Nonlinearity, multicollinearity and the probability of type II error in detecting interaction

The paper analyzes the impact of the inclusion of quadratic terms on the probability of type II error in testing for interaction in the presence of multicollinearity. The analysis focuses on two situations: (a) when the true model includes only linear and interaction terms; and (b) when the true model includes linear interaction and quadratic terms. The implications of this analysis on the estimation of interaction in multiple regression are discussed.