Applied Multivariate Statistical Concepts

Cover
Endorsements
Half Title
Title
Copyright
Brief Contents
Detailed Contents
Preface
Acknowledgments
1 Multivariate Statistics
	What Are Multivariate Statistics?
		Decision Rules
	Coverage of the Textbook
		Multiple Regression
		Logistic Regression
		Multivariate Analysis of Variance
		Discriminant Analysis
		Cluster Analysis
		Exploratory Factor Analysis (EFA)
		Path Analysis, Confirmatory Factor Analysis, and Structural Equation Modeling (SEM)
		Multilevel Linear Modeling
		Propensity Score Analysis
	Layout of the Textbook
	Overarching Goal of the Textbook
2 Univariate and Bivariate Statistics Review
	Fundamental Concepts
	Hypothesis Testing
	Types of Decision Errors
		Level of Significance (α)
		Type II Error (β) and Power (1 – β)
	Statistical Versus Practical Significance
	Foundational Univariate Statistics
		Histogram
		Box and Whisker Plot
		Scatterplot
		Measures of Central Tendency
			Mode
			Median
			Mean
			Summary of Measures of Central Tendency
		Measures of Dispersion
			Variance
			Sample Variance and Standard Deviation
	Foundational Bivariate Statistics
		Independent and Dependent Samples t Test
		Analysis of Variance
			ANOVA Summary Table
		Covariance
		Pearson Product Moment Correlation Coefficient
		Simple Linear Regression
			Standardized Regression Model
			Prediction Errors
			Least Squares Criterion
	Segue Into Multivariate Statistics
3 Data Screening
	Data
	Understanding Your Data via Frequencies
	Missing Data
	Approaches for Dealing with Missing Data
		Historical Approaches for Addressing Missing Data
		Complete Case Analysis
		Last Observation Carried Forward
		Single Imputation: Mean, Median, or Mode Replacement
		Contemporary Approaches for Handling Missing Data
			Multiple Imputation
			Bayesian Multiple Imputation
			Inverse Probability Weighting
			Maximum Likelihood
	Addressing Missing Data Using Statistical Software
		Introduction to R
		R Basics
		Downloading R and RStudio
		Packages
		Working in R
		R for Missing Data: Multiple Imputation
		R for Missing Data: FIML
	Acknowledgment
4 Multiple Linear Regression
	What Multiple Linear Regression Is and How It Works
	Characteristics
		Partial Correlation
		Semipartial (Part) Correlation
	Unstandardized Regression Model
	Standardized Regression Model
	Coefficient of Multiple Determination and Multiple Correlation
	Significance Tests
		Test of Significance of the Overall Regression Model
		Test of Significance of bk
		Other Tests
	Methods of Entering Predictors
		Simultaneous Regression
		Backward Elimination
		Forward Selection
		Stepwise Selection
		“All Possible Subsets” Regression
		Hierarchical Regression
		Commentary on Sequential Regression Procedures
	Non-Linear Relationships
	Interactions
	Categorical Predictors
	Sample Size
	Power
	Effect Size
		Coefficient of Multiple Determination, R2
		Multiple Partial R2
		Partial f2
		Additional Effect Size Considerations
	Assumptions
		Independence
		Homoscedasticity
		Normality
		Linearity
		Fixed X
		Non-Collinearity
		Summary of Assumptions
	Mathematical Introduction Snapshot
	Computing Multiple Linear Regression Using Statistical Software
		Bootstrapping
		SPSS
		R
			Reading Data Into R
		Generating the Multiple Regression Model and Saving Values
		Generating Correlation Coefficients and Confidence Intervals of Coefficient Estimates
	Data Screening
		Independence
		Homoscedasticity
		Linearity
		Normality
			Interpreting Normality Evidence
	Screening Data for Influential Points
		Casewise Diagnostics
		Cook’s Distance
		Mahalanobis Distances
		Centered Leverage Values
		DFBETA
		Diagnostic Plots
	Non-Collinearity
	Power Using G*Power
		Post Hoc Power
		A Priori Power
	Research Question Template and Example Write-Up
	Additional Resources
5 Logistic Regression
	What Logistic Regression Is and How It Works
	Characteristics
		Logistic Regression Equation
		Probability
		Odds and Logit (or Log Odds)
		Estimation and Model Fit
		Significance Tests
			Test of Significance of the Overall Regression Model
			Test of Significance of the Logistic Regression Coefficients
			Methods of Predictor Entry
	Sample Size
	Power
	Effect Size
	Assumptions
		Non-Collinearity
		Linearity
		Independence of Errors
		Fixed X
		Conditions
			Non-Zero Cell Counts
			Non-Separation of Data
			Lack of Influential Points
	Mathematical Introduction Snapshot
	Computing Logistic Regression Using Statistical Software
		SPSS
		R
		Reading Data into R
		Generating the Logistic Regression Model and Saving Values
			Generating Confidence Intervals of Coefficient Estimates
			Exponentiating Coefficients
			Producing Odds Ratios and Their Confidence Intervals
	Data Screening
		Non-Collinearity
		Linearity
		Independence
		Absence of Outliers
			Cook’s Distance
			Leverage Values
			DFBETA
		Assessing Classification Accuracy
			ROC Curves and AUC
	Power Using G*Power
		Post Hoc Power
		A Priori Power
	Research Question Template and Example Writeup
	Additional Resources
6 Multivariate Analysis of Variance: Single-Factor, Factorial, and Repeated Measures Designs
	What Multivariate Analysis of Variance Is and How It Works
	Characteristics
		Characteristics of One-Way and k-Way MANOVA Models
		Hypotheses of One-Way and k-Way MANOVA Models
		Omnibus Multivariate Tests of One-Way and k-Way MANOVA Models
			Planned and Post Hoc Comparison Procedures of One-Way and k-Way MANOVA Models
		Characteristics of Repeated Measures MANOVA
		Hypothesis of Repeated Measures MANOVA
		Omnibus Multivariate Tests for Repeated Measures MANOVA
		Planned and Post Hoc Comparison Procedures for Repeated Measures MANOVA
	Sample Size
		Sample Size for One-Way and k-Way MANOVA Models
		Sample Size for Repeated Measures MANOVA
	Power
	Effect Size
		Effect Size for One-Way and k-Way MANOVA Models
		Effect Size for Repeated Measures MANOVA
	Assumptions
		Assumptions for One-Way and k-Way MANOVA Models
			Independence
			Multivariate Normality for the Dependent Variables
			Linearity
			Homogeneity of Variance-Covariance Matrices for the Dependent Variables
			Concluding Thoughts on Assumptions
		Assumptions for Repeated Measures MANOVA
	Conditions
	Mathematical Introduction Snapshot
		Mathematical Introduction Snapshot for One-Way and k-Way MANOVA Models
			Partitioning the Variation
		Mathematical Introduction Snapshot for Repeated Measures MANOVA
	Computing MANOVA Using Statistical Software
		Computing Factorial MANOVA Using SPSS
		Computing Factorial MANOVA Using R
		Computing Repeated Measures MANOVA Using SPSS
	Data Screening
		Data Screening for One-Way and k-Way MANOVA Models
			Independence
			Multivariate Normality of the Dependent Variables
			Linearity
			Homogeneity of Variance-Covariance Matrices
		Data Screening for Repeated Measures MANOVA
			Independence
			Univariate and Multivariate Normality of the Dependent Variables
			Linearity
			Homogeneity of Variance-Covariance Matrices
	Power Using G*Power
		Power for One-Way and k-Way MANOVA Models
		Post Hoc Power for Factorial MANOVA Using G*Power
			Global Effects
			Power for Interactions
		A Priori Power for Factorial MANOVA Using G*Power
		Power for Repeated Measures MANOVA
			Post Hoc Power for Repeated Measures MANOVA Using G*Power
			A Priori Power for Repeated Measures MANOVA Using G*Power
	Research Question Template and Example Write-Up
		Research Question Template and Example Write-Up for One-Way and k-Way MANOVA Models
		Research Question Template and Example Write-Up for Repeated Measures MANOVA
7 Discriminant Analysis
	What Discriminant Analysis Is and How It Works
	Characteristics
		Discriminant Function
		Discrimination
		Standardized Coefficients
		Classification
		Classification Matrix
		Interpreting the Discriminant Functions
			Eigenvalues
			Canonical Correlations
			Wilks’ Lambda
			Structure Coefficients
			Centroids
		Discriminant Function Plots
			Cut Score
		Cross-Validation
		Putting the Pieces Together
	Sample Size
	Power
	Effect Size
		Overall Discriminant Analysis Effect Size
		Individual Discriminant Function Effect Size
		Acceptable Classification
			Standards of Comparison
			Press’s Q
			Kappa
	Assumptions
		Independence
		Linearity
		Non-Collinearity
		Multivariate Normality
		Homogeneity of Variance-Covariance Matrices
		Concluding Thoughts on Assumptions
	Mathematical Introduction Snapshot
	Computing Discriminant Analysis Using Statistical Software
		Computing Discriminant Analysis Using SPSS
		Computing Discriminant Analysis Using R
			Generating Kappa Statistic for Classification Accuracy
	Data Screening
		Independence
		Linearity
		Non-Collinearity
		Normality of Independent Variables
		Homogeneity of Variance-Covariance Matrices
	Power Using G*Power
		Post Hoc Power for Discriminant Analysis Using G*Power
		A Priori Power for Discriminant Analysis Using G*Power
	Research Question Template and Example Write-Up
8 Cluster Analysis
	What Cluster Analysis Is and How It Works
	Characteristics
		Variable Selection
		Clustering Procedure Selection
	Hierarchical Methods
	Non-Hierarchical Methods
	Number of Clusters
		Cross-Validation of Cluster Solution
		Interpreting the Cluster Solution
	Sample Size
	Power
	Effect Size
	Assumptions
	Conditions
	Mathematical Introduction Snapshot
	Computing Cluster Analysis Using Statistical Software
		Cluster Analysis Using SPSS
		Cluster Analysis Using R
	Data Screening
	Latent Class Analysis
	Research Question Template and Example Write-Up
9 Exploratory Factor Analysis
	What Exploratory Factor Analysis Is and How It Works
	Characteristics
		Principal Components versus Exploratory Factor Analysis
		Exploratory Factor Analysis Specification Conditions and Decisions
		Factorability
			Measurement Scale of Variables
			Homogeneity of the Sample in Relation to the Underlying Factor Structure
			Initial Factorability Assessment
		Fitting the Factor Model
			Factor Extraction
		Factor Retention
			Scree Plots
			Kaiser’s Rule (Eigenvalues Greater Than One)
			Parallel Analysis
			Number of Variables per Factor
		Factor Rotation
			Orthogonal Rotation
			Oblique Rotation
			Associated Matrices
		Factor Loadings
	Sample Size
	Power
	Effect Size
	Assumptions
		Independence
		Linearity
		Absence of Outliers in Cases and Variables
		Lack of Extreme Multicollinearity and Singularity
		Concluding Thoughts on Assumptions
	Mathematical Introduction Snapshot
	Computing EFA Using Statistical Software
		Computing EFA with Continuous Data Using SPSS
		SPSS Parallel Analysis for Determining Factor Retention
		Computing EFA with R
	Data Screening
		Independence
		Linearity
		Multivariate Normality
		Extreme Multicollinearity and Singularity
	Research Question Template and Example Write-Up
10 Path Analysis, Confirmatory Factor Analysis, and Structural Equation Modeling
	Introduction
	What Path Analysis and Confirmatory Factor Analysis Are and How They Work
	Characteristics
		Path Analysis
		CFA Model Specification, Identification, Estimation, Evaluation, and Interpretation
	CFA Model Specification
		CFA Model Identification
		CFA Model Estimation
		CFA Model Evaluation and Interpretation
		Parameter Estimate Evaluation
		CFA Model Modification
	Structural Equation Modeling
	Related Models
		Multiple Group Models
		Second-Order CFA
		Dynamic Factor Models
		Multiple Indicator Multiple Cause (MIMIC) Model
		Mixed Variable and Latent Class Mixture Models
		Multilevel SEM
		Latent Growth Models
	CFA Sample Size
	CFA Effect Size
	CFA Assumptions
		Independence
		Linearity
		Multivariate Normality and Absence of Outliers
		Lack of Extreme Multicollinearity and Singularity
		Concluding Thoughts on Assumptions
	Mathematical Introduction Snapshot
	Computing CFA Using R
		Data for CFA
		Reading Data into R
		Generating a One-Factor CFA
		Generating a One-Factor CFA with Modification
		Generating a Two-Factor CFA
		Estimating Degrees of Freedom
		Generating a Path Diagram
	Data Screening
		Diagnostics
		Assumptions
			Linearity
		Generating CFA With Ordinal Data
	Power
		Power Using G*Power
		Power Using semPower
	Research Question Template and Example Write-Up
	Model Specification
	Substantive Conclusions
11 Multilevel Linear Modeling
	What Multilevel Linear Modeling Is and How It Works
	Characteristics
		Intercepts and Slopes as Outcomes
		Level One
		Level Two
		Fixed, Random, and Non-Randomly Varying Effects
		Level One
		Level Two
		Level One
		Level Two
		Level One
		Level Two
		Level Two
		Intraclass Correlation Coefficient
		Centering
			Uncentered
			Grand Mean Centering
			Group Mean Centering
			Centering Recommendations
		Model Estimation
			Null Model: The One-Way Random Effects ANOVA
			Random Intercepts Model
			Random Coefficients Model: Random Intercepts and Random Slopes Model
			Additional Models
		Estimation Methods
		Model Fit
			Deviance Test
			AIC
			BIC
			SBIC
	Sample Size
	Power
		Power for Cluster Randomized Trials
		Resources for Computing Power in Multilevel Models
	Effect Size
		Effect Size: Overall Model
		Effect Size: Within-Group
		Effect Size: Between-Groups for Intercepts
		Effect Size: Between-Groups for Slopes
	Assumptions
		Linearity
		Normality
		Homoscedasticity or Homogeneity of Variance
			Level One Homoscedasticity
			Level Two Homoscedasticity
		Uncorrelated Predictors and Random Effects
	Conditions
	Mathematical Introduction Snapshot
	Computing Multilevel Modeling Using Statistical Software
		Computing Multilevel Modeling Using HLM
		Computing Multilevel Modeling Using R
	Data Screening
		Level One Residuals
		Level Two Residuals
		Graphing
	Model Fit
		Difference in Deviances Likelihood Ratio Test
		Model Fit: Bayesian Information Criteria
		Saving Residuals in R
		Testing Interactions in R
	Research Question Template and Example Write-Up
12 Propensity Score Analysis
	What Propensity Score Analysis Is and How It Works
	Characteristics
		Analytic Decisions in Propensity Score Analysis
		Estimating the Propensity Score
		Covariate Selection
		Propensity Score Estimation Method
		Checking Model Adequacy
		Conditioning on the Propensity Score
		Propensity Score Matching
			Distance
			Algorithms
			Additional Propensity Score Methods
			Structure
	Sample Size
	Assumptions
	Conditions
	Mathematical Introduction Snapshot
	Computing Propensity Score Analysis Using R
	Example Write-Up
Appendix A: An Introduction to Matrix Algebra
	Matrices
	Calculations with Matrices
		Matrix Addition and Subtraction
		Matrix Multiplication and (Almost) Division
	Types of Matrices
		Vector
		Square Matrix
		Diagonal Matrix
		Symmetric Matrix
		Identity Matrix
		Singular Matrix
	Matrices and Multivariate Statistics
Appendix B: Distribution Tables
	1 Percentage Points of the t Distribution
	2 Percentage Points of the F Distribution
Index