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Applied Multivariate Research

Applied Multivariate Research
Design and Interpretation

Third Edition

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

Sample Materials & Chapters

Chapter 1

Chapter 5

Lawrence S. Meyers

Lawrence S. Meyers earned his doctorate in experimental psychology and has been a Professor in the Psychology Department at California State University, Sacramento, for a number of years. He supervises research students and teaches research design courses as well as history of psychology at both the undergraduate and graduate levels. His areas of expertise include test development and validation. More About Author

Glenn C. Gamst

Glenn Gamst is Professor and Chair of the Psychology Department at the University of La Verne, where he teaches the doctoral advanced statistics sequence. His research interests include the effects of multicultural variables on clinical outcome. Additional research interests focus on conversation memory and discourse processing. He received his PhD in experimental psychology from the University of Arkansas. More About Author

Anthony J. Guarino

A. J. Guarino is a professor of biostatistics at Massachusetts General Hospital, Institute of Health Professions. He is the statistician on numerous National Institutes of Health grants and a reviewer on several research journals. He received his BA from the University of California, Berkeley, and a PhD in statistics and research methodologies from the Department of Educational Psychology, the University of Southern California. More About Author

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ISBN: 9781506329765

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