Global Validation of Linear Model Assumptions.
An easy-to-implement global procedure for testing the four assumptions of the linear model is proposed. The test can be viewed as a Neyman smooth test and it only relies on the standardized residual vector. If the global procedure indicates a violation of at least one of the assumptions, the components of the global test statistic can be utilized to gain insights into which assumptions have been violated. The procedure can also be used in conjunction with associated deletion statistics to detect unusual observations. Simulation results are presented indicating the sensitivity of the procedure in detecting model violations under a variety of situations, and its performance is compared with three potential competitors, including a procedure based on the Box-Cox power transformation. The procedure is demonstrated by applying it to a new car mileage data set and a water salinity data set that has been used previously to illustrate model diagnostics.
E. Peña is Professor in the Department of Statistics, University of South Carolina, Columbia, SC 29208. His e-mail address is pena@stat.sc.edu . He acknowledges the research support provided by NSF Grant DMS 0102870, NIH Grant GM056182, NIH COBRE Grant RR17698, and the USC/MUSC Collaborative Research Program.
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