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Interaction Effects in Linear and Generalized Linear Models

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

October 2018 | 480 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 data sets and the Stata code to reproduce the results of the application examples are available both in the book and online.

Chapter 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 Generalized linear Models  
Diagnostic Testing and Consequences of Model Misspecification  
Roadmap for the Rest of the Book  
Chapter 2: Basics of Interpreting the Focal Variable's Effect in the Modeling Component
GFI Basics: Algebraic Regrouping, Point Estimates, and Sign Changes  
Plotting Effects  
Chapter 3: The Varying Significance of the Focal Variable's Effect
Johnson-Neyman Mathematically Derived Significance Region  
Empirically-Defined Significance Region  
Confidence Bounds and Error Bar Plots  
Chapter 4: Linear (Identity Link) Models: Using the Predicted Outcome for Interpretation
Options for Display and Reference Values  
Reference Values for the Other Predictors  
Constructing Tables of Predicted Outcome Values  
Charts and Plots of the Expected Value of the Outcome  
Chapter 5: Non-identity Link Functions: Challenges of Interpreting Interactions in Non-Linear Models
Identifying the Issues  
Mathematically Defining the Confounded Sources of Nonlinearity  
Revisiting Options for Display and Reference Values  
Summary and Recommendations  
Derivations and Calculations  
Chapter 6: ICALC Toolkit: Syntax, Options, and Examples
INTSPEC: Interaction Specification Syntax and Options  
GFI Tool: Syntax and Options  
SIGREG Tool: Syntax and Options  
EFFDISP Tool: Syntax and Options  
OUTDISP Tool: Syntax and Options  
Chapter 7: Linear Regression Model Applications
Single Moderator Example  
The Effect of SES Moderated by Age  
Two Moderators Example  
Data and Testing  
The Effect of Birth Cohort Moderated by Family Income  
The Effect of Education Moderated by Family Income  
The Effect of Family Income Moderated by Birth Cohort and Education  
Special Topics  
Chapter 8: Logistic Regression and Probit Applications
One Moderator Example  
Three-Way Interaction Example (Interval by Nominal)  
Special Topics  
Chapter 9: Multinomial Logistic Regression Applications
One Moderator Example  
Two Moderators Example  
Special Topics  
Chapter 10: Ordinal Regression Models
One Moderator Example  
Two Moderators Interaction Example (Nominal by Two Interval)  
Special Topics  
Chapter 11: Count Models
Properties and Use of Count Models  
One Moderator Example (Interval by Nominal)  
Three-Way Interaction Example (Interval by Interval by Nominal)  
Special Topics  
Chapter 12: Extensions and Final Thoughts
Final Thoughts: Do's, Don'ts, and Cautions  
Appendix: Data For Examples
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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