A deviance-based criterion for model selection in GLM

Abstract

Model selection is the most persuasive problem in generalized linear models. A model selection criterion based on deviance called the deviance-based criterion (DBC) is proposed. The DBC is obtained by penalizing the difference between the deviance of the fitted model and the full model. Under certain weak conditions, DBC is shown to be a consistent model selection criterion in the sense that with probability approaching to one, the selected model asymptotically equals the optimal model relating response and predictors. Further, the use of DBC in link function selection is also discussed. We compare the proposed model selection criterion with existing methods. The small sample efficiency of proposed model selection criterion is evaluated by the simulation study.

Keywords:

• GLM
• deviance
• model selection
• consistency
• observed L₂ efficiency

AMS Subject Classification:

• 62J12

Acknowledgements

We thank the Editor and the anonymous referee for their valuable suggestions which led to the improvement of this paper.