Primer of Applied Regression & Analysis of Variance, Third Edition

Halftitle Page
Title Page
Copyright Page
Dedication
Contents
Preface
CHAPTER ONE Why Do Multivariate Analysis?
	Our First Visit to Mars
	Dummies on Mars
	Summary
	Problem
CHAPTER TWO The First Step: Understanding Simple Linear Regression
	More on Mars
		The Population Parameters
	How to Estimate the Line of Means from a Sample
		The Best Straight Line Through the Data
		Variability About the Regression Line
		Standard Errors of the Regression Coefficients
	How Convincing is the Trend?
		Testing the Slope of the Regression Line
		Comparing Slopes and Intercepts of Two Regression Lines
		Testing the Regression as a Whole
		Cell Phone Radiation, Reactive Oxygen Species, and DNA Damage in Human Sperm
	Confidence Intervals for Regression
		Confidence Interval for the Line of Means
		Confidence Interval for an Observation
	Correlation and Correlation Coefficients
		The Relationship Between Regression and Correlation
	Doing Regression and Correlation Analysis with a Computer
	Heat Exchange in Gray Seals
	Summary
	Problems
CHAPTER THREE Regression with Two or More Independent Variables
	What We Really Did on Mars
	How to Fit the Best Plane Through a Set of Data
		Computing the Regression Coefficients
		Variability About the Regression Plane
		Standard Errors of the Regression Coefficients
		Muddying the Water: Multicollinearity
	Does the Regression Equation Describe the Data?
		Incremental Sums of Squares and the Order of Entry
		Relationship to t Tests of Individual Regression Coefficients
	The Coefficient of Determination and the Multiple Correlation Coefficient
	More Dummies on Mars
	Mechanisms of Toxic Shock
	Protein Synthesis in Newborns and Adults
	General Multiple Linear Regression
		Multiple Regression in Matrix Notation
	Diabetes, Cholesterol, and the Treatment of High Blood Pressure
	Baby Birds Breathing in Burrows
	Polynomial (And Some Other Nonlinear) Regressions
		Heat Exchange in Gray Seals Revisited
		Other Nonlinear Regressions
	Interactions Between the Independent Variables
		How Bacteria Adjust to Living in Salty Environments
		The Response of Smooth Muscle to Stretching
	Summary
	Problems
CHAPTER FOUR Do the Data Fit the Assumptions?
	Another Trip to Mars
	Looking at the Residuals
	A Quantitative Approach to Residual Analysis
		Standardized Residuals
		Using Residuals to Test for Normality of the Residuals
		Leverage
		Studentized Residuals
		Cook’s Distance
	What do you do with an Influential Observation once you have Found it?
		Problems with the Data
		Problems with the Model
		Data Transformations
	Water Movement Across the Placenta
	Cheaper Chicken Feed
	How the Body Protects itself from Excess Zinc and Copper
		Back to Square One
	Cheaper Chicken Feed Revisited: Bootstrapping and Robust Standard Errors
		Bootstrap Standard Errors
		Robust Standard Errors
	Clustered Data
	Aids Orphans in Uganda
	Summary
	Problems
CHAPTER FIVE Multicollinearity and What to Do About It
	Where Multicollinearity Comes from
	back To Mars
	Detecting and Evaluating Multicollinearity
		Qualitative Suggestions of Harmful Multicollinearity
		Correlations Among the Independent Variables
		The Variance Inflation Factor
		Auxiliary Regressions
		The Correlations of the Regression Coefficients
	The Consequences of having Two Pumps in One Heart
	Fixing the Regression Model
		Centering the Independent Variables
		Deleting Predictor Variables
		More on Two Pumps in One Heart
	Fixing the Data
		Getting More Data on the Heart
	Using Principal Components to Diagnose and Treat Multicollinearity
		Standardized Variables, Standardized Regression, and the Correlation Matrix
		Principal Components of the Correlation Matrix
		Principal Components to Diagnose Multicollinearity on Mars
		Principal Components and the Heart
		Principal Components Regression
		More Principal Components on Mars
		The Catch
		Recapitulation
	Summary
	Problems
CHAPTER SIX Selecting the “Best” Regression Model
	So What do you do?
	What Happens When the Regression Equation Contains the Wrong Variables?
	What does “Best” Mean?
		The Coefficient of Determination R2
		The Adjusted R2
		The Standard Error of the Estimate sy|x
		Independent Validations of the Model with New Data
		The Predicted Residual Error Sum of Squares, Press
		Bias Due to Model Underspecification and Cp
		But What Is “Best”?
	Selecting Variables with all Possible Subsets Regression
		What Determines an Athlete’s Time in a Triathlon?
	Sequential Variable Selection Techniques
		Forward Selection
		Backward Elimination
		Stepwise Regression
		Interpreting the Results of Sequential Variable Selection
		Another Look at the Triathlon
	Predictive Optimism
	Summary
	Problems
CHAPTER SEVEN Missing Data
	Prevention is Key
	Missing Data Mechanisms
	Ad Hoc Missing Data Handling Methods
		Listwise Deletion
		Single Imputation: Mean and Regression Imputation
	Maximum Likelihood Estimation with Complete Data
		Using Maximum Likelihood to Estimate Population Mean and Standard Deviation
		Maximum Likelihood Regression
		Putting It All Together: Martian Weights Predicted by Heights and Water Consumption via Maximum Likelihood Estimation
	Regression Analysis via Means, Variances, and Covariances
		The Multivariate Normal Distribution and Covariance
		Estimating the Regression Coefficients Based on the Mean and Covariance Matrices
		Back to Mars
	Maximum Likelihood Regression Estimation with Incomplete Data
		Missing Martians
		Excess Zinc and Copper and Missing Data
		Missing Data Mechanisms Revisited: Three Mechanisms for Missing Martians
	Non-Normal Data and Maximum Likelihood Estimation
		Smoking, Social Networks, and Personality
		The Multivariate Normality Assumption
	Multiple Imputation
		Generate the Multiply-Imputed Data Sets
		Analyzing the Multiply-Imputed Data Sets
		Combining Results from Multiply-Imputed Data Sets and Quantifying the Uncertainty Due to Multiple Imputation
	Multiple Imputation Extensions and Complications
		Number of Imputations
		How Many and Which Independent Variables Should be Included in the Imputation Process?
		Should a Dependent Variable with Complete Data be Included in Generating Multiple Imputations?
		Small Samples
		Non-Normal Data
		Clustered Data
		Data Not Missing at Random
		Excess Zinc and Copper and Missing Data Revisited
	Summary
	Problems
CHAPTER EIGHT One-Way Analysis of Variance
	Using A t Test to Compare two Groups
		Does Secondhand Tobacco Smoke Nauseate Martians?
		Using Linear Regression to Compare Two Groups
	The Basics of one-way Analysis of Variance
		Traditional Analysis-of-Variance Notation
		Accounting for All the Variability in the Observations
		Expected Mean Squares
		Using Linear Regression to Do Analysis of Variance with Two Groups
	Using Linear Regression to do one-way Analysis of Variance with any Number of Treatments
		Hormones and Depression
	Multiple Comparison Testing
		The Bonferroni t Test
		More on Hormones and Depression
		Holm t Test
		Holm–Sidak t Test
		What Is a Family?
		Diet, Drugs, and Atherosclerosis
	Testing the Assumptions in Analysis of Variance
		Formal Tests of Homogeneity of Variance
		More on Diet, Drugs, and Atherosclerosis
		Alternatives to the Usual F Statistic When Variances Are Unequal
		Alternatives to the t Test Statistic When Variances Are Unequal
		Maturing Rat Lungs
	Summary
	Problems
CHAPTER NINE Two-Way Analysis of Variance
	Traditional two-way Analysis of Variance
	Personality Assessment and Faking High Gender Identification
		Traditional Analysis of Variance
		Using Regression to Perform Two-Way Analysis of Variance
	An Alternative Approach for Coding Dummy Variables
		An Alternative Approach to Personality
		Why Does It Matter How We Code the Dummy Variables?
		The Kidney, Sodium, and High Blood Pressure
		What Do Interactions Tell Us?
		Multiple Comparisons in Two-Way Analysis of Variance
		More on the Kidney, Sodium, and High Blood Pressure
	Unbalanced Data
	All Cells Filled, but some Cells have Missing Observations
		The Case of the Missing Kidneys
		Summary of the Procedure
		What If You Use the Wrong Sum of Squares?
		Multiple Comparisons with Missing Data
	One or More Cells Empty
		Multiple Comparisons with Empty Cells
		More on the Missing Kidney
		Multiple Comparisons for the Missing Kidney
		Recapitulation
	Randomized Block Designs
		A More Thorough Study of Martian Nausea
		What Do You Gain by Blocking?
		Regression Implementation of Randomized Blocks
		Recapitulation
	Summary
	Problems
CHAPTER TEN Repeated Measures
	One-Way Repeated-Measures Analysis of Variance
		Hormones and Food
		Comparison with Simple Analysis of Variance
		Multiple Comparisons in Repeated-Measures Analysis of Variance
		Recapitulation
	Two-Factor Analysis of Variance with Repeated Measures on one Factor
		Partitioning the Variability
		Testing the Non–Repeated-Measures Factor
		Testing the Repeated-Measures Factor
		Is Alcoholism Associated with a History of Childhood Aggression?
	The General Linear Model
		Traditional Regression Model Structure for Mixed Models Estimated by Maximum Likelihood
		Maximum Likelihood Estimation for Linear Mixed Models
	Hypothesis Testing in Maximum Likelihood Estimation
		Testing the ANOVA Effects Using the Regression Equation
		Testing the Individual Coefficients
		The Wald χ2 and F Tests
		Maximum Likelihood Mixed Models Analysis of Drinking and Antisocial Personality Using an Overspecified Model
		Maximum Likelihood Mixed Models Analyses of the Study of Drinking and Antisocial Personality: Including Subjects with Missing Data on the Dependent Variable
	Better Estimates of the Covariance Structure for Repeated Measures
		Treating Between-Subjects Effects as Random Effects
		Estimating the Covariance in the Residuals
		This Is Your Rat’s Brain on Drugs
	Two-Way Analysis of Variance with Repeated Measures on both Factors
		Candy, Chewing Gum, and Tooth Decay
	Missing Data in Repeated Measures on both of two Factors
		More on Chewing Gum
	Restricted Maximum Likelihood Estimation
		Secondhand Smoke and the Cardiovascular System
	Missing Data in Two-Factor Ols Analysis of Variance with Repeated Measures on one Factor
		Assumptions Underlying Repeated-Measures Analysis of Variance
		Expected Mean Squares, Fixed Effects, Random Effects, and Mixed Models
		What Happens to the Expected Mean Squares in Mixed Models When There Are Missing Data?
		More on Drinking and Antisocial Personality
	Ols Methods for two-way Analysis of Variance with Repeated Measures on both Factors
		Partitioning the Variability
		Candy, Chewing Gum, and Tooth Decay Revisited
		What Happens to the Expected Mean Squares When There Are Missing Data?
		More on Chewing Gum
		Compound Symmetry Revisited: Rat Brains and Cocaine
	Accounting for Between-Subjects Variability in Linear Regression
		Random-Effects Regression: Reduced Nausea Cigarettes
	Summary
	Problems
CHAPTER ELEVEN Mixing Continuous and Categorical Variables: Analysis of Covariance
	High-Pressure Pregnancies
		From the Regression Perspective
		From the ANOVA Perspective
		Confounding Variables
	How does Analysis of Covariance Work?
		The Relationship of ANCOVA to Regression
		Adjusted Means
		Testing the Assumption of Homogeneous Slopes
	Cool Hearts
		Multiple Comparisons After Traditional ANCOVA
		Did We Gain Anything by Doing ANCOVA Instead of ANOVA?
	What Happens When the Range of Values of the Covariates is Very Different among the Groups?
		Fat-Free Exercising
	What Happens When the Slopes are not Homogeneous?
	More Assumption Checking
		Ridding Your Body of Drugs
	More Complicated Analyses of Covariance
	Summary
	Problems
CHAPTER TWELVE Regression with a Qualitative Dependent Variable: Logistic Regression
	Logistic Regression
		Our Last Visit to Mars
		Odds
		The Multiple Logistic Equation
	Estimating the Coefficients in a Logistic Regression
		Maximum Likelihood Estimation
	Hypothesis Testing in Logistic Regression
		Testing the Logistic Equation
		Testing the Individual Coefficients
		Confidence Intervals for Individual Coefficients
		Back to Mars
	Is the Logistic Regression Equation an Appropriate Description of the Data?
		Regression Diagnostics for Logistic Regression
		Goodness-of-Fit Testing
	Are bone Cancer Patients Responding to Chemotherapy?
	Stepwise Logistic Regression
		Nuking the Heart
	Convergence Problems in Logistic Regression
	Logistic Regression for Longitudinal and Clustered Data
		Robust Standard Errors in Logistic Regression
		Generalized Estimating Equations
		Generalized Linear Mixed Models Analysis of Clustered Binary Data
		Selecting an Approach for Clustered Data
	Summary
	Problems
CHAPTER THIRTEEN Regression Modeling of Time-to-Event Data: Survival Analysis
	Surviving on Pluto
		Censoring on Pluto
		Estimating the Survival Curve
		The Hazard Function
	The Proportional Hazards Model
		Bone Marrow Transplantation to Treat Adult Leukemia
		Testing the Individual Coefficients
		Survival Following Surgery for Pancreatic Cancer
	Additional Topics in Proportional Hazards Regression
		Testing the Proportionality Assumption
		Variable Selection and Stepwise Techniques
		Recurrent Events and Clustered Data
		Missing Data
	Summary
	Problems
CHAPTER FOURTEEN Nonlinear Regression
	Exponential Models
	Martian Moods
		Grid Searches
	Finding the Bottom of the Bowl
		The Method of Steepest Descent
		The Gauss–Newton Method
		Marquardt’s Method
		Where Do You Get a Good First Guess?
		How Can You Tell That You Are at the Bottom of the Bowl?
	Mathematical Development of Nonlinear Regression Algorithms
		The Method of Steepest Descent
		The Gauss–Newton Method
		Marquardt’s Method
	Hypothesis Testing in Nonlinear Regression
	Regression Diagnostics in Nonlinear Regression
	Experimenting with Drugs
	Keeping Blood Pressure Under Control
		Is the Model Parameterized in the Best Form?
	Summary
	Problems
APPENDIX A A Brief Introduction to Matrices and Vectors
	Definitions
	Adding and Subtracting Matrices
	Matrix Multiplication
	Inverse of a Matrix
	Transpose of a Matrix
	Eigenvalues and Eigenvectors
APPENDIX B Statistical Package Cookbook
	General Comments on Software
	Regression
		Minitab
		SAS
		SPSS
		Stata
	Multicollinearity
		Minitab
		SAS
		SPSS
		Stata
	Variable Selection Methods
		Minitab
		SAS
		SPSS
		Stata
	Missing Data
		Minitab
		SAS
		SPSS
		Stata
	One-Way Analysis of Variance
		Minitab
		SAS
		SPSS
		Stata
	Two-Way Analysis of Variance
		Minitab
		SAS
		SPSS
		Stata
	One-Way Repeated-Measures Analysis of Variance
		Minitab
		SAS
		SPSS
		Stata
	Two-Way Repeated-Measures Analysis of Variance with Repeated Measures on one Factor
		Minitab
		SAS
		SPSS
		Stata
	Two-Way Repeated-Measures Analysis of Variance with Repeated Measures on both Factors
		Minitab
		SAS
		SPSS
		Stata
	Random-Effects Regression
	Analysis of Covariance
		Minitab
		SAS
		SPSS
		Stata
	Logistic Regression
		Minitab
		SAS
		SPSS
		Stata
	Cox Proportional Hazards Regression
		Minitab
		SAS
		SPSS
		Stata
	Nonlinear Regression
		Minitab
		SAS
		SPSS
		Stata
APPENDIX C Data for Examples
APPENDIX D Data for Problems
APPENDIX E Statistical Tables
APPENDIX F Solutions to Problems
Index