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Applied Multivariate Research
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Applied Multivariate Research
Design and Interpretation

Third Edition
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January 2017 | 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. 
 
Preface
 
About the Authors
 
PART I: FUNDAMENTALS OF MULTIVARIATE DESIGN
 
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

 
 
PART II: BASIC AND ADVANCED REGRESSION ANALYSIS
 
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

 
 
PART III: STRUCTURAL RELATIONSHIPS OF MEASURED AND LATENT VARIABLES
 
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

 
 
PART IV: CONSOLIDATING STIMULI AND CASES
 
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

 
 
PART V: COMPARING SCORES
 
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

 
 
References
 
Appendix A: Statistics Tables
 
Author Index
 
Subject Index

Supplements

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

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