The Impact of Parameterization on the Interpretation of the Main-Effect Term in the Presence of an Interaction

Abstract

This paper examines the meaning of the so-called main-effect term in a logistic model that contains an interaction term involving the main-effect factor. The interpretation of the main-effect term is given in conjunction with the parameterization used to formulate the model for identification purposes. It occurred to the authors, through a consulting project, that many applied statisticians were not aware of the impact of parameterization on the inferential conclusions concerning the main-effect term in the presence of an interaction. It was thus decided to bring this fact to the attention of a wider audience. The motivating project is included.