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Regression Analysis for Categorical Moderators : Methodology in the Social Sciences - Herman Aguinis

Regression Analysis for Categorical Moderators

Methodology in the Social Sciences

Hardcover Published: 23rd December 2003
ISBN: 9781572309692
Number Of Pages: 202

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Does the stability of personality vary by gender or ethnicity? Does a particular therapy work better to treat clients with one type of personality disorder than those with another? Providing a solution to thorny problems such as these, Aguinis shows readers how to better assess whether the relationship between two variables is moderated by group membership through the use of a statistical technique, moderated multiple regression (MMR). Clearly written, the book requires only basic knowledge of inferential statistics. It helps students, researchers, and practitioners determine whether a particular intervention is likely to yield dissimilar outcomes for members of various groups. Associated computer programs and data sets are available at the companion website (www.guilford.com/aguinis-materials).

"'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."

What Is a Moderator Variable and Why Should We Care?p. 1
Why Should We Study Moderator Variables?p. 3
Distinction between Moderator and Mediator Variablesp. 5
Importance of A Priori Rationale in Investigating Moderating Effectsp. 7
Conclusionsp. 8
Moderated Multiple Regressionp. 10
What Is MMR?p. 10
Endorsement of MMR as an Appropriate Techniquep. 16
Pervasive Use of MMR in the Social Sciences: Literature Reviewp. 18
Conclusionsp. 20
Performing and Interpreting Moderated Multiple Regression Analyses Using Computer Programsp. 22
Research Scenariop. 23
Data Setp. 24
Conducting an MMR Analysis Using Computer Programs: Two Stepsp. 26
Computation of Product Termp. 26
Computation of Regression Equationsp. 28
Output Interpretationp. 31
Interpretation of Model 1p. 31
Interpretation of Model 2p. 33
Additional Issues in Output Interpretationp. 35
Conclusionsp. 39
The Homogeneity of Error Variance Assumptionp. 42
What Is the Homogeneity of Error Variance Assumption?p. 42
Two Distinct Assumptions: Homoscedasticity and Homogeneity of Error Variancep. 44
Is It a Big Deal to Violate the Assumption?p. 47
Violation of the Homogeneity of Error Variance Assumption: Type I Error Ratesp. 48
Violation of the Homogeneity of Error Variance Assumption: Type II Error Ratesp. 50
Violation of the Assumption in Published Researchp. 51
How to Check Whether the Homogeneity Assumption Is Violatedp. 54
What to Do When the Homogeneity of Error Variance Assumption Is Violatedp. 56
ALTMMR: Computer Program to Check Assumption Compliance and Compute Alternative Statistics If Neededp. 58
Program Descriptionp. 59
Inputp. 60
Assessment of Variance Heterogeneityp. 60
Computation of Alternatives to MMRp. 61
Outputp. 61
Conclusionsp. 63
MMR's Low-Power Problemp. 65
Statistical Inferences and Powerp. 65
Controversy over Null Hypothesis Significance Testingp. 67
Purpose of NHSTp. 67
Meaning of NHSTp. 67
Controversy over NHST: A Human Factors Problemp. 68
Factors Affecting the Power of All Inferential Testsp. 69
Factors Affecting the Power of MMRp. 70
Variable Distributionsp. 70
Predictor Variable Variance Reductionp. 70
Transformations of Skewed Criterion Scoresp. 71
Operationalization of Criterion and Predictor Variablesp. 72
Measurement Errorp. 73
Scale Coarsenessp. 74
Polichotomization of a Truly Continuous Variablep. 75
Sample Sizep. 75
Total Sample Sizep. 75
Sample Size Across Moderator-Based Subgroupsp. 76
Characteristics of the Predictor Variablesp. 77
Correlation Between the Predictor X and the Moderator Zp. 77
Correlation Between the Predictor X and the Criterion Yp. 77
Interactive Effectsp. 78
Effect Sizes and Power in Published Researchp. 78
Implications of Small Observed Effect Sizes for Social Science Researchp. 80
Conclusionsp. 82
Light at the End of the Tunnel: How to Solve the Low-Power Problemp. 85
How to Minimize the Impact of Factors Affecting the Power of All Inferential Testsp. 86
Sample Sizep. 86
Preset Type I Error Ratep. 86
Moderating-Effect Sizep. 88
How to Minimize the Impact of Factors Affecting the Power of MMRp. 88
Reduction of Variance in Predictor Variablesp. 88
Transformations of Skewed Criterion Scoresp. 89
Measurement Errorp. 90
Scale Coarsenessp. 90
Polichotomization of Truly Continuous Variablesp. 92
Total Sample Sizep. 93
Sample Size across Moderator-Based Subgroupsp. 93
Correlation between the Predictor X and the Moderator Zp. 94
Correlation between the Predictor X and the Criterion Yp. 94
Conclusionsp. 94
Computing Statistical Powerp. 97
Usefulness of Computing Statistical Powerp. 97
Empirically Based Programsp. 100
Program POWERp. 100
Specificationsp. 100
Examplep. 101
Limitationsp. 101
Program MMRPWRp. 103
Specificationsp. 103
Examplep. 104
Limitationsp. 106
Theory-Based Programp. 107
Program MMRPOWERp. 107
Specificationsp. 108
Examplep. 110
Limitationsp. 110
Relative Impact of the Factors Affecting Powerp. 113
Conclusionsp. 115
Complex MMR Modelsp. 117
MMR Analyses Including a Moderator Variable with More Than Two Levelsp. 118
Dummy Codingp. 119
Unweighted Effect Codingp. 121
Weighted Effect Codingp. 122
Contrast Codingp. 123
How to Choose a Coding Scheme: The Importance of Theoryp. 124
Computing Statistical Powerp. 125
Linear Interactions and Nonlinear Effects: Friends or Foes?p. 126
Testing and Interpreting Three-way and Higher-Order Interaction Effectsp. 131
Examining "Targeted" Lower-Order Interactionsp. 134
Conclusionsp. 135
Further Issues in the Interpretation of Moderating Effectsp. 138
Is the Moderating Effect Practically Significant?p. 139
Measures of Improved Fitp. 139
Difference in Correlations Across Moderator-Based Subgroupsp. 139
Proportion of Variance Explained by the Moderating Effect as Indexed by R[superscript 2]p. 140
Proportion of Variance Explained by the Moderating Effect as Indexed by f[superscript 2]p. 141
Proportion of Variance Explained by the Moderating Effect as Indexed by Modified f[superscript 2]p. 141
Measures of Improved Predictionp. 143
Differences in Unstandardized Regression Coefficients Across Moderator-Based Subgroupsp. 143
Standardized Effect of the Moderator on the Y on X Slopep. 144
Differential Impact of the Moderator at Various Values of the Predictor Xp. 146
The Signed Coefficient Rule for Interpreting Moderating Effectsp. 149
The Importance of Identifying Criterion and Predictor A Priorip. 150
Conclusionsp. 152
Summary and Conclusionsp. 155
Moderators and Social Science Theory and Practicep. 155
Use of Moderated Multiple Regressionp. 156
Homogeneity of Error Variance Assumptionp. 159
Low Statistical Power and Proposed Remediesp. 159
More Complex MMR Modelsp. 162
Assessing Practical Significancep. 162
Conclusionsp. 164
Computation of Bartlett's (1937) M Statisticp. 167
Computation of James's (1951) J Statisticp. 168
Computation of Alexander's (Alexander & Govern, 1994) A Statisticp. 170
Computation of Modified f[superscript 2]p. 171
Theory-Based Power Approximationp. 173
Referencesp. 175
Author Indexp. 190
Subject Indexp. 194
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9781572309692
ISBN-10: 1572309695
Series: Methodology in the Social Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 202
Published: 23rd December 2003
Publisher: Guilford Publications
Country of Publication: US
Dimensions (cm): 22.9 x 15.2  x 1.3
Weight (kg): 0.48