Abstract #300649

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JSM 2003 Abstract #300649
Activity Number: 339
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Graphics
Abstract - #300649
Title: A Lack-of-Fit Test and a Graphical Diagnostic Tool based on Regional Residuals
Author(s): Ellen Deschepper*+ and Olivier Thas and Jean-Pierre Ottoy
Companies: Ghent University and University of Ghent and Ghent University
Address: , Ghent, 9000, Belgium
Keywords: regional residual plots ; multiple linear regression ; graphical methods ; regression diagnostics
Abstract:

Graphical methods are often used in applied statistics to assess the fit of parametric models, though these graphs can rarely be used as an inferential tool on their own. We propose a new graphical diagnostic tool and a corresponding statistical test to check how well a particular multiple linear model for the mean fits a set of observed data. The graphical method itself includes a formal testing procedure to assess the adequacy of a regression model, and, in particular it allows one to detect the location of lack-of-fit. The procedure is based on regional residuals defined over subsets of the space of the independent variables. An important issue is the standardization of the regional residuals for their variance not only depends on the model, but in addition also on the size of the subsets. By considering the standardized regional residuals in all such subsets, regional residual plots can be constructed. A simulation study shows that the power of our test is often larger than the power of many other lack-of-fit tests. Finally, a data example is presented.

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