Regression analysis for categorical moderators

Abstract

1. What Is a Moderator Variable and Why Should We Care? Why Should We Study Moderator Variables? Distinction between Moderator and Mediator Variables Importance of A Priori Rationale in Investigating Moderating Effects Conclusions 2. Moderated Multiple Regression What Is MMR? Endorsement of MMR as an Appropriate Technique Pervasive Use of MMR in the Social Sciences: Literature Review Conclusions 3. Performing and Interpreting Moderated Multiple Regression Analysis Using Computer Programs Research Scenario Data Set Conducting an MMR Analysis Using Computer Programs: Two Steps Output Interpretation Conclusions 4. Homogeneity of Error Variance Assumption What Is the Homogeneity of Error Variance Assumption? Two Distinct Assumptions: Homoscedasticity and Homogeneity of Error Variance Is It a Big Deal to Violate the Assumption? Violation of the Assumption in Published Research How to Check If the Homogeneity Assumption Is Violated What to Do When the Homogeneity of Error Variance Assumption Is Violated ALTMMR: Computer Program to Check Assumption Compliance and Compute Alternative Statistics If Needed Conclusions 5. MMR's Low-Power Problem Statistical Inferences and Power Controversy Over Null Hypothesis Significance Testing Factors Affecting the Power of All Inferential Tests Factors Affecting the Power of MMR Effect Sizes and Power in Published Research Implications of Small Observed Effect Sizes for Social Science Research Conclusions 6. Light at the End of the Tunnel: How to Solve the Low-Power Problem How to Minimize the Impact of Factors Affecting the Power of All Inferential Tests How to Minimize the Impact of Factors Affecting the Power of MMR Conclusions 7. Computing Statistical Power Usefulness of Computing Statistical Power Empirically Based Programs Theory-Based Program Relative Impact of the Factors Affecting Power Conclusions 8. Complex MMR Models MMR Analyses Including a Moderator Variable with More Than Two Levels Linear Interactions and Non-linear Effects: Friends or Foes? Testing and Interpreting Three-Way and Higher-Order Interaction Effects Conclusions 9. Further Issues in the Interpretation of Moderating Effects Is the Moderating Effect Practically Significant? The Signed Coefficient Rule for Interpreting Moderating Effects The Importance on Identifying Criterion and Predictor A Priori Conclusions 10. Summary and Conclusions Moderators and Social Science Theory and Practice Use of Moderated Multiple Regression Homogeneity of Error Variance Assumption Low Statistical Power and Proposed Remedies Complex MMR Models Assessing Practical Significance Conclusions Appendix A. Computation of Bartlett's (1937) \ital\M\ital Statistic Appendix B. Computation of James's (1951) \ital\J\ital Statistic Appendix C. Computation of Alexander's (Alexander & Govern, 1994) \ital\A\ital Statistic Appendix D. Computation of Modified \ital\f\ital\\superscript\2\superscript Appendix E. Theory-Based Power Approximation References Name Index Subject Index 1. What Is a Moderator Variable and Why Should We Care? Why Should We Study Moderator Variables? Distinction between Moderator and Mediator Variables Importance of A Priori Rationale in Investigating Moderating Effects Conclusions 2. Moderated Multiple Regression What Is MMR? Endorsement of MMR as an Appropriate Technique Pervasive Use of MMR in the Social Sciences: Literature Review Conclusions 3. Performing and Interpreting Moderated Multiple Regression Analysis Using Computer Programs Research Scenario Data Set Conducting an MMR Analysis Using Computer Programs: Two Steps Output Interpretation Conclusions 4. Homogeneity of Error Variance Assumption What Is the Homogeneity of Error Variance Assumption? Two Distinct Assumptions: Homoscedasticity and Homogeneity of Error Variance Is It a Big Deal to Violate the Assumption? Violation of the Assumption in Published Research How to Check If the Homogeneity Assumption Is Violated What to Do When the Homogeneity of Error Variance Assumption Is Violated ALTMMR: Computer Program to Check Assumption Compliance and Compute Alternative Statistics If Needed Conclusions 5. MMR's Low-Power Problem Statistical Inferences and Power Controversy Over Null Hypothesis Significance Testing Factors Affecting the Power of All Inferential Tests Factors Affecting the Power of MMR Effect Sizes and Power in Published Research Implications of Small Observed Effect Sizes for Social Science Research Conclusions 6. Light at the End of the Tunnel: How to Solve the Low-Power Problem How to Minimize the Impact of Factors Affecting the Power of All Inferential Tests How to Minimize the Impact of Factors Affecting the Power of MMR Conclusions 7. Computing Statistical Power Usefulness of Computing Statistical Power Empirically Based Programs Theory-Based Program Relative Impact of the Factors Affecting Power Conclusions 8. Complex MMR Models MMR Analyses Including a Moderator Variable with More Than Two Levels Linear Interactions and Non-linear Effects: