Table of contents for Regression analysis for categorical moderators / by Herman Aguinis.


Bibliographic record and links to related information available from the Library of Congress catalog. Note: Contents data are machine generated based on pre-publication information provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding.


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Contents
1 
What Is a Moderator Variable and Why Should We Care?
1
Why Should We Study Moderator Variables? / 3
Distinction between Moderator and Mediator Variables / 5
Importance of A Priori Rationale in Investigating Moderating Effects / 7
··· Conclusions / 8 ···
2 
Moderated Multiple Regression
10
What Is MMR? / 10
Endorsement of MMR as an Appropriate Technique / 16
Pervasive Use of MMR in the Social Sciences: Literature Review / 18
··· Conclusions / 20 ···
3 
Performing and Interpreting Moderated Multiple Regression Analyses Using Computer Programs
22
Research Scenario / 23
Data Set / 24
Conducting an MMR Analysis Using Computer Programs: Two Steps / 26
Step 1: Computation of Product Term / 26
Step 2: Computation of Regression Equations / 28
Output Interpretation / 31
Interpretation of Model 1 / 31
Interpretation of Model 2 / 33
Additional Issues in Output Interpretation / 35
··· Conclusions / 39 ···
4 
The Homogeneity of Error Variance Assumption
42
What Is the Homogeneity of Error Variance Assumption? / 42
Two Distinct Assumptions: Homoscedasticity and Homogeneity of Error Variance / 44
Is It a Big Deal to Violate the Assumption? / 47
Violation of the Homogeneity of Error Variance Assumption: Type I Error Rates / 48
Violation of the Homogeneity of Error Variance Assumption: Type II Error Rates / 50
Violation of the Assumption in Published Research / 51
How to Check Whether the Homogeneity Assumption Is Violated / 54
What to Do When the Homogeneity of Error Variance Assumption Is Violated / 56
ALTMMR: Computer Program to Check Assumption Compliance and Compute Alternative Statistics if Needed / 58
Program Description / 59
Input / 60 · Assessment of Variance Heterogeneity / 60 · Computation of Alternatives to MMR / 61 · Output / 61
··· Conclusions / 63 ···
5 
MMR's Low-Power Problem
65
Statistical Inferences and Power / 65
Controversy over Null Hypothesis Significance Testing / 67
Purpose of NHST / 67
Meaning of NHST / 67
Controversy over NHST: A Human Factors Problem / 68
Factors Affecting the Power of All Inferential Tests / 69
Factors Affecting the Power of MMR / 70
Variable Distributions / 70
Predictor Variable Variance Reduction / 70 · Transformations of Skewed Criterion Scores / 71
Operationalization of Criterion and Predictor Variables / 72
Measurement Error / 73 · Scale Coarseness / 74 · Polichotomization of a Truly Continuous Variable / 75
Sample Size / 75
Total Sample Size / 75 · Sample Size across Moderator-Based Subgroups / 76
Characteristics of the Predictor Variables / 77
Correlation between the Predictor X and the Moderator Z / 77 · Correlation between the Predictor X and the Criterion Y / 77
Interactive Effects / 78
Effect Sizes and Power in Published Research / 78
Implications of Small Observed Effect Sizes for Social Science Research / 80
··· Conclusions / 82 ···
6 
Light at the End of the Tunnel: How to Solve the Low-Power Problem
85
How to Minimize the Impact of Factors Affecting the Power of All Inferential Tests / 86
Sample Size / 86
Preset Type I Error Rate / 86
Moderating-Effect Size / 88
How to Minimize the Impact of Factors Affecting the Power of MMR / 88
Reduction of Variance in Predictor Variables / 88
Transformations of Skewed Criterion Scores / 89
Measurement Error / 90
Scale Coarseness / 90
Polichotomization of Truly Continuous Variables / 92
Total Sample Size / 93
Sample Size across Moderator-Based Subgroups / 93
Correlation between the Predictor X and the Moderator Z / 94
Correlation between the Predictor X and the Criterion Y / 94
··· Conclusions / 94 ···
7 
Computing Statistical Power
97
Usefulness of Computing Statistical Power / 97
Empirically Based Programs / 100
Program POWER / 100
Specifications / 100 · Example / 101 · Limitations / 101
Program MMRPWR / 103
Specifications / 103 · Example / 104 · Limitations / 106
Theory-Based Program / 107
Program MMRPOWER / 107
Specifications / 108 · Example / 110 · Limitations / 110
Relative Impact of the Factors Affecting Power / 113
··· Conclusions / 115 ···
8 
Complex MMR Models
117
MMR Analyses Including a Moderator Variable with More Than Two Levels / 118
Dummy Coding / 119
Unweighted Effect Coding / 121
Weighted Effect Coding / 122
Contrast Coding / 123
How to Choose a Coding Scheme: The Importance of Theory / 124
Computing Statistical Power / 125
Linear Interactions and Nonlinear Effects: Friends or Foes? / 126
Testing and Interpreting Three-way and Higher-Order Interaction Effects / 131
Examining "Targeted" Lower-Order Interactions / 134
··· Conclusions / 135 ···
9 
Further Issues in the Interpretation of Moderating Effects
138
Is the Moderating Effect Practically Significant? / 139
Measures of Improved Fit / 139
Difference in Correlations across Moderator-Based Subgroups / 139 · Proportion of Variance Explained by the Moderating Effect as Indexed by R2 / 140 · Proportion of Variance Explained by the Moderating Effect as Indexed by f2 / 141 · Proportion of Variance Explained by the Moderating Effect as Indexed by Modified f2 / 141
Measures of Improved Prediction / 143
Differences in Unstandardized Regression Coefficients across Moderator-Based Subgroups / 143 · Standardized Effect of the Moderator on the Y on X Slope / 144 · Differential Impact of the Moderator at Various Values of the Predictor X / 146
The Signed Coefficient Rule for Interpreting Moderating Effects / 149
The Importance of Identifying Criterion and Predictor A Priori / 150
··· Conclusions / 152 ···
10
Summary and Conclusions
155
Moderators and Social Science Theory and Practice / 155
Use of Moderated Multiple Regression / 156
Homogeneity of Error Variance Assumption / 159
Low Statistical Power and Proposed Remedies / 159
More Complex MMR Models / 162
Assessing Practical Significance / 162
··· Conclusions / 164 ···
Appendix A 
Computation of Bartlett's (1937) M Statistic
167
Appendix B 
Computation of James's (1951) J Statistic
168
Appendix C 
Computation of Alexander's (Alexander & Govern, 1994) A Statistic
170
Appendix D 
Computation of Modified f2
171
Appendix E 
Theory-Based Power Approximation
173
References
175
Name Index
000
Subject Index
000




Library of Congress Subject Headings for this publication: Regression analysis, Social sciences Statistical methods Data processing, Regression analysis Computer programs