Using Piecewise Linear Regression and Interrupted Regression to Understand Non-linearity

• In Event: 4351 - Measurement Issues in Social Statistical Models

Abstract

The relationship between an interval independent variable and an interval dependent variable in linear regression appears to be straightforward at first glance. This paper explores the complexity in the effects of the interval independent variable that lies beneath this seemingly simple relationship. The paper considers two parallel approaches to relaxing linear constraints for the effect of an interval independent variable. The first is piecewise linear regression using knotted spline variables. The second is interrupted regression using a less common type of spline variable, the group spline. The paper shows that when all constraints are relaxed, a fully-specified piecewise linear regression model fits the data the same as a fully-specified interrupted regression model. The paper also shows that both fully-specified models stem from a fully-specified dummy variable model. Finally the paper shows that squared, cubed, and higher order polynomial variables also stem from the fully-specified dummy variable model. The fact that the polynomial variables are all constrained linear combinations of the same set of underlying variables explains the multicollinearity problem that arises when using polynomial variables.

Author

• Roger A. Wojtkiewicz, Ball State University