Abstract
Generalized linear models (GLM) are widely used to model social, medical and ecological data. Choosing predictors for building a good GLM is a widely studied problem. Likelihood based procedures like Akaike Information criterion and Bayes Information Criterion are usually used for model selection in GLM. The non-robustness property of likelihood based procedures in the presence of outliers or deviation from assumed distribution of response is widely studied in the literature. The deviance based criterion (DBC) is modified to define a robust and consistent model selection criterion called robust deviance based criterion (RDBC). Further, bootstrap version of RDBC is also proposed. A simulation study is performed to compare proposed model selection criterion with the existing one. It indicates that the performance of proposed criteria is compatible with the existing one. A key advantage of the proposed criterion is that it is very simple to compute. The proposed model selection criterion is applied to arboreal marsupials data and model selection is carried out. The proposed criterion can be applied to data from any discipline mitigating the effect of outliers or deviation from the assumption of distribution of response. It can be implemented in any statistical software. In this article, R software is used for the computations.
Highlights
Generalized linear models (GLM) are widely used to model social, medical and ecological data
We propose a new robust model selection criterion in GLM
We propose a robust version of deviance based criterion (DBC) called robust DBC (RDBC)
Summary
Generalized linear models (GLM) are widely used to model social, medical and ecological data. GLM builds a predictive model for a response variable based on the predictors. Given a data on response and predictors, the model is fitted using maximum likelihood estimates (MLE) of the unknown regression coefficients. In the process of model building, the researcher may be confronted to a pool of predictors of which some might be redundant in nature. If such predictors are included in the model, the response will be predicted with less accuracy. The fitted GLM may contain some predictors which are redundant in nature and are required to be eliminated from the model based on the observed data
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