Assumptions in Regression Models: Additivity and Linearity

Abstract

In this chapter, we discuss the assessment of assumptions in multivariable regression models. Specifically, we consider the additivity assumption, which can be assessed with interaction terms. We also consider the linearity assumption of continuous predictors in a multivariable regression model, where multiple nonlinear terms can be included to allow for nonlinear relations between predictors and outcome. Throughout we stress parsimony in strategies to extend a prediction model with interactions and nonlinear terms, since better fulfillment of assumptions in a particular sample does not necessarily imply better predictive performance for future subjects. We consider several case studies for illustration of strategies to deal with additivity and linearity.