Applied Multivariate Research

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