Regression Analysis for Categorical Moderators

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: 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