Adding interaction
terms is related to the additivity assumption. Instead, linearity
can be tested by adding transformations of a predictor variable.
For example, for age, we might study: log(age), age^2, sqrt(age)
(=age^0.5), 1/age (=age^-1). Also, more general terms can be
used, such as restricted cubic splines (Harrell
et al., 1988) or fractional polynomials (e.g. age^2+age^0.5)
(Royston,
2000).