The Use of Recursive Residuals in Checking Model Fit in Linear Regression

Recursive residuals are independently and identically distributed and, unlike ordinary residuals, do not have the problem of deficiencies in one part of the data being smeared over all the residuals.In addition, recursive residuals may be interpreted as showing the effect of successively deleting observations from the data set.We propose the use of the normal probability plot and the cumulative sum plots of the recursive residuals, and of the square roots of the absolute values of the recursive residuals to check the model assumptions of normality and homoscedasticity, and other aspects of model misfits such as change of regime, outliers, and omitted predictors, in place of plots based on ordinary residuals.A further advantage of recursive residuals is that they are open to formal statistical testing, so that these plots can be automated and in fact produced only when a model misfit has been detected.