Book description
This classic text on multiple regression is noted for its nonmathematical, applied, and dataanalytic approach. Readers profit from its verbalconceptual exposition and frequent use of examples.
The applied emphasis provides clear illustrations of the principles and provides worked examples of the types of applications that are possible. Researchers learn how to specify regression models that directly address their research questions. An overview of the fundamental ideas of multiple regression and a review of bivariate correlation and regression and other elementary statistical concepts provide a strong foundation for understanding the rest of the text. The third edition features an increased emphasis on graphics and the use of confidence intervals and effect size measures, and an accompanying website with data for most of the numerical examples along with the computer code for SPSS, SAS, and SYSTAT, at www.psypress.com/9780805822236 .
Applied Multiple Regression serves as both a textbook for graduate students and as a reference tool for researchers in psychology, education, health sciences, communications, business, sociology, political science, anthropology, and economics. An introductory knowledge of statistics is required. Selfstanding chapters minimize the need for researchers to refer to previous chapters.
Table of contents
 Cover
 Halftitle
 Title
 Copyright
 Dedication
 Contents
 Preface

Chapter 1: Introduction
 1.1 Multiple Regression/Correlation as a General DataAnalytic System
 1.2 A Comparison of Multiple Regression/Correlation and Analysis of Variance Approaches
 1.3 Multiple Regression/Correlation and the Complexity of Behavioral Science
 1.4 Orientation of the Book
 1.5 Computation, the Computer, and Numerical Results
 1.6 The Spectrum of Behavioral Science
 1.7 Plan for the Book
 1.8 Summary

Chapter 2: Bivariate Correlation and Regression
 2.1 Tabular and Graphic Representations of Relationships
 2.2 The Index of Linear Correlation Between Two Variables: The Pearson Product Moment Correlation Coefficient
 2.3 Alternative Formulas for the Product Moment Correlation Coefficient
 2.4 Regression Coefficients: Estimating Y From X
 2.5 Regression Toward the Mean
 2.6 The Standard Error of Estimate and Measures of the Strength of Association
 2.7 Summary of Definitions and Interpretations
 2.8 Statistical Inference With Regression and Correlation Coefficients
 2.9 Precision and Power
 2.10 Factors Affecting the Size of r
 2.11 Summary

Chapter 3: Multiple Regression/Correlation With Two or More Independent Variables
 3.1 Introduction: Regression and Causal Models
 3.2 Regression With Two Independent Variables
 3.3 Measures of Association With Two Independent Variables
 3.4 Patterns of Association Between Y and Two Independent Variables
 3.5 Multiple Regression/Correlation With k Independent Variables
 3.6 Statistical Inference With k Independent Variables
 3.7 Statistical Precision and Power Analysis
 3.8 Using Multiple Regression Equations in Prediction
 3.9 Summary
 Chapter 4: Data Visualization, Exploration, and Assumption Checking: Diagnosing and Solving Regression Problems I

Chapter 5: DataAnalytic Strategies Using Multiple Regression/Correlation

5.1 Research Questions Answered by Correlations and Their Squares
 5.1.1 Net Contribution to Prediction
 5.1.2 Indices of Differential Validity
 5.1.3 Comparisons of Predictive Utility
 5.1.4 Attribution of a Fraction of the XY Relationship to a Third Variable
 5.1.5 Which of Two Variables Accounts for More of the XY Relationship?
 5.1.6 Are the Various Squared Correlations in One Population Different From Those in Another Given the Same Variables?

5.2 Research Questions Answered by B Or β
 5.2.1 Regression Coefficients as Reflections of Causal Effects
 5.2.2 Alternative Approaches to Making BYX Substantively Meaningful
 5.2.3 Are the Effects of a Set of Independent Variables on Two Different Outcomes in a Sample Different?
 5.2.4 What Are the Reciprocal Effects of Two Variables on One Another?
 5.3 Hierarchical Analysis Variables in Multiple Regression/Correlation
 5.4 The Analysis of Sets of Independent Variables
 5.5 Significance Testing for Sets
 5.6 Power Analysis for Sets
 5.7 Statistical Inference Strategy in Multiple Regression/Correlation
 5.8 Summary

5.1 Research Questions Answered by Correlations and Their Squares

Chapter 6: Quantitative Scales, Curvilinear Relationships, and Transformations
 6.1 Introduction

6.2 Power Polynomials
 6.2.1 Method
 6.2.2 An Example: Quadratic Fit
 6.2.3 Centering Predictors in Polynomial Equations
 6.2.4 Relationship of Test of Significance of Highest Order Coefficient and Gain in Prediction
 6.2.5 Interpreting Polynomial Regression Results
 6.2.6 Another Example: A Cubic Fit
 6.2.7 Strategy and Limitations
 6.2.8 More Complex Equations
 6.3 Orthogonal Polynomials

6.4 Nonlinear Transformations
 6.4.1 Purposes of Transformation and the Nature of Transformations
 6.4.2 The Conceptual Basis of Transformations and Model Checking Before and After Transformation—Is It Always Ideal to Transform?
 6.4.3 Logarithms and Exponents; Additive and Proportional Relationships
 6.4.4 Linearizing Relationships
 6.4.5 Linearizing Relationships Based on Strong Theoretical Models
 6.4.6 Linearizing Relationships Based on Weak Theoretical Models
 6.4.7 Empirically Driven Transformations in the Absence of Strong or Weak Models
 6.4.8 Empirically Driven Transformation for Linearization: The Ladder of Reexpression and the Bulging Rule
 6.4.9 Empirically Driven Transformation for Linearization in the Absence of Models: BoxCox Family of Power Transformations on Y
 6.4.10 Empirically Driven Transformation for Linearization in the Absence of Models: BoxTidwell Family of Power Transformations on X
 6.4.11 Linearization of Relationships With Correlations: Fisher z′ Transform of r
 6.4.12 Transformations That Linearize Relationships for Counts and Proportions
 6.4.13 Variance Stabilizing Transformations and Alternatives for Treatment of Heteroscedasticity
 6.4.14 Transformations to Normalize Variables
 6.4.15 Diagnostics Following Transformation
 6.4.16 Measuring and Comparing Model Fit
 6.4.17 SecondOrder Polynomial Numerical Example Revisited
 6.4.18 When to Transform and the Choice of Transformation
 6.5 Nonlinear Regression
 6.6 Nonparametric Regression
 6.7 Summary

Chapter 7: Interactions Among Continuous Variables
 7.1 Introduction

7.2 Centering Predictors and the Interpretation of Regression Coefficients in Equations Containing Interactions
 7.2.1 Regression with Centered Predictors
 7.2.2 Relationship Between Regression Coefficients in the Uncentered and Centered Equations
 7.2.3 Centered Equations With No Interaction
 7.2.4 Essential Versus Nonessential Multicollinearity
 7.2.5 Centered Equations With Interactions
 7.2.6 The Highest Order Interaction in the Centered Versus Uncentered Equation
 7.2.7 Do Not Center Y
 7.2.8 A Recommendation for Centering

7.3 Simple Regression Equations and Simple Slopes
 7.3.1 Plotting Interactions
 7.3.2 Moderator Variables
 7.3.3 Simple Regression Equations
 7.3.4 Overall Regression Coefficient and Simple Slope at the Mean
 7.3.5 Simple Slopes From Uncentered Versus Centered Equations Are Identical
 7.3.6 Linear by Linear Interactions
 7.3.7 Interpreting Interactions in Multiple Regression and Analysis of Variance

7.4 Post Hoc Probing of Interactions
 7.4.1 Standard Error of Simple Slopes
 7.4.2 Equation Dependence of Simple Slopes and Their Standard Errors
 7.4.3 Tests of Significance of Simple Slopes
 7.4.4 Confidence Intervals Around Simple Slopes
 7.4.5 A Numerical Example
 7.4.6 The Uncentered Regression Equation Revisited
 7.4.7 FirstOrder Coefficients in Equations Without and With Interactions
 7.4.8 Interpretation and the Range of Data
 7.5 Standardized Estimates for Equations Containing Interactions
 7.6 Interactions as Partialed Effects: Building Regression Equations With Interactions
 7.7 Patterns of FirstOrder and Interactive Effects
 7.8 ThreePredictor Interactions in Multiple Regression
 7.9 Curvilinear by Linear Interactions
 7.10 Interactions Among Sets of Variables
 7.11 Issues in the Detection of Interactions: Reliability, Predictor Distributions, Model Specification
 7.12 Summary

Chapter 8: Categorical or Nominal Independent Variables
 8.1 Introduction

8.2 DummyVariable Coding
 8.2.1 Coding the Groups
 8.2.2 Pearson Correlations of Dummy Variables With Y
 8.2.3 Correlations Among DummyCoded Variables
 8.2.4 Multiple Correlation of the DummyVariable Set With Y
 8.2.5 Regression Coefficients for Dummy Variables
 8.2.6 Partial and Semipartial Correlations for Dummy Variables
 8.2.7 DummyVariable Multiple Regression/Correlation and OneWay Analysis of Variance
 8.2.8 A Cautionary Note: DummyVariableLike Coding Systems
 8.2.9 DummyVariable Coding When Groups Are Not Mutually Exclusive
 8.3 Unweighted Effects Coding
 8.4 Weighted Effects Coding
 8.5 Contrast Coding
 8.6 Nonsense Coding

8.7 Coding Schemes in the Context of Other Independent Variables
 8.7.1 Combining Nominal and Continuous Independent Variables
 8.7.2 Calculating Adjusted Means for Nominal Independent Variables
 8.7.3 Adjusted Means for Combinations of Nominal and Quantitative Independent Variables
 8.7.4 Adjusted Means for More Than Two Groups and Alternative Coding Methods
 8.7.5 Multiple Regression/Correlation With Nominal Independent Variables and the Analysis of Covariance
 8.8 Summary

Chapter 9: Interactions With Categorical Variables
 9.1 Nominal Scale by Nominal Scale Interactions

9.2 Interactions Involving More Than Two Nominal Scales
 9.2.1 An Example of Three Nominal Scales Coded by Alternative Methods
 9.2.2 Interactions Among Nominal Scales in Which Not All Combinations Are Considered
 9.2.3 What If the Categories for One or More Nominal “Scales” Are Not Mutually Exclusive?
 9.2.4 Consideration of pr, β, and Variance Proportions for Nominal Scale Interaction Variables
 9.2.5 Summary of Issues and Recommendations for Interactions Among Nominal Scales

9.3 Nominal Scale by Continuous Variable Interactions
 9.3.1 A Reminder on Centering
 9.3.2 Interactions of a Continuous Variable With DummyVariable Coded Groups
 9.3.3 Interactions Using Weighted or Unweighted Effects Codes
 9.3.4 Interactions With a ContrastCoded Nominal Scale
 9.3.5 Interactions Coded to Estimate Simple Slopes of Groups
 9.3.6 Categorical Variable Interactions With Nonlinear Effects of Scaled Independent Variables
 9.3.7 Interactions of a Scale With Two or More Categorical Variables
 9.4 Summary
 Chapter 10: Outliers and Multicollinearity: Diagnosing and Solving Regression Problems II
 Chapter 11: Missing Data

Chapter 12: Multiple Regression/Correlation and Causal Models
 12.1 Introduction
 12.2 Models Without Reciprocal Causation
 12.3 Models With Reciprocal Causation
 12.4 Identification and Overidentification

12.5 Latent Variable Models
 12.5.1 An Example of a Latent Variable Model
 12.5.2 How Latent Variables Are Estimated
 12.5.3 Fixed and Free Estimates in Latent Variable Models
 12.5.4 GoodnessofFit Tests of Latent Variable Models
 12.5.5 Latent Variable Models and the Correction for Attenuation
 12.5.6 Characteristics of Data Sets That Make Latent Variable Analysis the Method of Choice
 12.6 A Review of Causal Model and Statistical Assumptions
 12.7 Comparisons of Causal Models
 12.8 Summary

Chapter 13: Alternative Regression Models: Logistic, Poisson Regression, and the Generalized Linear Model
 13.1 Ordinary Least Squares Regression Revisited

13.2 Dichotomous Outcomes and Logistic Regression
 13.2.1 Extending Linear Regression: The Linear Probability Model and Discriminant Analysis
 13.2.2 The Nonlinear Transformation From Predictor to Predicted Scores: Probit and Logistic Transformation
 13.2.3 The Logistic Regression Equation
 13.2.4 Numerical Example: Three Forms of the Logistic Regression Equation
 13.2.5 Understanding the Coefficients for the Predictor in Logistic Regression
 13.2.6 Multiple Logistic Regression
 13.2.7 Numerical Example
 13.2.8 Confidence Intervals on Regression Coefficients and Odds Ratios
 13.2.9 Estimation of the Regression Model: Maximum Likelihood
 13.2.10 Deviances: Indices of Overall Fit of the Logistic Regression Model
 13.2.11 Multiple R2 Analogs in Logistic Regression
 13.2.12 Testing Significance of Overall Model Fit: The Likelihood Ratio Test and the Test of Model Deviance
 13.2.13 χ2 Test for the Significance of a Single Predictor in a Multiple Logistic Regression Equation
 13.2.14 Hierarchical Logistic Regression: Likelihood Ratio χ2 Test for the Significance of a Set of Predictors Above and Beyond Another Set
 13.2.15 Akaike’s Information Criterion and the Bayesian Information Criterion for Model Comparison
 13.2.16 Some Treachery in Variable Scaling and Interpretation of the Odds Ratio
 13.2.17 Regression Diagnostics in Logistic Regression
 13.2.18 Sparseness of Data
 13.2.19 Classification of Cases
 13.3 Extensions of Logistic Regression to Multiple Response Categories: Polytomous Logistic Regression and Ordinal Logistic Regression
 13.4 Models for Count Data: Poisson Regression and Alternatives
 13.5 Full Circle: Parallels Between Logistic and Poisson Regression, and the Generalized Linear Model
 13.6 Summary

Chapter 14: Random Coefficient Regression and Multilevel Models
 14.1 Clustering Within Data Sets
 14.2 Analysis of Clustered Data With Ordinary Least Squares Approaches
 14.3 The Random Coefficient Regression Model

14.4 Random Coefficient Regression Model and Multilevel Data Structure
 14.4.1 Ordinary Least Squares (Fixed Effects) Regression Revisited
 14.4.2 Fixed and Random Variables
 14.4.3 Clustering and Hierarchically Structured Data
 14.4.4 Structure of the Random Coefficient Regression Model
 14.4.5 Level 1 Equations
 14.4.6 Level 2 Equations
 14.4.7 Mixed Model Equation for Random Coefficient Regression
 14.4.8 Variance Components—New Parameters in the Multilevel Model
 14.4.9 Variance Components and Random Coefficient Versus Ordinary Least Squares (Fixed Effects) Regression
 14.4.10 Parameters of the Random Coefficient Regression Model: Fixed and Random Effects
 14.5 Numerical Example: Analysis of Clustered Data With Random Coefficient Regression
 14.6 Clustering as a Meaningful Aspect of the Data
 14.7 Multilevel Modeling With a Predictor at Level
 14.8 An Experimental Design as a Multilevel Data Structure: Combining Experimental Manipulation With Individual Differences
 14.9 Numerical Example: Multilevel Analysis
 14.10 Estimation of the Multilevel Model Parameters: Fixed Effects, Variance Components, and Level 1 Equations
 14.11 Statistical Tests in Multilevel Models
 14.12 Some Model Specification Issues
 14.13 Statistical Power of Multilevel Models
 14.14 Choosing Between the Fixed Effects Model and the Random Coefficient Model
 14.15 Sources on Multilevel Modeling
 14.16 Multilevel Models Applied to Repeated Measures Data
 14.17 Summary

Chapter 15: Longitudinal Regression Methods
 15.1 Introduction
 15.2 Analyses of TwoTimePoint Data
 15.3 Repeated Measure Analysis of Variance

15.4 Multilevel Regression of Individual Changes Over Time
 15.4.1 Patterns of Individual Change Over Time
 15.4.2 Adding Other Fixed Predictors to the Model
 15.4.3 Individual Differences in Variation Around Individual Slopes
 15.4.4 Alternative Developmental Models and Error Structures
 15.4.5 Alternative Link Functions for Predicting Y From Time
 15.4.6 Unbalanced Data: Variable Timing and Missing Data
 15.5 Latent Growth Models: Structural Equation Model Representation of Multilevel Data
 15.6 Time Varying Independent Variables
 15.7 Survival Analysis
 15.8 Time Series Analysis
 15.9 Dynamic System Analysis
 15.10 Statistical Inference and Power Analysis in Longitudinal Analyses
 15.11 Summary

Chapter 16: Multiple Dependent Variables: Set Correlation
 16.1 Introduction to Ordinary Least Squares Treatment of Multiple Dependent Variables
 16.2 Measures of Multivariate Association
 16.3 Partialing in Set Correlation
 16.4 Tests of Statistical Significance and Statistical Power
 16.5 Statistical Power Analysis in Set Correlation
 16.6 Comparison of Set Correlation With Multiple Analysis of Variance
 16.7 New Analytic Possibilities With Set Correlation
 16.8 Illustrative Examples
 16.9 Summary

Appendices
 Appendix 1: The Mathematical Basis for Multiple Regression/Correlation and Identification of the Inverse Matrix Elements
 Appendix 2: Determination of the Inverse Matrix and Applications Thereof

Appendix Tables
 Table A t Values for α = .01, .05 (Two Tailed)
 Table B z′ Transformation of r
 Table C Normal Distribution
 Table D F Values for α = .01, .05
 Table E L Values for α = .01, .05
 Table F Power of Significance Test of r at α = .01, .05 (Two Tailed)
 Table G n* to Detect r by t Test at α = .01, .05 (Two Tailed)
 References
 Glossary
 Statistical Symbols and Abbreviations
 Author Index
 Subject Index
Product information
 Title: Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences, 3rd Edition
 Author(s):
 Release date: June 2013
 Publisher(s): Routledge
 ISBN: 9781134801015
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