Assumptions in regression models:Additivity and linearity

Background

In this chapter, we discuss 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 non-linear terms can be included to allow for non-linear relationships between predictors and outcome. Throughout we stress parsimony in strategies to extend a prediction model with interactions and non-linear 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 various strategies to deal with additivity and linearity.