Applied Regression Analysis and Other Multivariable Methods


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1 THIRD EDITION Applied Regression Analysis and Other Multivariable Methods David G. Kleinbaum Emory University Lawrence L. Kupper University of North Carolina, Chapel Hill Keith E. Muller University of North Carolina, Chapel Hill Azhar Nizam Emory University An Alexander Kugushev Book ^P> Duxbury Press An Imprint of Brooks/Cole Publishing Company l P An International Thomson Publishing Company Pacific Grove Albany Belmont Bonn Boston Cincinnati Detroit Johannesburg London Madrid Melbourne Mexico City New York Paris Singapore Tokyo Toronto Washington
2 Contents 1 CONCEPTS AND EXAMPLES OF RESEARCH 11 Concepts Examples Concluding Remarks References 6 2 CLASSIFICATION OF VARIABLES AND THE CHOICE OF ANALYSIS 21 Classification of Variables Overlapping of Classification Schemes Choice of Analysis 11 References 13 3 BASIC STATISTICS: A REVIEW Preview Descriptive Statistics Random Variables and Distributions Sampling Distributions of /, # 2, and F Statistical Inference: Estimation Statistical Inference: Hypothesis Testing 24 xi
3 xii Contents 37 Error Rates, Power, and Sample Size 28 Problems 30 References 33 4 INTRODUCTIONTO REGRESSION ANALYSIS Preview Association versus Causality Statistical versus Deterministic Models Concluding Remarks 38 References 38 5 STRAIGHTLINE REGRESSION ANALYSIS Preview Regression with a Single Independent Variable Mathematical Properties of a Straight Line Statistical Assumptions for a Straightline Model Determining the Bestfitting Straight Line Measure of the Quality of the Straightline Fit and Estimate of a Inferences About the Slope and Intercept Interpretations of Tests for Slope and Intercept Inferences About the Regression Line JU Y \X = ßo + ßi% Prediction of a New Value of FatX Assessing the Appropriateness of the Straightline Model 60 Problems 60 References 87 THE CORRELATION COEFFICIENT AND STRAIGHTLINE REGRESSION ANALYSIS Definition of r ras a Measure of Association The Bivariate Normal Distribution r and the Strength of the Straightline Relationship What r Does Not Measure Tests of Hypotheses and Confidence Intervals for the Correlation Coefficient Testing for the Equality of Two Correlations 99 Problems 101 References 103
4 Contents xiii 7 THE ANALYSISOFVARIANCE TABLE Preview The ANOVA Table for Straightline Regression 104 Problems 108 ß ö MULTIPLE REGRESSION ANALYSIS: GENERAL CONSIDERATIONS Preview Multiple Regression Models Graphical Look at the Problem Assumptions of Multiple Regression Determining the Best Estimate of the Multiple Regression Equation The ANOVA Table for Multiple Regression Numerical Examples 121 Problems 123 References TESTING HYPOTHESES IN MULTIPLE REGRESSION Preview Test for Significant Overall Regression PartialFTest Multiple PartialFTest Strategies for Using Partial F Tests Tests Involving the Intercept 150 Problems 151 References 159 CORRELATIONS: MULTIPLE, PARTIAL, AND MULTIPLE PARTIAL Preview Correlation Matrix Multiple Correlation Coefficient Relationship of Ry\x h x 2,...,x k to the Multivariate Normal Distribution Partial Correlation Coefficient Alternative Representation of the Regression Model 172
5 xiv Contents 107 Multiple Partial Correlation Concluding Remarks 174 Problems 174 Reference CONFOUNDING AND INTERACTION IN REGRESSION 111 Preview Overview Interaction in Regression Confounding in Regression Summary and Conclusions 199 Problems 199 Reference REGRESSION DIAGNOSTICS Preview Simple Approaches to Diagnosing Problems in Data Residual Analysis Treating Outliers Collinearity Scaling Problems Treating Collinearity and Scaling Problems Alternate Strategies of Analysis An Important Caution 252 Problems 253 References POLYNOMIAL REGRESSION Preview Polynomial Models Leastsquares Procedure for Fitting a Parabola ANOVA Table for Secondorder Polynomial Regression Inferences Associated with Secondorder Polynomial Regression 136 Example Requiring a Secondorder Model Fitting and Testing Higherorder Models Lackoffit Tests Orthogonal Polynomials 292
6 Contents xv Strategies for Choosing a Polynomial Model 301 Problems DUMMY VARIABLES IN REGRESSION Preview Definitions Rule for Defming Dummy Variables Comparing Two Straightline Regression Equations: An Example Questions for Comparing Two Straight Lines Methods of Comparing Two Straight Lines Method I: Using Separate Regression Fits to Compare Two Straight Lines Method II: Using a Single Regression Equation to Compare Two Straight Lines Comparison of Methods I and II Testing Strategies and Interpretation: Comparing Two Straight Lines Other Dummy Variable Models Comparing Four Regression Equations Comparing Several Regression Equations Involving Two Nominal Variables 336 Problems 338 References 360 , c ANALYSIS OF COVARIANCE AND OTHER 1 ^ METHODS FOR ADJUSTING CONTINUOUS DATA Preview Adjustment Problem Analysis of Covariance Assumption of Parallelism: A Potential Drawback Analysis of Covariance: Several Groups and Several Covariates Comments and Cautions Summary 371 Problems 371 Reference SELECTING THE BEST REGRESSION EQUATION Preview Steps in Selecting the Best Regression Equation Step 1: Specifying the Maximum Model Step 2: Specifying a Criterion for Selecting a Model Step 3: Specifying a Strategy for Selecting Variables 392
7 xvi Contents 166 Step 4: Conducting the Analysis Step 5: Evaluating Reliability with Split Samples Example Analysis ofactual Data Issues in Selecting the Most Valid Model 409 Problems 409 References ONEWAY ANALYSIS OFVARIANCE Preview Oneway ANOVA: The Problem, Assumptions, and Data Configuration Methodology for Oneway Fixedeffects ANOVA Regression Model for Fixedeffects Oneway ANOVA Fixedeffects Model for Oneway ANOVA Randomeffects Model for Oneway ANOVA Multiplecomparison Procedures for Fixedeffects Oneway ANOVA Choosing a Multiplecomparison Technique Orthogonal Contrasts and Partitioning an ANOVA Sum of Squares 457 Problems 463 References RANDOMIZED BLOCKS: SPECIAL CASE OF TWOWAY ANOVA 181 Preview Equivalent Analysis of a Matched Pairs Experiment PrincipleofBlocking Analysis of a Randomizedblocks Experiment ANOVA Table for a Randomizedblocks Experiment Regression Models for a Randomizedblocks Experiment Fixedeffects ANOVA Model for a Randomizedblocks Experiment 502 Problems 503 References TWOWAY ANOVA WITH EQUAL CELL NUMBERS Preview Usinga Table of Cell Means General Methodology F Tests for Twoway ANOVA Regression Model for Fixedeffects Twoway ANOVA Interactions in Twoway ANOVA Random and Mixedeffects Twoway ANOVA Models 541 Problems 544 References 560
8 Contents xvii 20 TWOWAY ANOVA WITH UNEQUAL CELL NUMBERS Preview Problems with Unequal Cell Numbers: Nonorthogonality Regression Approach for Unequal Cell Sample Sizes Higherway ANOVA 571 Problems 572 References ANALYSIS OF REPEATED MEASURES DATA Preview Examples General Approach for Repeated Measures ANOVA Overview of Selected Repeated Measures Designs and ANOVAbased Analyses Repeated Measures ANOVA for Unbalanced Data Other Approaches to Analyzing Repeated Measures Data 612 Appendix 21A Examples of SAS's GLM and MIXED Procedures 613 Problems 616 References THE METHOD OF MAXIMUM LIKELIHOOD Preview The Principle of Maximum Likelihood Statistical Inference via Maximum Likelihood Summary 652 Problems 653 References LOGISTIC REGRESSION ANALYSIS Preview The Logistic Model Estimating the Odds Ratio Using Logistic Regression A Numerical Example of Logistic Regression Theoretical Considerations An Example of Conditional ML Estimation Involving Pairmatched Data with Unmatched Covariates Summary 681 Problems 682 References 686
9 xviii Contents 24 POISSON REGRESSION ANALYSIS Preview The Poisson Distribution An Example of Poisson Regression Poisson Regression: General Considerations Measures of Goodness of Fit Continuation of Skin Cancer Data Example A Second Illustration of Poisson Regression Analysis Summary 704 Problems 705 References 709 A APPENDIX A TABLES 711 Al Standard Normal Cumulative Probabilities 712 A2 Percentiles of the t Distribution 715 A3 Percentiles of the Chisquare Distribution 716 A4 Percentiles of the F Distribution 717 A5 Values off In 1 +r 1 r 724 A6 Upper a Point of Studentized Range 726 A7 Orthogonal Polynomial Coefficients 728 A8 Bonferroni Corrected Jackknife and Studentized Residual Critical Values 729 A9 Critical Values for Leverages 730 A10 Critical Values for the Maximum of N Values of Cook's d(i) times (nk\) 731 B APPENDIX B MATRICES AND THEIR RELATIONSHIP TO REGRESSION ANALYSIS 732 APPENDIX C ANOVA INFORMATION FOR FOUR COMMON BALANCED REPEATED MEASURES DESIGNS 744 C1 Balanced Repeated Measures Design with One Crossover Factor (Treatments) 744 C2 Balanced Repeated Measures Design with Two Crossover Factors 746 C3 Balanced Repeated Measures Design with One Nest Factor (Treatments) 750 C4 Balanced Repeated Measures Design with One Crossover Factor and One Nest Factor 752 C5 Balanced Twogroup Pre/Posttest Design 755 References 757 ) SOLUTIONS TO EXERCISES 758 INDEX 787
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