Using Residual Plots to Distinguish Cases of Predictor Omission in Linear Models

Abstract

Residual plots are commonly used to diagnose possible model misspecification, including predictor omission. In this paper, we present a systematic workflow for using residual plots and partial residual plots to detect and distinguish several types of model misspecification in linear models. Our workflow uses a set of four Yes/No questions and is accessible to statisticians and practitioners of all experience levels.
 Types of model misspecification considered by our workflow include four cases of predictor omission and two types of nonconstant variance. In particular, these cases of predictor omission are defined by the correlation and interaction status between the omitted predictor and the predictor included in the fitted model. Distinguishing cases of predictor omission is important because the impact of predictor omission can vary among cases. The interpretation of the parameter estimates in the statistical model can change depending on the approach.