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Title: | Smooth tests of goodness of fit for the distributional assumption of regression models | Authors: | Rayner, J. C. W. Rippon, Paul Suesse, Thomas THAS, Olivier |
Issue Date: | 2022 | Publisher: | WILEY | Source: | AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 64 (1) , p. 67 -85 | Status: | Early view | Abstract: | We focus on regression models that consist of (i) a model for the conditional mean of the outcome and (ii) a distributional assumption about the distribution of the outcome, both conditional on the regressors. Generalised linear models form a well-known example. The choice of the outcome distribution is often motivated by prior or background knowledge of the researcher, or it is simply chosen for convenience. We propose smooth goodness of fit tests for testing the distributional assumption in regression models. The tests arise from embedding the regression model in a smooth family of alternatives, and constructing appropriate score tests that correctly account for nuisance parameter estimation. The tests are customised, focussed and comprehensive. We present several examples to illustrate the wide applicability of our method. A small simulation study demonstrates that our tests have power to detect important deviations from the hypothesised model. | Notes: | Thas, O (corresponding author), Univ Wollongong, Natl Inst Appl Stat Res Australia NIASRA, Wollongong, NSW 2522, Australia.; Thas, O (corresponding author), Hasselt Univ, Data Sci Inst, I BioStat, B-3500 Diepenbeek, Belgium.; Thas, O (corresponding author), Univ Ghent, Dept Appl Math Comp Sci & Stat, B-9000 Ghent, Belgium. olivier.thas@uhasselt.be |
Keywords: | GLM;GLM;model diagnostics;model diagnostics;Poisson regression;Poisson regression;score test;score test;ZIP regression;ZIP regression | Document URI: | http://hdl.handle.net/1942/37334 | ISSN: | 1369-1473 | e-ISSN: | 1467-842X | DOI: | 10.1111/anzs.12361 | ISI #: | WOS:000783218800001 | Rights: | 2022 Statistical Society of Australia | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2023 |
Appears in Collections: | Research publications |
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Smooth tests of goodness of fit for the distributional assumption of regression models.pdf Restricted Access | Published version | 862.2 kB | Adobe PDF | View/Open Request a copy |
Smooth_GLM_R2 (1).pdf | Peer-reviewed author version | 403.54 kB | Adobe PDF | View/Open |
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