Modeling Nonlinearity and Interaction in Regression Analysis Using Spline Variables: (Quantitative Applications in the Social Sciences)

"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

About the Author :
Roger A. Wojtkiewicz is a professor in the Department of Sociology at Ball State University in Muncie, Indiana. He spent the first 12 years of his career in the Department of Sociology at Louisiana State University and has since been at Ball State where he served as department chairperson for 12 years. At LSU, he taught undergraduate statistics and a graduate course in regression modeling in the PhD program. At Ball State, he has taught both the first and second semester courses in the statistics sequence in the master’s program. He was trained as a quantitative methodologist in the graduate sociology program at the University of Wisconsin—Madison. He is author of Elementary Regression Modeling: A Discrete Approach published by Sage Publications in 2017.

Review :
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. 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.