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Interaction Effects in Linear and Generalized Linear Models
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Interaction Effects in Linear and Generalized Linear Models
Examples and Applications Using Stata



October 2018 | 608 pages | SAGE Publications, Inc
“This book is remarkable in its accessible treatment of interaction effects. Although this concept can be challenging for students (even those with some background in statistics), this book presents the material in a very accessible manner, with plenty of examples to help the reader understand how to interpret their results.”  

–Nicole Kalaf-Hughes, Bowling Green State University  

Offering a clear set of workable examples with data and explanations, Interaction Effects in Linear and Generalized Linear Models is a comprehensive and accessible text that provides a unified approach to interpreting interaction effects. The book develops the statistical basis for the general principles of interpretive tools and applies them to a variety of examples, introduces the ICALC Toolkit for Stata, and offers a series of start-to-finish application examples to show students how to interpret interaction effects for a variety of different techniques of analysis, beginning with OLS regression.  

The author’s website at www.icalcrlk.com provides a downloadable toolkit of Stata® routines to produce the calculations, tables, and graphics for each interpretive tool discussed. Also available are the Stata® dataset files to run the examples in the book.
 
Series Editor’s Introduction
 
Preface
 
Acknowledgments
 
About the Author
 
1. Introduction and Background
Overview: Why Should You Read This Book?  
The Logic of Interaction Effects in Linear Regression Models  
The Logic of Interaction Effects in GLMs  
Diagnostic Testing and Consequences of Model Misspecification  
Roadmap for the Rest of the Book  
Chapter 1 Notes  
 
PART I. PRINCIPLES
 
2. Basics of Interpreting the Focal Variable’s Effect in the Modeling Component
Mathematical (Geometric) Foundation for GFI  
GFI Basics: Algebraic Regrouping, Point Estimates, and Sign Changes  
Plotting Effects  
Summary  
Special Topics  
Chapter 2 Notes  
 
3. The Varying Significance of the Focal Variable’s Effect
Test Statistics and Significance Levels  
JN Mathematically Derived Significance Region  
Empirically Defined Significance Region  
Confidence Bounds and Error Bar Plots  
Summary and Recommendations  
Chapter 3 Notes  
 
4. Linear (Identity Link) Models: Using the Predicted Outcome for Interpretation
Options for Display and Reference Values  
Reference Values for the Other Predictors (Z)  
Constructing Tables of Predicted Outcome Values  
Charts and Plots of the Expected Value of the Outcome  
Conclusion  
Special Topics  
Chapter 4 Notes  
 
5. Nonidentity Link Functions: Challenges of Interpreting Interactions in Nonlinear Models
Identifying the Issues  
Mathematically Defining the Confounded Sources of Nonlinearity  
Revisiting Options for Display and Reference Values  
Solutions  
Summary and Recommendations  
Derivations and Calculations  
Chapter 5 Notes  
 
PART II. APPLICATIONS
 
6. ICALC Toolkit: Syntax, Options, and Examples
Overview  
INTSPEC: Syntax and Options  
GFI Tool: Syntax and Options  
SIGREG Tool: Syntax and Options  
EFFDISP Tool: Syntax and Options  
OUTDISP Tool: Syntax and Options  
Next Steps  
Chapter 6 Notes  
 
7. Linear Regression Model Applications
Overview  
Single-Moderator Example  
Two-Moderator Example  
Special Topics  
Chapter 7 Notes  
 
8. Logistic Regression and Probit Applications
Overview  
One-Moderator Example (Nominal by Nominal)  
Three-Way Interaction Example (Interval by Interval by Nominal)  
Special Topics  
Chapter 8 Notes  
 
9. Multinomial Logistic Regression Applications
Overview  
One-Moderator Example (Interval by Interval)  
Two-Moderator Example (Interval by Two Nominal)  
Special Topics  
Chapter 9 Notes  
 
10. Ordinal Regression Models
Overview  
One-Moderator Example (Interval by Nominal)  
Two-Moderator Interaction Example (Nominal by Two Interval)  
Special Topics  
Chapter 10 Notes  
 
11. Count Models
Overview  
One-Moderator Example (Interval by Nominal)  
Three-Way Interaction Example (Interval by Interval by Nominal)  
Special Topics  
Chapter 11 Notes  
 
12. Extensions and Final Thoughts
Extensions  
Final Thoughts: Dos, Don’ts, and Cautions  
Chapter 12 Notes  
 
Appendix: Data for Examples
Chapter 2: One-Moderator Example  
Chapter 2: Two-Moderator Mixed Example  
Chapter 2: Two-Moderator Interval Example  
Chapter 2: Three-Way Interaction Example  
Chapter 3: One-Moderator Example  
Chapter 3: Two-Moderator Example  
Chapter 3: Three-Way Interaction Example  
Chapter 4: Tables One-Moderator Example and Figures Example 3  
Chapter 4: Tables Two-Moderator Example  
Chapter 4: Figures Examples 1 and 2  
Chapter 4: Figures Example 4  
Chapter 4: Tables Three-Way Interaction Example and Figures Example 5  
Chapter 5: Examples 1 and 2  
Chapter 5: Example 3  
Chapter 5: Example 4  
Chapter 6: One-Moderator Example  
Chapter 6: Two-Moderator Example  
Chapter 6: Three-Way Interaction Example  
Chapter 7: One-Moderator Example  
Chapter 7: Two-Moderator Example  
Chapter 8: One-Moderator Example  
Chapter 8: Three-Way Interaction Example  
Chapter 9: One-Moderator Example  
Chapter 9: Two-Moderator Example  
Chapter 10: One-Moderator Example  
Chapter 10: Two-Moderator Example  
Chapter 11: One-Moderator Example  
Chapter 11: Three-Way Interaction Example  
Chapter 12: Polynomial Example  
Chapter 12: Heckman Example  
Chapter 12: Survival Analysis Example  
 
References
Data Sources  
 
Index

Supplements

Companion Website

The author’s website at www.icalcrlk.com provides a downloadable toolkit of Stata routines to produce the calculations, tables and graphics for each interpretive tool discussed. Also available are the data files and Stata do files to run the examples in the book.

“This book is remarkable in its accessible treatment of interaction effects. Although this concept can be challenging for students (even those with some background in statistics), this book presents the material in a very accessible manner, with plenty of examples to help the reader understand how to interpret their results.”

Nicole Kalaf-Hughes
Bowling Green State University

“Interaction Effects in Linear and Generalized Linear Models provides an intuitive approach that benefits both new users of Stata getting acquainted with these statistical models as well as experienced students looking for a refresher. The topic of interactions is greatly important given that many of our main theories in the social and behavioral sciences rely on moderating effects of variables. This book does a terrific job of guiding the reader through the various statistical commands available in Stata and explaining the results and taking the reader through different considerations in graphically presenting their results.”

Jennifer Hayes Clark
University of Houston
Key features

KEY FEATURES:

  • Detailed discussions show students how to apply and interpret results for linear, multinomial logistic regression, ordinal regression models, and poison and negative binomial regression models (including zero-inflated variants). 
  • Downloadable software to apply interpretive tools automates the calculation and creation of numeric results, tables and graphics, reducing the need for more complex programming skills.
  • Sufficient mathematical detail and application of underlying formulas, as well as discussion of specific applications, enables readers to develop their own spreadsheet formulas or software applications.
  • The ICALC toolkit saves all graphics as memory graphs which can be customized during a Stata session or saved/exported for later customization and use and optionally saves numeric results, tables and the underlying data for graphics into an Excel spreadsheet to provide flexibility for users to create their own graphics from the data using other platforms.

 


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