Applied Multivariate Research

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. 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. 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.

"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."

• PrefaceAbout the AuthorsPART I: FUNDAMENTALS OF MULTIVARIATE DESIGNChapter 1: An Introduction to Multivariate Design1.1 The Use of Multivariate Designs1.2 The Definition of the Multivariate Domain1.3 The Importance of Multivariate Designs1.4 The General Form of a Variate1.5 The Type of Variables Combined to Form a Variate1.6 The General Organization of the BookChapter 2: Some Fundamental Research Design Concepts2.1 Populations and Samples2.2 Variables and Scales of Measurement2.3 Independent Variables, Dependent Variables, and Covariates2.4 Between Subjects and Within Subjects Independent Variables2.5 Latent Variables and Measured Variables2.6 Endogenous and Exogenous Variables2.7 Statistical Significance2.8 Statistical Power2.9 Recommended ReadingsChapter 3A: Data Screening3A.1 Overview3A.2 Value Cleaning3A.3 Patterns of Missing Values3A.4 Overview of Methods of Handling Missing Data3A.5 Deletion Methods of Handling Missing Data3A.6 Single Imputation Methods of Handling Missing Data3A.7 Modern Imputation Methods of Handling Missing Data3A.8 Recommendations for Handling Missing Data3A.9 Outliers3A.10 Using Descriptive Statistics in Data Screening3A.11 Using Pictorial Representations in Data Screening3A.12 Multivariate Statistical Assumptions Underlying the General Linear Model3A.13 Data Transformations3A.14 Recommended ReadingsChapter 3B: Data Screening Using IBM SPSS3B.1 The Look of IBM SPSS3B.2 Data Cleaning: All Variables3B.3 Screening Quantitative Variables3B.4 Missing Values: Overview3B.5 Missing Value Analysis3B.6 Multiple Imputation3B.7 Mean Substitution as a Single Imputation Approach3B.8 Univariate Outliers3B.9 Normality3B.10 Linearity3B.11 Multivariate Outliers3B.12 Screening Within Levels of Categorical Variables3B.13 Reporting the Data Screening ResultsPART II: BASIC AND ADVANCED REGRESSION ANALYSISChapter 4A: Bivariate Correlation and Simple Linear Regression4A.1 The Concept of Correlation4A.2 Different Types of Relationships4A.3 Statistical Significance of the Correlation Coefficient4A.4 Strength of Relationship4A.5 Pearson Correlation Using a Quantitative Variable and a Dichotomous Nominal Variable4A.6 Simple Linear Regression4A.7 Statistical Error in Prediction: Why Bother With Regression?4A.8 How Simple Linear Regression Is Used4A.9 Factors Affecting the Computed Pearson r and Regression Coefficients4A.10 Recommended ReadingsChapter 4B: Bivariate Correlation and Simple Linear Regression Using IBM SPSS4B.1 Bivariate Correlation: Analysis Setup4B.2 Simple Linear Regression4B.3 Reporting Simple Linear Regression ResultsChapter 5A: Multiple Regression Analysis5A.1 General Considerations5A.2 Statistical Regression Methods5A.3 The Two Classes of Variables in a Multiple Regression Analysis5A.4 Multiple Regression Research5A.5 The Regression Equations5A.6 The Variate in Multiple Regression5A.7 The Standard (Simultaneous) Regression Method5A.8 Partial Correlation5A.9 The Squared Multiple Correlation5A.10 The Squared Semipartial Correlation5A.11 Structure Coefficients5A.12 Statistical Summary of the Regression Solution5A.13 Evaluating the Overall Model5A.14 Evaluating the Individual Predictor Results5A.15 Step Methods of Building the Model5A.16 The Forward Method5A.17 The Backward Method5A.18 Backward Versus Forward Solutions5A.19 The Stepwise Method5A.20 Evaluation of the Statistical Methods5A.21 Collinearity and Multicollinearity5A.22 Recommended ReadingsChapter 5B: Multiple Regression Analysis Using IBM SPSS5B.1 Standard Multiple Regression5B.2 Stepwise Multiple RegressionChapter 6A: Beyond Statistical Regression6A.1 A Larger World of Regression6A.2 Hierarchical Linear Regression6A.3 Suppressor Variables6A.4 Linear and Nonlinear Regression6A.5 Dummy and Effect Coding6A.6 Moderator Variables and Interactions6A.7 Simple Mediation: A Minimal Path Analysis6A.8 Recommended ReadingsChapter 6B: Beyond Statistical Regression Using IBM SPSS6B.1 Hierarchical Linear Regression6B.2 Polynomial Regression6B.3 Dummy and Effect Coding6B.4 Interaction Effects of Quantitative Variables in Regression6B.5 MediationChapter 7A: Canonical Correlation Analysis7A.1 Overview7A.2 Canonical Functions or Roots7A.3 The Index of Shared Variance7A.4 The Dynamics of Extracting Canonical Functions7A.5 Accounting for Variance: Eigenvalues and Theta Values7A.6 The Multivariate Tests of Statistical Significance7A.7 Specifying the Amount of Variance Explained in Canonical Correlation Analysis7A.8 Coefficients Associated With the Canonical Functions7A.9 Interpreting the Canonical Functions7A.10 Recommended ReadingsChapter 7B: Canonical Correlation Analysis Using IBM SPSS7B.1 Canonical Correlation: Analysis Setup7B.2 Canonical Correlation: Overview of Output7B.3 Canonical Correlation: Multivariate Tests of Significance7B.4 Canonical Correlation: Eigenvalues and Canonical Correlations7B.5 Canonical Correlation: Dimension Reduction Analysis7B.6 Canonical Correlation: How Many Functions Should Be Interpreted?7B.7 Canonical Correlation: The Coefficients in the Output7B.8 Canonical Correlation: Interpreting the Dependent Variates7B.9 Canonical Correlation: Interpreting the Predictor Variates7B.10 Canonical Correlation: Interpreting the Canonical Functions7B.11 Reporting of the Canonical Correlation Analysis ResultsChapter 8A: Multilevel Modeling8A.1 The Name of the Procedure8A.2 The Rise of Multilevel Modeling8A.3 The Defining Feature of Multilevel Modeling: Hierarchically Structured Data8A.4 Nesting and the Independence Assumption8A.5 The Intraclass Correlation as an Index of Clustering8A.6 Consequences of Violating the Independence Assumption8A.7 Some Ways in Which Level 2 Groups Can Differ8A.8 The Random Coefficient Regression Model8A.9 Centering the Variables8A.10 The Process of Building the Multilevel Model8A.11 Recommended ReadingsChapter 8B: Multilevel Modeling Using IBM SPSS8B.1 Numerical Example8B.2 Assessing the Unconditional Model8B.3 Centering the Covariates8B.4 Building the Multilevel Models: Overview8B.5 Building the First Model8B.6 Building the Second Model8B.7 Building the Third Model8B.8 Building the Fourth Model8B.9 Reporting the Multilevel Modeling ResultsChapter 9A: Binary and Multinomial Logistic Regression and ROC Analysis9A.1 Overview9A.2 The Variables in Logistic Regression Analysis9A.3 Assumptions of Logistic Regression9A.4 Coding of the Binary Variables in Logistic Regression9A.5 The Shape of the Logistic Regression Function9A.6 Probability, Odds, and Odds Ratios9A.7 The Logistic Regression Model9A.8 Interpreting Logistic Regression Results in Simpler Language9A.9 Binary Logistic Regression With a Single Binary Predictor9A.10 Binary Logistic Regression With a Single Quantitative Predictor9A.11 Binary Logistic Regression With a Categorical and a Quantitative Predictor9A.12 Evaluating the Logistic Model9A.13 Strategies for Building the Logistic Regression Model9A.14 ROC Analysis9A.15 Recommended ReadingsChapter 9B: Binary and Multinomial Logistic Regression and ROC Analysis Using IBM SPSS9B.1 Binary Logistic Regression9B.2 ROC Analysis9B.3 Multinomial Logistic RegressionPART III: STRUCTURAL RELATIONSHIPS OF MEASURED AND LATENT VARIABLESChapter 10A: Principal Components Analysis and Exploratory Factor Analysis10A.1 Orientation and Terminology10A.2 Origins of Factor Analysis10A.3 How Factor Analysis Is Used in Psychological Research10A.4 The General Organization of This Chapter10A.5 Where the Analysis Begins: The Correlation Matrix10A.6 Acquiring Perspective on Factor Analysis10A.7 Important Distinctions Within Our Generic Label of Factor Analysis10A.8 The First Phase: Component Extraction10A.9 Distances of Variables From a Component10A.10 Principal Components Analysis Versus Factor Analysis10A.11 Different Extraction Methods10A.12 Recommendations Concerning Extraction10A.13 The Rotation Process10A.14 Orthogonal Factor Rotation Methods10A.15 Oblique Factor Rotation10A.16 Choosing Between Orthogonal and Oblique Rotation Strategies10A.17 The Factor Analysis Output10A.18 Interpreting Factors Based on the Rotated Matrices10A.19 Selecting the Factor Solution10A.20 Sample Size Issues10A.21 Building Reliable Subscales10A.22 Recommended ReadingsChapter 10B: Principal Components Analysis and Exploratory Factor Analysis Using IBM SPSS10B.1 Numerical Example10B.2 Preliminary Principal Components Analysis10B.3 Principal Components Analysis With a Promax Rotation: Two-Component Solution10B.4 ULS Analysis With a Promax Rotation: Two-Factor Solution10B.5 Wrap-Up of the Two-Factor Solution10B.6 Looking for Six Dimensions10B.7 Principal Components Analysis With a Promax Rotation: Six-Component Solution10B.8 ULS Analysis With a Promax Rotation: Six-Component Solution10B.9 Principal Axis Factor Analysis With a Promax Rotation: Six-Component Solution10B.10 Wrap-Up of the Six-Factor Solution10B.11 Assessing Reliability: Our General Strategy10B.12 Assessing Reliability: The Global Domains10B.13 Assessing Reliability: The Six Item Sets Based on the ULS/Promax Structure10B.14 Computing Scales Based on the ULS Promax Structure10B.15 Using the Computed Variables in Further Analyses10B.16 Reporting the Exploratory Factor Analysis ResultsChapter 11A: Confirmatory Factor Analysis11A.1 Overview11A.2 The General Form of a Confirmatory Model11A.3 The Difference Between Latent and Measured Variables11A.4 Contrasting Principal Components Analysis and Exploratory Factor Analysis With Confirmatory Factor Analysis11A.5 Confirmatory Factor Analysis Is Theory Based11A.6 The Logic of Performing a Confirmatory Factor Analysis11A.7 Model Specification11A.8 Model Identification11A.9 Model Estimation11A.10 Model Evaluation Overview11A.11 Assessing Fit of Hypothesized Models11A.12 Model Estimation: Assessing Pattern Coefficients11A.13 Model Respecification11A.14 General Considerations11A.15 Recommended ReadingsChapter 11B: Confirmatory Factor Analysis Using IBM SPSS Amos11B.1 Using IBM SPSS Amos11B.2 Numerical Example11B.3 Analysis Setup to Specify the Model11B.4 Model Identification11B.5 Structuring and Performing the Analysis11B.6 Working With the Analysis Output11B.7 Respecifying the Model11B.8 Output From the Respecified Model11B.9 Reporting Confirmatory Factor Analysis ResultsChapter 12A: Path Analysis: Multiple Regression Analysis12A.1 Overview12A.2 The Concept of a Path Model12A.3 The Appeal of Path Over Multiple Regression Analysis12A.4 Causality and Path Analysis12A.5 The Roles Played by Variables in a Path Structure12A.6 The Assumptions of Path Analysis12A.7 Missing Values in Path Analysis12A.8 The Multiple Regression Approach to Path Analysis12A.9 Indirect and Total Effects12A.10 Recommended ReadingsChapter 12B: Path Analysis: Multiple Regression Analysis Using IBM SPSS12B.1 The Data Set and Model Used in Our Example12B.2 Identifying the Variables in Each Analysis12B.3 Predicting Months_Teaching12B.4 Predicting Good_Teaching12B.5 Reporting the Path Analysis ResultsChapter 13A: Path Analysis: Structural Equation Modeling13A.1 Comparing Multiple Regression and Structural Equation Model Approaches13A.2 Differences Between the Equations Underlying Multiple Regression and Structural Equation Model Procedures13A.3 Configuring the Structural Model13A.4 Identifying the Structural Equation Model13A.5 Recommended ReadingsChapter 13B: Path Analysis: Structural Equation Modeling Using IBM SPSS Amos13B.1 Overview13B.2 The Data Set and Model Used in Our Example13B.3 Analysis Setup13B.4 The Analysis Output13B.5 Reporting the Path Analysis ResultsChapter 14A: Structural Equation Modeling14A.1 Overview of Structural Equation Modeling14A.2 Model Quality and the Structural Aspects of the Model14A.3 Latent Variables and Their Indicators14A.4 Identifying Structural Equation Models14A.5 Recommended ReadingsChapter 14B: Structural Equation Modeling Using IBM SPSS Amos14B.1 Overview14B.2 The Data Set and Model Used in Our Example14B.3 Model Configuration and Analysis Setup14B.4 Model Identification14B.5 Generating the Output14B.6 Analysis Output for the Model14B.7 Configuring and Evaluating the Respecified Model14B.8 Summary of the Results of the Model and Noting the Follow-up Analyses14B.9 Assessing the Indirect Effects in the Full Model14B.10 Assessing the Possibility of Having Obtained Complete Mediation in the Full Model14B.11 Assessing Mediation Through Self_ Regulation14B.12 Assessing Mediation Through Extrinsic_Goals14B.13 Synthesis of the Results14B.14 Reporting the SEM ResultsChapter 15A: Measurement and Structural Equation Modeling Invariance: Applying a Model to a Different Group15A.1 Overview15A.2 The General Strategy Used to Compare Groups15A.3 The Omnibus Model Comparison Phase15A.4 The Coefficient Comparison Phase15A.5 Recommended ReadingsChapter 15B: Assessing Measurement and Structural Invariance for Confirmatory Factor Analysis and Structural Equation Models Using IBM SPSS Amos15B.1 Overview and General Analysis Strategy15B.2 The Data Set Used for Examining Invariance in Both the Confirmatory Factor Analysis and Structural Equation Model Examples15B.3 Confirmatory Factor Analysis Invariance: Global Preliminary Analysis15B.4 Confirmatory Factor Analysis Invariance: Group 1 (Rural) Analysis15B.5 Confirmatory Factor Analysis Invariance: Group 2 Analysis15B.6 Confirmatory Factor Analysis Invariance: Model Evaluation Setup15B.7 Confirmatory Factor Analysis Invariance: Model Evaluation Output15B.8 Reporting the Confirmatory Factor Analysis Invariance Results15B.9 Structural Equation Model Invariance: Global Preliminary Analysis15B.10 Structural Equation Model Invariance: Group 1 (Rural) Analysis15B.11 Structural Equation Model Invariance: Group 2 Analysis15B.12 Structural Equation Model Invariance: Model Evaluation Setup15B.13 Structural Equation Model Invariance: Model Evaluation Output15B.14 Reporting the Structural Equation Model Invariance ResultsPART IV: CONSOLIDATING STIMULI AND CASESChapter 16A: Multidimensional Scaling16A.1 Overview16A.2 The Paired Comparison Method16A.3 Dissimilarity Data in MDS16A.4 Similarity/Dissimilarity Conceived as an Index of Distance16A.5 Dimensionality in MDS16A.6 Data Collection Methods16A.7 Similarity Versus Dissimilarity16A.8 Distance Models16A.9 A Classification Schema for MDS Techniques16A.10 Types of MDS Models16A.11 Assessing Model Fit16A.12 Recommended ReadingsChapter 16B: Multidimensional Scaling Using IBM SPSS16B.1 The Structure of This Chapter16B.2 Metric CMDS16B.3 Nonmetric CMDS16B.4 Metric WMDSChapter 17A: Cluster Analysis17A.1 Introduction17A.2 Two Types of Clustering17A.3 Hierarchical Clustering17A.4 k-Means Clustering17A.5 Recommended ReadingsChapter 17B: Cluster Analysis Using IBM SPSS17B.1 Hierarchical Cluster Analysis17B.2 k-Means Cluster AnalysisPART V: COMPARING SCORESChapter 18A: Between Subjects Comparisons of Means18A.1 Overview18A.2 Historical Context18A.3 A Brief Review of Some Basic Concepts18A.4 Using Multiple Dependent Variables18A.5 Evaluating Statistical Significance18A.6 Strength of Effect18A.7 Designs, Effects, and Partitioning of the Variance18A.8 Post-ANOVA Comparisons of Means18A.9 Hierarchical Analysis of Effects18A.10 Covariance Analysis18A.11 Recommended ReadingsChapter 18B: Between Subjects ANCOVA, MANOVA, and MANCOVA Using IBM SPSS18B.1 One-Way ANOVA Without the Covariate18B.2 One-Way ANCOVA18B.3 Three-Group MANOVA18B.4 Two-Group MANCOVA18B.5 Two-Way MANOVA Without the Covariate18B.6 Two-Way MANOVA Incorporating the Covariate (MANCOVA)Chapter 19A: Discriminant Function Analysis19A.1 Overview19A.2 The Formal Roles of the Variables in Discriminant Function Analysis and MANOVA19A.3 Discriminant Function Analysis and Logistic Analysis Compared19A.4 Sample Size for Discriminant Analysis19A.5 The Discriminant Model19A.6 Extracting Multiple Discriminant Functions19A.7 Dynamics of Extracting Discriminant Functions19A.8 Interpreting the Discriminant Function19A.9 Assessing Statistical Significance and the Relative Strength of the Discriminative Functions19A.10 Using Discriminant Function Analysis for Classification19A.11 Different Discriminant Function Methods19A.12 Recommended ReadingsChapter 19B: Three-Group Discriminant Function Analysis Using IBM SPSS19B.1 Numerical Example19B.2 Analysis Setup19B.3 Analysis Output19B.4 Reporting the Results of a Three- Group Discriminant Function AnalysisChapter 20A: Survival Analysis20A.1 Overview20A.2 The Dependent Variable in Survival Analysis20A.3 Ordinary Least Squares Regression Versus Survival Analysis20A.4 Censored Observations20A.5 Overview of Analysis Techniques for Survival Analysis in IBM SPSS20A.6 Life Table Analysis20A.7 Kaplan–Meier (Product-Limit) Survival Function Analysis20A.8 Cox Proportional Hazard Regression Model20A.9 Recommended ReadingsChapter 20B: Survival Analysis Using IBM SPSS20B.1 Numerical Example20B.3 Kaplan–Meier (Product-Limit) Survival Function Analysis20B.4 Cox Proportional Hazard Regression ModelReferencesAppendix A: Statistics TablesAuthor IndexSubject Index