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Modeling Nonlinearity and Interaction in Regression Analysis Using Spline Variables
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Modeling Nonlinearity and Interaction in Regression Analysis Using Spline Variables



April 2025 | SAGE Publications, Inc

"Spline variables and their interactions play a crucial role in the field of social science. This book offers a comprehensive and detailed exploration of this method, providing valuable insights and information for researchers in the field."
--Man-Kit Lei, The University of Georgia

This volume addresses the issue of linear constraints in regression modeling. Author Roger A. Wojtkiewicz uses the method of knotted spline variables (also known as piecewise linear regression) and a new method involving group spline variables to model nonlinearity in a variety of situations. Using spline variables to model nonlinearity allows researchers to specify unrestricted models for models that involve interval variables, allowing for greater flexibility in modeling any possible interaction.

 
Series Editor Introduction
 
Acknowledgments
 
About the Author
 
Chapter 1: Introduction
Main Focus of the Book

 
The Necessity to Provide Theoretical Justifications for Interactions

 
Plan of the Book

 
 
Chapter 2: Basics of Spline Variables
Derivation of Knotted Spline Model

 
General Equation for Knotted Spline Model

 
Empirical Example for Knotted Spline Model

 
Derivation of Group Spline Model

 
General Equation for Group Spline Model

 
Empirical Example of Group Spline Model

 
Conceptual Difference Between Knotted Splines and Group Splines

 
Summary

 
 
Chapter 3: Applications of Spline Variables
Modeling an Interval Variable With a Smaller Number of Values

 
Modeling an Interval Variable With a Larger Number of Values

 
Problem in Using Dummy Variables to Model Interval Variable

 
Advantages of Spline Variables Over Polynomial Variables

 
Interrupted Regression and Spline Variables

 
General Equation for Interrupted Regression Model

 
Empirical Example of Interrupted Regression Model

 
Summary

 
 
Chapter 4: Interaction Between Interval and Categorical Variables
Derivation of Model for Interval Conditioned on Categorical Interaction

 
General Equation for Interval Conditioned on Categorical Interaction Model

 
Empirical Example for Interval Conditioned on Categorical Interaction Model

 
Derivation of Model for Categorical Conditioned on Interval Interaction

 
General Equation for Categorical Conditioned on Interval Interaction Model

 
Empirical Example for Categorical Conditioned on Interval Interaction Model

 
Summary

 
 
Chapter 5: Interaction Between Interval Variables
Derivation of Model for Interval and Interval Interaction With Fewer Values

 
General Equation for Interval Conditioned on Interval Interaction

 
Empirical Example for Interval and Interval Interaction With Fewer Values

 
Derivation of Model for Interval and Interval Interaction With Many Values

 
Empirical Example for Interval and Interval Interaction With Many Values

 
Summary

 
 
Chapter 6: Concluding Remarks
Key Points

 
Final Comments

 
 
Appendix 1: Example of Derivation of Interaction Model With Interval Variable Conditioned on Categorical Variable From Dummy Variable Model
 
Appendix 2: Example of Derivation of Interaction Model With Interval Variable Conditioned on Interval Variable From Dummy Variable Model
 
References
 
Index

Spline variables and their interactions play a crucial role in the field of social science. This book offers a comprehensive and detailed exploration of this method, providing valuable insights and information for researchers in the field.

Man-Kit Lei
The University of Georgia

In regression analyses, most books on interactions involving an interval variable knowingly or unknowingly often assume that the interaction effect is linear and the same for all participants in each of the created groups to explain the interaction effect. However, this may not always be the case. Splines, that are widely used to model non-linearity in regression models have not been extensively used to explain interaction effects. This easy-to-read book by Dr. Roger Wojtkiewicz, which has a strong conceptual framework, provides empirical evidence illustrating the use of knotted splines and group splines in modeling nonlinearity in interaction models. This book will be a valuable addition to the library of any analyst with at least intermediate knowledge of regression models who is interested in explaining regression effects across groups using interactions.

Duke Appiah
Texas Tech University Health Sciences Center

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