Interpreting the Predictor Variates  
7B.10 Canonical Correlation: Interpreting the Canonical Functions  
7B.11 Reporting of the Canonical Correlation Analysis Results  
Chapter 8A: Multilevel Modeling
8A.1 The Name of the Procedure  
8A.2 The Rise of Multilevel Modeling  
8A.3 The Defining Feature of Multilevel Modeling: Hierarchically Structured Data  
8A.4 Nesting and the Independence Assumption  
8A.5 The Intraclass Correlation as an Index of Clustering  
8A.6 Consequences of Violating the Independence Assumption  
8A.7 Some Ways in Which Level 2 Groups Can Differ  
8A.8 The Random Coefficient Regression Model  
8A.9 Centering the Variables  
8A.10 The Process of Building the Multilevel Model  
8A.11 Recommended Readings  
Chapter 8B: Multilevel Modeling Using IBM SPSS
8B.1 Numerical Example  
8B.2 Assessing the Unconditional Model  
8B.3 Centering the Covariates  
8B.4 Building the Multilevel Models: Overview  
8B.5 Building the First Model  
8B.6 Building the Second Model  
8B.7 Building the Third Model  
8B.8 Building the Fourth Model  
8B.9 Reporting the Multilevel Modeling Results  
Chapter 9A: Binary and Multinomial Logistic Regression and ROC Analysis
9A.1 Overview  
9A.2 The Variables in Logistic Regression Analysis  
9A.3 Assumptions of Logistic Regression  
9A.4 Coding of the Binary Variables in Logistic Regression  
9A.5 The Shape of the Logistic Regression Function  
9A.6 Probability, Odds, and Odds Ratios  
9A.7 The Logistic Regression Model  
9A.8 Interpreting Logistic Regression Results in Simpler Language  
9A.9 Binary Logistic Regression With a Single Binary Predictor  
9A.10 Binary Logistic Regression With a Single Quantitative Predictor  
9A.11 Binary Logistic Regression With a Categorical and a Quantitative Predictor  
9A.12 Evaluating the Logistic Model  
9A.13 Strategies for Building the Logistic Regression Model  
9A.14 ROC Analysis  
9A.15 Recommended Readings  
Chapter 9B: Binary and Multinomial Logistic Regression and ROC Analysis Using IBM SPSS
9B.1 Binary Logistic Regression  
9B.2 ROC Analysis  
9B.3 Multinomial Logistic Regression  
Chapter 10A: Principal Components Analysis and Exploratory Factor Analysis
10A.1 Orientation and Terminology  
10A.2 Origins of Factor Analysis  
10A.3 How Factor Analysis Is Used in Psychological Research  
10A.4 The General Organization of This Chapter  
10A.5 Where the Analysis Begins: The Correlation Matrix  
10A.6 Acquiring Perspective on Factor Analysis  
10A.7 Important Distinctions Within Our Generic Label of Factor Analysis  
10A.8 The First Phase: Component Extraction  
10A.9 Distances of Variables From a Component  
10A.10 Principal Components Analysis Versus Factor Analysis  
10A.11 Different Extraction Methods  
10A.12 Recommendations Concerning Extraction  
10A.13 The Rotation Process  
10A.14 Orthogonal Factor Rotation Methods  
10A.15 Oblique Factor Rotation  
10A.16 Choosing Between Orthogonal and Oblique Rotation Strategies  
10A.17 The Factor Analysis Output  
10A.18 Interpreting Factors Based on the Rotated Matrices  
10A.19 Selecting the Factor Solution  
10A.20 Sample Size Issues  
10A.21 Building Reliable Subscales  
10A.22 Recommended Readings  
Chapter 10B: Principal Components Analysis and Exploratory Factor Analysis Using IBM SPSS
10B.1 Numerical Example  
10B.2 Preliminary Principal Components Analysis  
10B.3 Principal Components Analysis With a Promax Rotation: Two-Component Solution  
10B.4 ULS Analysis With a Promax Rotation: Two-Factor Solution  
10B.5 Wrap-Up of the Two-Factor Solution  
10B.6 Looking for Six Dimensions  
10B.7 Principal Components Analysis With a Promax Rotation: Six-Component Solution  
10B.8 ULS Analysis With a Promax Rotation: Six-Component Solution  
10B.9 Principal Axis Factor Analysis With a Promax Rotation: Six-Component Solution  
10B.10 Wrap-Up of the Six-Factor Solution  
10B.11 Assessing Reliability: Our General Strategy  
10B.12 Assessing Reliability: The Global Domains  
10B.13 Assessing Reliability: The Six Item Sets Based on the ULS/Promax Structure  
10B.14 Computing Scales Based on the ULS Promax Structure  
10B.15 Using the Computed Variables in Further Analyses  
10B.16 Reporting the Exploratory Factor Analysis Results  
Chapter 11A: Confirmatory Factor Analysis
11A.1 Overview  
11A.2 The General Form of a Confirmatory Model  
11A.3 The Difference Between Latent and Measured Variables  
11A.4 Contrasting Principal Components Analysis and Exploratory Factor Analysis With Confirmatory Factor Analysis  
11A.5 Confirmatory Factor Analysis Is Theory Based  
11A.6 The Logic of Performing a Confirmatory Factor Analysis  
11A.7 Model Specification  
11A.8 Model Identification  
11A.9 Model Estimation  
11A.10 Model Evaluation Overview  
11A.11 Assessing Fit of Hypothesized Models  
11A.12 Model Estimation: Assessing Pattern Coefficients  
11A.13 Model Respecification  
11A.14 General Considerations  
11A.15 Recommended Readings  
Chapter 11B: Confirmatory Factor Analysis Using IBM SPSS Amos
11B.1 Using IBM SPSS Amos  
11B.2 Numerical Example  
11B.3 Analysis Setup to Specify the Model  
11B.4 Model Identification  
11B.5 Structuring and Performing the Analysis  
11B.6 Working With the Analysis Output  
11B.7 Respecifying the Model  
11B.8 Output From the Respecified Model  
11B.9 Reporting Confirmatory Factor Analysis Results  
Chapter 12A: Path Analysis: Multiple Regression Analysis
12A.1 Overview  
12A.2 The Concept of a Path Model  
12A.3 The Appeal of Path Over Multiple Regression Analysis  
12A.4 Causality and Path Analysis  
12A.5 The Roles Played by Variables in a Path Structure  
12A.6 The Assumptions of Path Analysis  
12A.7 Missing Values in Path Analysis  
12A.8 The Multiple Regression Approach to Path Analysis  
12A.9 Indirect and Total Effects  
12A.10 Recommended Readings  
Chapter 12B: Path Analysis: Multiple Regression Analysis Using IBM SPSS
12B.1 The Data Set and Model Used in Our Example  
12B.2 Identifying the Variables in Each Analysis  
12B.3 Predicting Months_Teaching  
12B.4 Predicting Good_Teaching  
12B.5 Reporting the Path Analysis Results  
Chapter 13A: Path Analysis: Structural Equation Modeling
13A.1 Comparing Multiple Regression and Structural Equation Model Approaches  
13A.2 Differences Between the Equations Underlying Multiple Regression and Structural Equation Model Procedures  
13A.3 Configuring the Structural Model  
13A.4 Identifying the Structural Equation Model  
13A.5 Recommended Readings  
Chapter 13B: Path Analysis: Structural Equation Modeling Using IBM SPSS Amos
13B.1 Overview  
13B.2 The Data Set and Model Used in Our Example  
13B.3 Analysis Setup  
13B.4 The Analysis Output  
13B.5 Reporting the Path Analysis Results  
Chapter 14A: Structural Equation Modeling
14A.1 Overview of Structural Equation Modeling  
14A.2 Model Quality and the Structural Aspects of the Model  
14A.3 Latent Variables and Their Indicators  
14A.4 Identifying Structural Equation Models  
14A.5 Recommended Readings  
Chapter 14B: Structural Equation Modeling Using IBM SPSS Amos
14B.1 Overview  
14B.2 The Data Set and Model Used in Our Example  
14B.3 Model Configuration and Analysis Setup  
14B.4 Model Identification  
14B.5 Generating the Output  
14B.6 Analysis Output for the Model  
14B.7 Configuring and Evaluating the Respecified Model  
14B.8 Summary of the Results of the Model and Noting the Follow-up Analyses  
14B.9 Assessing the Indirect Effects in the Full Model  
14B.10 Assessing the Possibility of Having Obtained Complete Mediation in the Full Model  
14B.11 Assessing Mediation Through Self_ Regulation  
14B.12 Assessing Mediation Through Extrinsic_Goals  
14B.13 Synthesis of the Results  
14B.14 Reporting the SEM Results  
Chapter 15A: Measurement and Structural Equation Modeling Invariance: Applying a Model to a Different Group
15A.1 Overview  
15A.2 The General Strategy Used to Compare Groups  
15A.3 The Omnibus Model Comparison Phase  
15A.4 The Coefficient Comparison Phase  
15A.5 Recommended Readings  
Chapter 15B: Assessing Measurement and Structural Invariance for Confirmatory Factor Analysis and Structural Equation Models Using IBM SPSS Amos
15B.1 Overview and General Analysis Strategy  
15B.2 The Data Set Used for Examining Invariance in Both the Confirmatory Factor Analysis and Structural Equation Model Examples  
15B.3 Confirmatory Factor Analysis Invariance: Global Preliminary Analysis  
15B.4 Confirmatory Factor Analysis Invariance: Group 1 (Rural) Analysis  
15B.5 Confirmatory Factor Analysis Invariance: Group 2 Analysis  
15B.6 Confirmatory Factor Analysis Invariance: Model Evaluation Setup  
15B.7 Confirmatory Factor Analysis Invariance: Model Evaluation Output  
15B.8 Reporting the Confirmatory Factor Analysis Invariance Results  
15B.9 Structural Equation Model Invariance: Global Preliminary Analysis  
15B.10 Structural Equation Model Invariance: Group 1 (Rural) Analysis  
15B.11 Structural Equation Model Invariance: Group 2 Analysis  
15B.12 Structural Equation Model Invariance: Model Evaluation Setup  
15B.13 Structural Equation Model Invariance: Model Evaluation Output  
15B.14 Reporting the Structural Equation Model Invariance Results  
Chapter 16A: Multidimensional Scaling
16A.1 Overview  
16A.2 The Paired Comparison Method  
16A.3 Dissimilarity Data in MDS  
16A.4 Similarity/Dissimilarity Conceived as an Index of Distance  
16A.5 Dimensionality in MDS  
16A.6 Data Collection Methods  
16A.7 Similarity Versus Dissimilarity  
16A.8 Distance Models  
16A.9 A Classification Schema for MDS Techniques  
16A.10 Types of MDS Models  
16A.11 Assessing Model Fit  
16A.12 Recommended Readings  
Chapter 16B: Multidimensional Scaling Using IBM SPSS
16B.1 The Structure of This Chapter  
16B.2 Metric CMDS  
16B.3 Nonmetric CMDS  
16B.4 Metric WMDS  
Chapter 17A: Cluster Analysis
17A.1 Introduction  
17A.2 Two Types of Clustering  
17A.3 Hierarchical Clustering  
17A.4 k-Means Clustering  
17A.5 Recommended Readings  
Chapter 17B: Cluster Analysis Using IBM SPSS
17B.1 Hierarchical Cluster Analysis  
17B.2 k-Means Cluster Analysis  
Chapter 18A: Between Subjects Comparisons of Means
18A.1 Overview  
18A.2 Historical Context  
18A.3 A Brief Review of Some Basic Concepts  
18A.4 Using Multiple Dependent Variables  
18A.5 Evaluating Statistical Significance  
18A.6 Strength of Effect  
18A.7 Designs, Effects, and Partitioning of the Variance  
18A.8 Post-ANOVA Comparisons of Means  
18A.9 Hierarchical Analysis of Effects  
18A.10 Covariance Analysis  
18A.11 Recommended Readings  
Chapter 18B: Between Subjects ANCOVA, MANOVA, and MANCOVA Using IBM SPSS
18B.1 One-Way ANOVA Without the Covariate  
18B.2 One-Way ANCOVA  
18B.3 Three-Group MANOVA  
18B.4 Two-Group MANCOVA  
18B.5 Two-Way MANOVA Without the Covariate  
18B.6 Two-Way MANOVA Incorporating the Covariate (MANCOVA)  
Chapter 19A: Discriminant Function Analysis
19A.1 Overview  
19A.2 The Formal Roles of the Variables in Discriminant Function Analysis and MANOVA  
19A.3 Discriminant Function Analysis and Logistic Analysis Compared  
19A.4 Sample Size for Discriminant Analysis  
19A.5 The Discriminant Model  
19A.6 Extracting Multiple Discriminant Functions  
19A.7 Dynamics of Extracting Discriminant Functions  
19A.8 Interpreting the Discriminant Function  
19A.9 Assessing Statistical Significance and the Relative Strength of the Discriminative Functions  
19A.10 Using Discriminant Function Analysis for Classification  
19A.11 Different Discriminant Function Methods  
19A.12 Recommended Readings  
Chapter 19B: Three-Group Discriminant Function Analysis Using IBM SPSS
19B.1 Numerical Example  
19B.2 Analysis Setup  
19B.3 Analysis Output  
19B.4 Reporting the Results of a Three- Group Discriminant Function Analysis  
Chapter 20A: Survival Analysis
20A.1 Overview  
20A.2 The Dependent Variable in Survival Analysis  
20A.3 Ordinary Least Squares Regression Versus Survival Analysis  
20A.4 Censored Observations  
20A.5 Overview of Analysis Techniques for Survival Analysis in IBM SPSS  
20A.6 Life Table Analysis  
20A.7 Kaplan–Meier (Product-Limit) Survival Function Analysis  
20A.8 Cox Proportional Hazard Regression Model  
20A.9 Recommended Readings  
Chapter 20B: Survival Analysis Using IBM SPSS
20B.1 Numerical Example  
20B.3 Kaplan–Meier (Product-Limit) Survival Function Analysis  
20B.4 Cox Proportional Hazard Regression Model  
Appendix A: Statistics Tables
Author Index
Subject Index


Student Resource Site

Use the Student Study Site to get the most out of your course!
Our Student Study Site is completely open-access and offers a wide range of additional features.


The open-access Student Study Site includes the following:

o   Data files are provided for the analyses demonstrated in each of the "B" chapters.

o   Exercises with data files are provided for each of the "B" chapters.

“A major strength of this text is that it covers the new features of the most recent SPSS® edition. With the step-by-step tutorial on the new features, students and empirical researchers can use it as a handbook when they conduct data analysis.” 

Haiyan Bai
University of Central Florida
Key features

  • Extensively updated and rewritten chapters on confirmatory factor analysis, structural equation modeling, and model invariance improve accessibility and offer more complete examples.
  • A new chapter on survival analysis enhances the scope of the book.
  • Reorganized content for a more logical flow includes correlation and regression appearing immediately after data screening to serve as foundation for the rest of the book; canonical correlation analysis appearing earlier to follow advanced regression techniques; confirmatory factor analysis appearing after exploratory factor analysis; and discriminant function analysis appearing after MANOVA content.
  • Restructured chapters on ANCOVA and MANOVA include one-way and two-way MANCOVA for a greater emphasis on covariance analysis.
  • Updated content is compatible with IBM® SPSS® v. 23.
  • Practical coverage on how to perform, interpret, and report the results of multivariate analyses is presented in a direct and understandable manner.
  • Two companion (paired) chapters for each topic include an “A” chapter presenting the conceptual treatment of the topic and a “B” chapter presenting the step-by-step data analysis, data interpretation, and reporting of the results.
  • Integrated SPSS® examples from one large study provide hands-on learning and consistency of application throughout the text.
  • Practical applications of the techniques using contemporary studies are drawn from a wide range of disciplines in the social and behavioral sciences. 

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