Applied Multivariate Research : Design and Interpretation
- 3rd
- New Delhi Sage Publications India Pvt. Ltd. 2017
- 978
Part I. The Basics of Multivariate Design Chapter 1. An Introduction to Multivariate Design Chapter 2. Some Fundamental Research Design Concepts Chapter 3A. Data Screening Chapter 3B. Data Screening Using IBM SPSS Part II. Comparisons of Means Chapter 4A. Univariate Comparison of Means Chapter 4B. Univariate Comparison of Means Using IBM SPSS Chapter 5A. Multivariate Analysis of Variance (MANOVA) Chapter 5B. Multivariate Analysis of Variance (MANOVA) Using IBM SPSS Part III. Predicting the Value of a Single Variable Chapter 6A. Bivariate Correlation and Simple Linear Regression Chapter 6B. Bivariate Correlation and Simple Linear Regression Using IBM SPSS Chapter 7A. Multiple Regression: Statistical Methods Chapter 7B. Multiple Regression: Statistical Methods Using IBM SPSS Chapter 8A. Multiple Regression: Beyond Statistical Regression Chapter 8B. Multiple Regression: Beyong Statistical Regression Using IBM SPSS Chapter 9A. Multilevel Modeling Chapter 9B. Multilevel Modeling Using IBM SPSS Chapter 10A. Binary and Multinomial Logistic Regression and ROC Analysis Chapter 10B. Binary and Multinomial Logistic Regression and ROC Analysis Using IBM SPSS Part IV. Analysis of Structure Chapter 11A. Discriminant Function Analysis Chapter 11B. Discriminant Function Analysis Using IBM SPSS Chapter 12A. Principal Components and Exploratory Factor Analysis Chapter 12B. Principal Components and Exploratory Factor Analysis Using IBM SPSS Chapter 13A. Canonical Correlation Analysis Chapter 13B. Canonical Correlation Analysis Using IBM SPSS Chapter 14A. Multidimensional Scaling Chapter 14B. Multidimensional Scaling Using IBM SPSS Chapter 15A. Cluster Analysis Chapter 15B. Cluster Analysis Using IBM SPSS Part V. Fitting Models to Data Chapter 16A. Confirmatory Factor Analysis Chapter 16B. Confirmatory Factor Analysis Using Amos Chapter 17A. Path Analysis: Multiple Regression Chapter 17B. Path Analysis: Multiple Regression Using IBM SPSS Chapter 18A. Path Analysis: Structural Modeling Chapter 18B. Path Analysis: Structural Modeling Using Amos Chapter 19A. Structural Equation Modeling Chapter 19B. Structural Equation Modeling Using Amos Chapter 20A. Model Invariance: Applying a Model to Different Groups Chapter 20B. Assessing Model Invariance Using Amos
PART I: THE BASICS OF MULTIVARIATE DESIGN 1 Chapter 1: An Introduction to Multivariate Design 2 1.1: The Use of Multivariate Designs 2 1.2: The Definition of the Multivariate Domain 2 1.3: The Importance of Multivariate Designs 3 1.4: The General Form of a Variate 4 1.5: The Type of Variables Combined to Form a Variate 5 1.6: The General Organization of the Book 6 1.7: Recommended Readings 10 Chapter 2: Some Fundamental Research Design Concepts 11 2.1: Populations and Samples 11 2.2: Scales of Measurement 12 2.3: Independent Variables, Dependent Variables, and Covariates 18 2.4: Between-Subjects and Within-Subjects Independent Variables 21 2.5: Latent Variables or Variates and Measured Variables 22 2.6: Endogenous and Exogenous Variables 24 2.7: Statistical Significance 24 2.8: Statistical Power 32 2.9: Recommended Readings 36 Chapter 3A: Data Screening 37 3A.1: Overview 37 3A.2: Value Cleaning 38 3A.3: Patterns of Missing Values 44 3A.4: Overview of Methods of Handling Missing Data 48 3A.5: Deletion Methods of Handling Missing Data 49 3A.6: Single Imputation Methods of Handling Missing Data 51 3A.7: Modern Imputation Methods of Handling Missing Data 54 3A.8: Recommendations for Handling Missing Data 57 3A.9: Outliers 57 3A.10: Using Descriptive Statistics in Data Screening 63 3A.11: Using Pictorial Representations in Data Screening 64 3A.12: Multivariate Statistical Assumptions Underlying the General Linear Model 67 3A.13: Data Transformations 72 3A.14: Recommended Readings 73 Chapter 3B: Data Screening Using IBM SPSS 75 3B.1: The Look of IBM SPSS 75 3B.2: Data Cleaning: All Variables 76 3B.3: Screening Quantitative Variables 80 3B.4: Missing Values: Overview 81 3B.5: Missing Value Analysis 81 3B.6: Multiple Imputation 89 3B.7: Mean Substitution as a Single Imputation Approach 102 3B.8: Univariate Outliers 106 3B.9: Normality 109 3B.10: Linearity 120 3B.11: Multivariate Outliers 122 3B.12: Screening Within Levels of Categorical Variables 128 3B.13: Reporting the Results 136 PART II: COMPARISONS OF MEANS 139 Chapter 4A: Univariate Comparison of Means 140 4A.1: Overview 140 4A.2: Means are Compared With Respect to Their Associated Variability 141 4A.3: The t and F Tests 143 4A.4: One-Way Between-Subjects Designs 144 4A.5: Two-Way (Factorial) BetweenSubjects Design 148 4A.6: One-Way Within-Subjects Design 152 4A.7: Two-Way Simple Mixed Design 153 4A.8: One-Way Between-Subjects ANCOVA 156 4A.9: The General Linear Model 162 4A.10: Recommended Readings 164 Chapter 4B: Univariate Comparison of Means Using IBM SPSS 165 4B.1: One-Way Between-Subjects Design 165 4B.2: Two-Way Between-Subjects Design 172 4B.3: One-Way Within-Subjects Design 181 4B.4: Simple Mixed Design 187 4B.5: Trend Analysis 196 4B.6: Analysis of Covariance 201 4B.7: One-Way Between-Subjects Design Using Generalized Linear Models 211 4B.8: Simple Mixed Design Using Generalized Linear Models 215 Chapter 5A: Multivariate Analysis of Variance 224 5A.1: Overview 224 5A.2: Working With Multiple Dependent Variables 224 5A.3: Benefits of and Drawbacks to Using MANOVA 227 5A.4: Hotelling’s T2 229 5A.5: Multivariate Significance Testing With More Than Two Groups 232 5A.6: What to Do After a Significant Multivariate Effect 235 5A.7: Advantages of Multivariate Factorial Designs 237 5A.8: A Strategy For Examining TwoWay Between-Subjects MANOVA Results 238 5A.9: The Time Dimension in Multivariate Data Analysis 242 5A.10: Recommended Readings 245 Chapter 5B: Multivariate Analysis of Variance Using IBM SPSS 247 5B.1: Numerical Example 247 5B.2: Alternatives to Performing a MANOVA Analysis 248 5B.3: Two-Group MANOVA 248 5B.4: k-Group MANOVA 257 5B.5: Two-Way Between-Subjects Factorial MANOVA 269 PART III: PREDICTING THE VALUE OF A SINGLE VARIABLE 283 Chapter 6A: Bivariate Correlation and Simple Linear Regression 284 6A.1: The Concept of Relationship 284 6A.2: Different Types of Relationships 285 6A.3: Statistical Significance of the Correlation Coefficient 292 6A.4: Strength of Relationship 294 6A.5: Pearson Correlation Using a Quantitative Variable and a Dichotomous Nominal Variable 298 6A.6: Simple Linear Regression 302 6A.7: Statistical Error in Prediction: Why Bother With Regression? 309 6A.8: How Simple Linear Regression Is Used 311 6A.9: Factors Affecting the Computed Pearson r and Regression Coefficients 311 6A.10: Recommended Readings 314 Chapter 6B: Bivariate Correlation and Simple Linear Regression Using IBM SPSS 315 6B.1: Bivariate Correlation: Analysis Setup 315 6B.2: Simple Linear Regression 319 6B.3: Reporting Results 323 Chapter 7A: Multiple Regression: Statistical Methods 324 7A.1: General Considerations 324 7A.2: A Range of Regression Methods 325 7A.3: The Variables in a Multiple Regression Analysis 325 7A.4: Multiple Regression Research 327 7A.5: The Regression Equations 329 7A.6: The Variate in Multiple Regression 332 7A.7: The Standard (Simultaneous) Regression Method 333 7A.8: Partial Correlation 337 7A.9: The Squared Multiple Correlation 338 7A.10: The Squared Semipartial Correlation 339 7A.11: Structure Coefficients 344 7A.12: Statistical Summary of the Regression Solution 345 7A.13: Evaluating the Overall Model 346 7A.14: Evaluating the Individual Predictor Results 351 7A.15: Step Methods of Building the Model 357 7A.16: The Forward Method 357 7A.17: The Backward Method 358 7A.18: The Backward Versus Forward Solutions 358 7A.19: The Stepwise Method 359 7A.20: Evaluation of the Statistical Methods 361 7A.21: Collinearity and Multicollinearity 363 7A.22: Recommended Readings 365 Chapter 7B: Multiple Regression: Statistical Methods Using IBM SPSS 366 7B.1: Standard Multiple Regression 366 7B.2: Stepwise Multiple Regression 372 Chapter 8A: Multiple Regression: Beyond Statistical Regression 382 8A.1: A Larger World of Regression 382 8A.2: Hierarchical Linear Regression 382 8A.3: Suppressor Variables 386 8A.4: Linear and Nonlinear Regression 388 8A.5: Dummy and Effect Coding 391 8A.6: Moderator Variables and Interactions 396 8A.7: Simple Mediation 399 8A.8: Recommended Readings 411 Chapter 8B: Multiple Regression: Beyond Statistical Regression Using IBM SPSS 413 8B.1: Hierarchical Linear Regression 413 8B.2: Polynomial Regression 419 8B.3: Dummy and Effect Coding 428 8B.4: Interaction Effects of Quantitative Variables in Regression 439 8B.5: Mediation 457 Chapter 9A: Multilevel Modeling 466 9A.1: The Name of the Procedure 466 9A.2: The Rise of Multilevel Modeling 466 9A.3: The Defining Feature of Multilevel Modeling: Hierarchically Structured Data 467 9A.4: Nesting and the Independence Assumption 468 9A.5: The Intraclass Correlation as an Index of Clustering 469 9A.6: Consequences of Violating the Independence Assumption 470 9A.7: Some Ways in Which Level 2 Groups Can Differ 472 9A.8: The Random Coefficient Regression Model 474 9A.9: Centering the Variables 476 9A.10: The Process of Building the Multilevel Model 479 9A.11: Recommended Readings 483 Chapter 9B: Multilevel Modeling Using IBM SPSS 484 9B.1: Numerical Example 484 9B.2: Assessing the Unconditional Model 484 9B.3: Centering the Variables 490 9B.4: Building the Multilevel Models: Overview 493 9B.5: Building the First Model 496 9B.6: Building the Second Model 504 9B.7: Building the Third Model 509 9B.8: Building the Fourth Model 515 9B.9: Reporting Multilevel Modeling Results 519 Chapter 10A: Binary and Multinomial Logistic Regression and ROC Analysis 522 10A.1: Overview 522 10A.2: The Variables in Logistic Regression Analysis 523 10A.3: Assumptions of Logistic Regression 524 10A.4: Coding of the Binary Variables in Logistic Regression 524 10A.5: The Logistic Regression Model 528 10A.6: Logistic Regression and Odds 530 10A.7: The Logistic Regression Model 532 10A.8: Calculating the Changes of Cases Belonging to the Target Group 534 10A.9: Binary Logistic Regression With a Single Binary Predictor 534 10A.10: Binary Logistic Regression With a Single Quantitative Predictor 536 10A.11: Binary Logistic Regression With a Categorical and a Quantitative Predictor 540 10A.12: Evaluating the Logistic Model 541 10A.13: Strategies For Building the Logistic Regression Model 544 10A.14: ROC Analysis 545 10A.15: Recommended Readings 556 Chapter 10B: Binary and Multinomial Logistic Regression and ROC Analysis Using IBM SPSS 557 10B.1: Binary Logistic Regression 557 10B.2: ROC Analysis 565 10B.3: Multinomial Logistic Regression 575 PART IV: ANALYSIS OF STRUCTURE 585 Chapter 11A: Discriminant Function Analysis 586 11A.1: Overview 586 11A.2: Discriminant Function Analysis and Logistic Analysis Compared 588 11A.3: Discriminant Function Analysis and MANOVA 588 11A.4: Assumptions Underlying Discriminant Function Analysis 589 11A.5: Sample Size for Discriminant Analysis 590 11A.6: The Discriminant Function 590 11A.7: The Number of Discriminant Functions That Can Be Extracted 592 11A.8: Dynamics of Extracting Discriminant Functions 593 11A.9: Testing Statistical Significance 594 11A.10: Evaluating the Quality of the Solution 596 11A.11: Coefficients Associated With the Interpretation of Discriminant Functions 601 11A.12: Different Discriminant Function Methods 606 11A.13: Recommended Readings 608 Chapter 11B: Discriminant Function Analysis Using IBM SPSS 609 11B.1: Two-Group Disciminant Function Analysis Setup 609 11B.2: Two-Group Discriminant Function Analysis Output 613 11B.3: Reporting the Results of a TwoGroup Discriminant Function Analysis 620 11B.4: Three-Group Discriminant Function Analysis Setup 622 11B.5: Three-Group Discriminant Function Analysis Output 625 11B.6: Reporting the Results of a Three-Group Discriminant Function Analysis 637 Chapter 12A: Principal Components Analysis and Exploratory Factor Analysis 640 12A.1: Orientation and Terminology 640 12A.2: How Factor Analysis Is Used in Psychological Research 641 12A.3: Origins of Factor Analysis 641 12A.4: The General Organization of This Chapter 642 12A.5: Where the Analysis Begins: The Correlation Matrix 642 12A.6: Acquiring Perspective on Factor Analysis 648 12A.7: Distinctions Within Factor Analysis 651 12A.8: The First Phase: Component Extraction 652 12A.9: Distances of Variables From a Component 658 12A.10: Principal Components Analysis Versus Factor Analysis 662 12A.11: Different Extraction Methods 664 12A.12: Recommendations Concerning Extraction 666 12A.13: The Rotation Process 667 12A.14: Orthogonal Factor Rotation 672 12A.15: Oblique Factor Rotation 673 12A.16: Choosing Between Orthogonal and Oblique Rotation Strategies 674 12A.17: The Factor Analysis Printout 676 12A.18: Interpreting Factors 680 12A.19: Selecting the Factor Solution 683 12A.20: Sample Size Issues 686 12A.21: Recommended Readings 687 Chapter 12B: Principal Components Analysis and Exploratory Factor Analysis Using IBM SPSS 688 12B.1: Numerical Example 688 12B.2: Preliminary Principal Components Analysis 690 12B.3: Principal Components Analysis With a Promax Rotation: Two-Component Solution 700 12B.4: ULS Analysis With a Promax Rotation: Two-Factor Solution 704 12B.5: Wrap-Up of the Two-Factor Solution 708 12B.6: Looking For Six Dimensions 708 12B.7: Principal Components Analysis With a Promax Rotation: SixComponent Solution 708 12B.8: ULS Analysis With a Promax Rotation: Six-Component Solution 713 12B.9: Principal Axis Factor Analysis With a Promax Rotation: SixComponent Solution 717 12B.10: Wrap-Up of the Six-Factor Solution 720 12B.11: Assessing Reliability: General Principles 721 12B.12: Assessing Reliability: The Global Domains 724 12B.13: Assessing Reliability: The Six Item Sets Based on the ULS/Promax Structure 729 12B.14: Computing Scales Based on the ULS Promax Structure 729 12B.15: Using the Computed Variables in Further Analyses 736 12B.16: Reporting the Results 745 Chapter 13A: Canonical Correlation Analysis 750 13A.1: Overview 750 13A.2: Canonical Functions or Roots 751 13A.3: The Index of Shared Variance 752 13A.4: The Dynamics of Extracting Canonical Functions 753 13A.5: Testing Statistical Significance 754 13A.6: The Multivariate Tests 755 13A.7: Redundancy Index 756 13A.8: Coefficients Associated With the Canonical Functions 757 13A.9: Interpreting the Canonical Functions 758 13A.10: Recommended Readings 758 Chapter 13B: Canonical Correlation Analysis Using IBM SPSS 759 13B.1: Canonical Correlation: Analysis Setup 759 13B.2: Canonical Correlation: Overview of Output 760 13B.3: Canonical Correlation: Multivariate Tests of Significance 761 13B.4: Canonical Correlation: Eigenvalues and Canonical Correlations 761 13B.5: Canonical Correlation: Dimension Reduction Analysis 763 13B.6: Canonical Correlation: How Many Functions Should Be Interpreted? 764 13B.7: Canonical Correlation: The Coefficients in the Output 764 13B.8: Canonical Correlation: Interpreting the Dependent Variates 765 13B.9: Canonical Correlation: Interpreting the Predictor Variates 766 13B.10: Canonical Correlation: Interpreting the Canonical Functions 767 13B.11: Reporting Canonical Correlation Analysis Results 768 Chapter 14A: Multidimensional Scaling 770 14A.1: Overview 770 14A.2: The Paired Comparison Method 771 14A.3: Dissimilarity Data in MDS 772 14A.4: Similarity/Dissimilarity Conceived as an Index of Distance 773 14A.5: Dimensionality in MDS 774 14A.6: Data Collection Methods 775 14A.7: Similarity Versus Dissimilarity 777 14A.8: Distance Models 778 14A.9: A Classification Schema for MDS Techniques 780 14A.10: Types of MDS Models 782 14A.11: Assessing Model Fit 784 14A.12: Recommended Readings 788 Chapter 14B: Multidimensional Scaling Using IBM SPSS 790 14B.1: The Structure of This Chapter 790 14B.2: Metric CMDS 790 14B.3: Nonmetric CMDS 799 14B.4: Metric WMDS 807 Chapter 15A: Cluster Analysis 818 15A.1: Introduction 818 15A.2: Two Types of Clustering 818 15A.3: Hierarchical Clustering 819 15A.4: k-Means Clustering 829 15A.5: Recommended Readings 832 Chapter 15B: Cluster Analysis Using IBM SPSS 833 15B.1: Hierarchical Cluster Analysis 833 15B.2: k-Means Cluster Analysis 841 PART V: FITTING MODELS TO DATA 849 Chapter 16A: Confirmatory Factor Analysis 850 16A.1: Overview 850 16A.2: The General Form of a Confirmatory Model 851 16A.3: The Difference Between Latent and Indicator Variables 852 16A.4: Contrasting Principal Components Analysis, Exploratory Factor Analysis, and Confirmatory Factor Analysis 853 16A.5: Confirmatory Factor Analysis Is Theory Based 860 16A.6: The Logic of Performing a Confirmatory Factor Analysis 861 16A.7: Model Specification 861 16A.8: Model Identification 862 16A.9: Model Estimation 866 16A.10: Model Evaluation Overview 867 16A.11: Assessing Fit of Hypothesized Models 868 16A.12: Model Estimation: Assessing Pattern/Structure Coefficients 873 16A.13: Model Respecification 874 16A.14: General Considerations 878 16A.15: Recommended Readings 879 Chapter 16B: Confirmatory Factor Analysis Using Amos 880 16B.1: Using Amos 880 16B.2: Numerical Example 880 16B.3: Model Specification 881 16B.4: Model Identification 885 16B.5: Performing the Analysis 888 16B.6: Working With the Analysis Output 890 16B.7: Considering the Respecification of the Model 894 16B.8: Respecifying the Model 898 16B.9: Output From the Respecification 898 16B.10: Reporting Confirmatory Factor Analysis Results 901 Chapter 17A: Path Analysis: Multiple Regression 903 17A.1: Overview 903 17A.2: Principles of Path Analysis 904 17A.3: Causality and Path Analysis 905 17A.4: The Concept of a Path Model 907 17A.5: The Roles Played by Variables in a Path Structure 907 17A.6: The Assumptions of Path Analysis 909 17A.7: Missing Values in Path Analysis 910 17A.8: Analyzing the Path Structure 911 17A.9: The Multiple Regression Approach to Path Analysis 911 17A.10: Indirect and Total Effects 913 17A.11: Comparing Multiple Regression and Model-Fitting Approaches 914 17A.12: A Path Analysis Example 914 17A.13: The Multiple Regression Strategy to Perform a Path Analysis 916 17A.14: Examining Mediation Effects 917 17A.15: Respecifying the Model 919 17A.16: Recommended Readings 920 Chapter 17B: Path Analysis: Multiple Regression Using IBM SPSS 921 17B.1: The Data Set and Model Used in Our Example 921 17B.2: Specifying the Variables in Each Analysis 921 17B.3: Predicting Exercise 923 17B.4: Predicting Diet 925 17B.5: Predicting Social Desirability 926 17B.6: Predicting Acceptance 927 17B.7: Mediation Effects in the Larger Model 929 17B.8: Reporting Path Analysis Results 934 Chapter 18A: Path Analysis: Structural Modeling 937 18A.1: The Model-Fitting Approach to Path Analysis 937 18A.2: Comparing Multiple Regression and Model-Fitting Approaches 938 18A.3: The Model-Fitting Strategy to Perform a Path Analysis With Only Measured Variables 940 18A.4: Differences Between Regression and Structural Equations 940 18A.5: The Analysis of a Structural Model 941 18A.6: Configuring the Structural Model 942 18A.7: Identifying the Structural Model 942 18A.8: The Model Results 944 18A.9: Respecifying the Model 946 18A.10: Respecified Model Results 948 18A.11: Recommended Readings 949 Chapter 18B: Path Analysis: Structural Modeling Using Amos 951 18B.1: Overview 951 18B.2: The Data Set and Model Used in Our Example 951 18B.3: Drawing the Model 952 18B.4: Model Identification 954 18B.5: Performing the Analysis 955 18B.6: The Analysis Output 956 18B.7: The Structural Model 961 18B.8: Specification Search to Delete Paths 961 18B.9: Reporting Path Analysis Results 972 Chapter 19A: Structural Equation Modeling 974 19A.1: Overview 974 19A.2: The Measurement and Structural Models 974 19A.3: From Path Analysis to SEM 975 19A.4: Building a Structural Model From Our Path Model 977 19A.5: Results for our Structural Model 979 19A.6: Recommended Readings 981 Chapter 19B: Structural Equation Modeling Using Amos 982 19B.1: Overview 982 19B.2: The Example We Use 983 19B.3: The Variables in Our Example Model 984 19B.4: The Measurement Model 984 19B.5: The Variables Configured in the Full Structural Model 988 19B.6: Performing the Analysis 988 19B.7: Output for the Full Structural Model 990 19B.8: Respecification of the Model 994 19B.9: Output for the Full Respecified Structural Model 995 19B.10: Reporting SEM Analysis Results 998 Chapter 20A: Model Invariance: Applying a Model to Different Groups 1001 20A.1: Overview 1001 20A.2: The General Strategy Used to Compare Groups 1002 20A.3: The Omnibus Model Comparison Phase 1002 20A.4: The Coefficient Comparison Phase 1005 20A.5: Recommended Readings 1005 Chapter 20B: Assessing Model Invariance Using Amos 1007 20B.1: Overview 1007 20B.2: Confirmatory Factor Analysis 1007 20B.3: Path Analysis 1018