A robust diagnostic plot for explanatory variables under model mis-specification

Abstract

A typical added variable plot is a commonly used plot in assessing the accuracy of a normal linear model. This plot is often used to evaluate the effect of adding an explanatory variable into the model and to detect possibly high leverage points or influential observations on the added variable. However, this type of plot is generally in doubt, once the normal distributional assumptions are violated. In this article, we extend the robust likelihood technique introduced by Royall and Tsou [11] to propose a robust added variable plot. The validity of this diagnostic plot requires no knowledge of the true underlying distributions so long as their second moments exist. The usefulness of the robust graphical approach is demonstrated through a few illustrations and simulations.

Keywords:

• added variable plot
• high leverage points
• influential data
• adjusted normal regression