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Multiple Regression : Testing and Interpreting Interactions

by: Leona S. Aiken

Multiple Regression : Testing and Interpreting Interactions

by: Leona S. Aiken

ISBN 13:
9780761907121
ISBN 10:
0761907122
Format: Paperback
Copyright: 01/01/1991
Publisher: Sage Publications, Inc

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Summary

This successful book, now available in paperback, provides academics and researchers with a clear set of prescriptions for estimating, testing and probing interactions in regression models. Including the latest research in the area, such as Fuller's work on the corrected/constrained estimator, the book is appropriate for anyone who uses multiple regression to estimate models, or for those enrolled in courses on multivariate statistics.

Preface

Introduction

(8)

Interactions Between Continuous Predictors in Multiple Regression

(19)

What Interactions Signify in Regression

(1)

Data Set for Numerical Examples

(2)

Probing Significant Interactions in Regression Equations

(15)

Plotting the Interaction

(2)

Post Hoc Probing

(8)

Ordinal Versus Disordinal Interactions

(2)

Optional Section: The Derivation of Standard Errors of Simple Slopes

(3)

Summary

(1)

The Effects of Predictor Scaling on Coefficients of Regression Equations

(21)

The Problem of Scale Invariance

(8)

Linear Regression with no Higher Order Terms

(1)

Regression Equations with Higher Order Terms

(1)

Simple Slopes of Simple Regression Equations

(1)

Ordinal Versus Disordinal Interactions

(1)

Numerical Example---Centered Versus Uncentered Data

(3)

Should the Criterion Y Be Centered?

(1)

Multicollinearity: Essential Versus Nonessential Ill-Conditioning

(1)

Interpreting the Regression Coefficients

(4)

The Interaction Term XZ

(1)

The First Order Terms X and Z

(2)

A Geometric Interpretation

(1)

Standardized Solutions with Multiplicative Terms

(7)

Appropriate Standardized Solution with Interaction Terms

(1)

Simple Slope Analysis from the Standardized Solution

(1)

Relationship Between Raw and ``Standardized'' Solution

(2)

Summary

(2)

Testing and Probing Three-Way Interactions

(13)

Specifying, Testing, and Interpreting Three-Way Interactions

(1)

Probing Three-Way Interactions

(9)

Simple Regression Equation

(1)

Numerical Example

(2)

Graphing the Three-Way Interaction

(2)

Testing Simple Slopes for Significance

(1)

Standard Errors by Computer

(4)

Crossing Point of Simple Regression Equations with Three-Predictor Interaction

(1)

Simple Slopes and Their Variances in a Series of Regression Equations

(2)

Summary

(1)

Structuring Regression Equations to Reflect Higher Order Relationships

(38)

Structuring and Interpreting Regression Equations Involving Higher Order Relationships

(9)

Curvilinear X Relationship

(2)

A Progression of More Complex Equations with Curvilinear Relationships

(5)

Representation of Curvilinearity in ANOVA Versus MR

(2)

Post Hoc Probing of More Complex Regression Equations

(17)

Curvilinear X Equation

(6)

The Progression of More Complex Curvilinear Equations Revisited

(11)

Coefficients of Simple Slopes by Computer

(3)

Three Final Issues

(5)

Curvilinearity Versus Interaction

(1)

What Terms Should Be Included in the Regression Equation?

(2)

Other Methods of Representing Curvilinearity

(2)

Summary

(3)

Model and Effect Testing with Higher Order Terms

100

(16)

Some Issues in Testing Lower Order Effects in Models Containing Higher Order Terms

100

(5)

Interpretation of Lower Order Terms When b3 Is Significant

102

(1)

Should Lower Order Coefficients Be Tested in Reduced Models When b3 Is Nonsignificant?

103

(2)

Exploring Regression Equations Containing Higher Order Terms with Global Tests

105

(6)

Some Global Tests of Models with Higher Order Terms

107

(3)

Structuring Regression Equations with Higher Order Terms

110

(1)

Sequential Model Revision of Regression Equations Containing Higher Order Terms: Exploratory Tests

111

(3)

Application of Sequential Testing Following a Global Test

112

(1)

General Application of Sequential Testing

113

(1)

Present Approach Versus That Recommended by Cohen (1978)

113

(1)

Variable Selection Algorithms

114

(1)

Summary

114

(2)

Interactions Between Categorical and Continuous Variables

116

(23)

Coding Categorical Variables

116

(14)

Dummy Variable Coding

116

(11)

Unweighted Effects Coding

127

(2)

Choice of Coding System

129

(1)

Centering Revisited

130

(1)

Post Hoc Probing of Significant Interactions

130

(7)

Testing Simple Slopes Within Groups

131

(1)

Computer Procedure

131

(1)

Differences Between Regression Lines at a Specific Point

132

(2)

Identifying Regions of Significance

134

(3)

Summary

137

(2)

Reliability and Statistical Power

139

(33)

Reliability

140

(16)

Biased Regression Coefficients with Measurement Error

140

(5)

Corrected Estimates of Regression Coefficients in Equations Containing Higher Order Terms

145

(11)

Statistical Power

156

(13)

Statistical Power Analysis

156

(4)

The Effects of Measurement Error on Statistical Power

160

(5)

Some Corroborative Evidence: Simulation Studies

165

(2)

The Median Split Approach: The Cost of Dichotomization

167

(1)

Principal Component Regression Is Not a Cure for Power Woes

168

(1)

Coming Full Circle

169

(1)

Summary

170

(2)

Conclusion: Some Contrasts Between ANOVA and MR in Practice

172

(5)

Appendix A: Mathematical Underpinnings

177

(6)

Appendix B: Algorithm for Identifying Scale-Independent Terms

183

(5)

Appendix C: SAS Program for Test of Critical Region(s)

188

(2)

References

190

(8)

Glossary of Symbols

198

(6)

Author Index

204

(3)

Subject Index

207

(5)

About the Authors

212

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Multiple Regression : Testing and Interpreting Interactions

Multiple Regression : Testing and Interpreting Interactions

9780761907121

0761907122

Summary

Table of Contents

Supplemental Materials

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