SUGI 28: Let the Data Speak: New Regression Diagnostics Based on Cumulative Residuals

Residuals have long been used as the basis for graphical and numerical examination of the adequacy of regression models. Conventional residual analysis based on plotting raw residuals or their smoothed versions is highly subjective, whereas most goodness-offit tests provide little information about the nature of model inadequacy. In this paper, new model-checking techniques of Lin et al. (1993, 2002) based on cumulative sums and other aggregates of residuals are described. These techniques provide objective and informative checks on the adequacy of the fitted model for a variety of statistical models and data structures. Specific aspects of the adequacy of the fitted model can be assessed, depending on the particular model. In generalized linear models and marginal models for dependent responses (GEEs), special attention is given to checking the functional form of a covariate in the linear predictor and the form of the link function. In proportional hazards models, the focus is on checking the functional form of a covariate and the validity of the proportional hazards assumption. These methods are available for release 9.1 of SAS/STAT software in the GENMOD and PHREG procedures, and use ODS graphics for graphical output. Use of these graphical and numerical methods is illustrated with several examples.