Modeling Nonlinearity and Interaction in Regression Analysis Using Spline Variables

Roger A. Wojtkiewicz
Quantitative Applications in the Social Sciences
Modeling Nonlinearity and Interaction in Regression Analysis Using Spline Variables
May 2025 | 192 pages | Sage US
Create Flyer

If you’re in the Americas, please visit our Sage College Publishing website to purchase or sample this book:

Go to College Publishing Website

Description

"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.



Contents

Series Editor Introduction

Series Editor Introduction

Acknowledgments

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 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

Appendix 2: Example of Derivation of Interaction Model With Interval Variable Conditioned on Interval Variable From Dummy Variable Model

References

References

Index

Index

Description

"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.



Contents

Series Editor Introduction

Series Editor Introduction

Acknowledgments

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 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

Appendix 2: Example of Derivation of Interaction Model With Interval Variable Conditioned on Interval Variable From Dummy Variable Model

References

References

Index

Index

SAGE Publishing Logo

Modeling Nonlinearity and Interaction in Regression Analysis Using Spline Variables

Roger A. Wojtkiewicz
Cancel Print

May 2025 | 192 pages | Sage US

Format Published Date ISBN Price

"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.




Table Of Contents:

  • 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

Recent Product Reviews:

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

Recommendations