Estimating the Probability of Rare Events Occurring Using a Local Model Averaging |
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| Authors: | Jin‐Hua Chen Chun‐Shu Chen Meng‐Fan Huang Hung‐Chih Lin |
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| Institution: | 1. Biostatistics Center/Master Program in Big Data Technology and Management, College of Management, Taipei Medical University, Taipei, Taiwan;2. Institute of Statistics and Information Science, National Changhua University of Education, Changhua, Taiwan;3. China Medical University Children Hospital, Taichung, Taiwan;4. School of Chinese Medicine, China Medical University, Taichung, Taiwan |
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| Abstract: | In statistical applications, logistic regression is a popular method for analyzing binary data accompanied by explanatory variables. But when one of the two outcomes is rare, the estimation of model parameters has been shown to be severely biased and hence estimating the probability of rare events occurring based on a logistic regression model would be inaccurate. In this article, we focus on estimating the probability of rare events occurring based on logistic regression models. Instead of selecting a best model, we propose a local model averaging procedure based on a data perturbation technique applied to different information criteria to obtain different probability estimates of rare events occurring. Then an approximately unbiased estimator of Kullback‐Leibler loss is used to choose the best one among them. We design complete simulations to show the effectiveness of our approach. For illustration, a necrotizing enterocolitis (NEC) data set is analyzed. |
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| Keywords: | Kullback‐Leibler loss logistic regression maximum likelihood estimate uncertainty |
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