Using Recursive Residuals, Calculated on Adaptively-Ordered Observations, to Identify Outliers in Linear Regression

Abstract

A new procedure for identifying outliers or influential observations is proposed. The procedure uses recursive residuals, calculated on observations that have been ordered according to their Studentized residuals, values of Cook's D, or another regression diagnostic of the user's choice. Under the model, these recursive residuals, appropriately standardized, have approximate Student's t distributions. Thus, convenient critical values are available for deciding which observations merit scrutiny and, perhaps, special treatment. The power of the test procedure to identify one or more outliers is investigated through simulation, and its dependence on the number and configuration of the outliers, that is, their placement with respect to the main body of the data, explored. The proposed procedure and two variations of it, also based on these recursive residuals, are compared with alternatives based on internally or externally Studentized residuals. The use of recursive residuals, calculated on adaptively-ordered observations, increases power and helps to combat the masking of one outlier by another when multiple outliers are present in configurations that create masking.