Regression Analysis for Categorical Moderators

Herman Aguinis, PhD, is the Avram Tucker Distinguished Scholar and Professor of Management at George Washington University School of Business. Previously, he served on the faculties of the Kelley School of Business at Indiana University and the University of Colorado Denver Business School. In addition, he has been a visiting scholar at universities around the world. His research is interdisciplinary and addresses human capital acquisition, development, deployment, and research methods and analysis. Widely published, Dr. Aguinis currently serves as associate editor of the Annual Review of Organizational Psychology and Organizational Behavior. He is a Fellow of the Academy of Management, the American Psychological Association, the Association for Psychological Science, and the Society for Industrial and Organizational Psychology, and has been inducted into the Society of Organizational Behavior and the Society for Research Synthesis Methodology. His work has been recognized with numerous awards.

• 1. What Is a Moderator Variable and Why Should We Care?Why Should We Study Moderator Variables?Distinction between Moderator and Mediator VariablesImportance of A Priori Rationale in Investigating Moderating EffectsConclusions2. Moderated Multiple RegressionWhat Is MMR?Endorsement of MMR as an Appropriate TechniquePervasive Use of MMR in the Social Sciences: Literature ReviewConclusions3. Performing and Interpreting Moderated Multiple Regression Analysis Using Computer ProgramsResearch ScenarioData SetConducting an MMR Analysis Using Computer Programs: Two StepsOutput InterpretationConclusions4. Homogeneity of Error Variance AssumptionWhat Is the Homogeneity of Error Variance Assumption?Two Distinct Assumptions: Homoscedasticity and Homogeneity of Error VarianceIs It a Big Deal to Violate the Assumption?Violation of the Assumption in Published ResearchHow to Check If the Homogeneity Assumption Is ViolatedWhat to Do When the Homogeneity of Error Variance Assumption Is ViolatedALTMMR: Computer Program to Check Assumption Compliance and Compute Alternative Statistics If NeededConclusions5. MMR’s Low-Power ProblemStatistical Inferences and PowerControversy Over Null Hypothesis Significance TestingFactors Affecting the Power of All Inferential TestsFactors Affecting the Power of MMREffect Sizes and Power in Published ResearchImplications of Small Observed Effect Sizes for Social Science ResearchConclusions6. Light at the End of the Tunnel: How to Solve the Low-Power ProblemHow to Minimize the Impact of Factors Affecting the Power of All Inferential TestsHow to Minimize the Impact of Factors Affecting the Power of MMRConclusions7. Computing Statistical PowerUsefulness of Computing Statistical PowerEmpirically Based ProgramsTheory-Based ProgramRelative Impact of the Factors Affecting PowerConclusions8. Complex MMR ModelsMMR Analyses Including a Moderator Variable with More Than Two LevelsLinear Interactions and Non-linear Effects: Friends or Foes?Testing and Interpreting Three-Way and Higher-Order Interaction EffectsConclusions9. Further Issues in the Interpretation of Moderating EffectsIs the Moderating Effect Practically Significant?The Signed Coefficient Rule for Interpreting Moderating EffectsThe Importance on Identifying Criterion and Predictor A PrioriConclusions10. Summary and ConclusionsModerators and Social Science Theory and PracticeUse of Moderated Multiple RegressionHomogeneity of Error Variance AssumptionLow Statistical Power and Proposed RemediesComplex MMR ModelsAssessing Practical SignificanceConclusionsAppendix A. Computation of Bartlett’s (1937) \ital\M\ital\ StatisticAppendix B. Computation of James’s (1951) \ital\J\ital\ StatisticAppendix C. Computation of Alexander’s (Alexander & Govern, 1994) \ital\A\ital\ StatisticAppendix D. Computation of Modified \ital\f\ital\\superscript\2\superscript\Appendix E. Theory-Based Power ApproximationReferencesName IndexSubject Index1. What Is a Moderator Variable and Why Should We Care?Why Should We Study Moderator Variables?Distinction between Moderator and Mediator VariablesImportance of A Priori Rationale in Investigating Moderating EffectsConclusions2. Moderated Multiple RegressionWhat Is MMR?Endorsement of MMR as an Appropriate TechniquePervasive Use of MMR in the Social Sciences: Literature ReviewConclusions3. Performing and Interpreting Moderated Multiple Regression Analysis Using Computer ProgramsResearch ScenarioData SetConducting an MMR Analysis Using Computer Programs: Two StepsOutput InterpretationConclusions4. Homogeneity of Error Variance AssumptionWhat Is the Homogeneity of Error Variance Assumption?Two Distinct Assumptions: Homoscedasticity and Homogeneity of Error VarianceIs It a Big Deal to Violate the Assumption?Violation of the Assumption in Published ResearchHow to Check If the Homogeneity Assumption Is ViolatedWhat to Do When the Homogeneity of Error Variance Assumption Is ViolatedALTMMR: Computer Program to Check Assumption Compliance and Compute Alternative Statistics If NeededConclusions5. MMR’s Low-Power ProblemStatistical Inferences and PowerControversy Over Null Hypothesis Significance TestingFactors Affecting the Power of All Inferential TestsFactors Affecting the Power of MMREffect Sizes and Power in Published ResearchImplications of Small Observed Effect Sizes for Social Science ResearchConclusions6. Light at the End of the Tunnel: How to Solve the Low-Power ProblemHow to Minimize the Impact of Factors Affecting the Power of All Inferential TestsHow to Minimize the Impact of Factors Affecting the Power of MMRConclusions7. Computing Statistical PowerUsefulness of Computing Statistical PowerEmpirically Based ProgramsTheory-Based ProgramRelative Impact of the Factors Affecting PowerConclusions8. Complex MMR ModelsMMR Analyses Including a Moderator Variable with More Than Two LevelsLinear Interactions and Non-linear Effects: Friends or Foes?Testing and Interpreting Three-Way and Higher-Order Interaction EffectsConclusions9. Further Issues in the Interpretation of Moderating EffectsIs the Moderating Effect Practically Significant?The Signed Coefficient Rule for Interpreting Moderating EffectsThe Importance on Identifying Criterion and Predictor A PrioriConclusions10. Summary and ConclusionsModerators and Social Science Theory and PracticeUse of Moderated Multiple RegressionHomogeneity of Error Variance AssumptionLow Statistical Power and Proposed RemediesComplex MMR ModelsAssessing Practical SignificanceConclusionsAppendix A. Computation of Bartlett’s (1937) \ital\M\ital\ StatisticAppendix B. Computation of James’s (1951) \ital\J\ital\ StatisticAppendix C. Computation of Alexander’s (Alexander & Govern, 1994) \ital\A\ital\ StatisticAppendix D. Computation of Modified \ital\f\ital\\superscript\2\superscript\Appendix E. Theory-Based Power ApproximationReferencesName IndexSubject Index

Aguinis has produced the most comprehensive single-source treatment on the topic of why and how to conduct moderated regression analysis for categorical moderators. The book presents very clear steps for how to test for moderators, but is more than a cookbook in that it also explores in detail the underlying assumptions; issues that will affect interpretation (e.g., homogeneity of variance and power); and solutions to frequently encountered problems. Examples from different types of research problems help clarify the analytical strategy, and presentation of the software for examining underlying issues is very valuable. Aguinis also provides excellent coverage of the literature surrounding the analytical strategy. This volume is an excellent reference for any researcher or student interested in studying interactions with categorical variables.--Sheldon Zedeck, PhD, Department of Psychology, University of California, BerkeleyThis book presents a complete and current treatment of a topic of great importance to management and organizational studies researchers. Strengths of the book include the use of an integrative example with data that is available to readers, and the clear presentation style. The treatment of homogeneity of error variance and statistical power problems is especially impressive and provides readers with practical guidance for dealing with these issues. This book will be an excellent resource for any researcher who works with regression models.--Larry J. Williams, PhD, Center for the Advancement of Research Methods and Analysis, School of Business, Virginia Commonwealth UniversityAguinis has provided an extraordinarily understandable guide to conducting tests of moderation by categorical variables. The book contains clear examples for running the analyses, checking assumptions, and interpreting the results. This book is an excellent resource for courses on regression analysis at both the undergraduate and graduate levels, and for individuals who need a refresher on moderator analysis.--Lois Tetrick, PhD, Department of Psychology, George Mason University- A masterful presentation reflecting many years of research and study. It should prove to be valuable to any researcher who has even a basic understanding of statistical analysis. --International Journal of Consumer Studies, 12/25/2003