Modeling Nonlinearity and Interaction in Regression Analysis Using Spline Variables

Roger A. Wojtkiewicz - Ball State University, USA

Volume: 196

Series:
Quantitative Applications in the Social Sciences

Other Titles in:
Regression & Correlation | Research Methods | Sociological Research Methods

May 2025 | 192 pages | SAGE Publications, Inc

Description
Contents

"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

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Modeling Nonlinearity and Interaction in Regression Analysis Using Spline Variables

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