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Deletion diagnostics for generalized linear models using the adjusted Poisson likelihood function |
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| Authors: | Li-Chu Chien Tsung-Shan Tsou |
| Institution: | a Division of Biostatistics and Bioinformatics, Institute of Population Health Sciences, National Health Research Institutes, Zhunan, Taiwan b Institute of Statistics, Institute of Systems Biology and Bioinformatics, Center for Biotechnology and Biomedical Engineering, National Central University, Jhongli, Taiwan c Cathay Medical Research Institute, Cathay General Hospital, Taipei, Taiwan |
| Abstract: | In this article, we propose two novel diagnostic measures for the deletion of influential observations for regression parameters in the setting of generalized linear models. The proposed diagnostic methods are capable for detecting the influential observations under model misspecification, as long as the true underlying distributions have finite second moments.More specifically, it is demonstrated that the Poisson likelihood function can be properly adjusted to become asymptotically valid for practically all underlying discrete distributions. The adjusted Poisson regression model that achieves the robustness property is presented. Simulation studies and an illustration are performed to demonstrate the efficacy of the two novel diagnostic procedures. |
| Keywords: | Robust influential diagnostic method Generalized linear models Influential observations Poisson regression model |
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