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Estimating the Probability of Rare Events Occurring Using a Local Model Averaging

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  • Jin‐Hua Chen
  • Chun‐Shu Chen
  • Meng‐Fan Huang
  • Hung‐Chih Lin

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.

Suggested Citation

  • Jin‐Hua Chen & Chun‐Shu Chen & Meng‐Fan Huang & Hung‐Chih Lin, 2016. "Estimating the Probability of Rare Events Occurring Using a Local Model Averaging," Risk Analysis, John Wiley & Sons, vol. 36(10), pages 1855-1870, October.
    • Handle: RePEc:wly:riskan:v:36:y:2016:i:10:p:1855-1870
    DOI: 10.1111/risa.12558
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    References listed on IDEAS

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    1. Kan Shao & Jeffrey S. Gift, 2014. "Model Uncertainty and Bayesian Model Averaged Benchmark Dose Estimation for Continuous Data," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 101-120, January.
    2. A. John Bailer & Robert B. Noble & Matthew W. Wheeler, 2005. "Model Uncertainty and Risk Estimation for Experimental Studies of Quantal Responses," Risk Analysis, John Wiley & Sons, vol. 25(2), pages 291-299, April.
    3. Shen, Xiaotong & Huang, Hsin-Cheng, 2006. "Optimal Model Assessment, Selection, and Combination," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 554-568, June.
    4. Francis, Royce A. & Guikema, Seth D. & Henneman, Lucas, 2014. "Bayesian Belief Networks for predicting drinking water distribution system pipe breaks," Reliability Engineering and System Safety, Elsevier, vol. 130(C), pages 1-11.
    5. Chun‐Shu Chen & Hong‐Ding Yang & Yang Li, 2014. "A stabilized and versatile spatial prediction method for geostatistical models," Environmetrics, John Wiley & Sons, Ltd., vol. 25(2), pages 127-141, March.
    6. Roshanak Nateghi & Seth D. Guikema & Steven M. Quiring, 2011. "Comparison and Validation of Statistical Methods for Predicting Power Outage Durations in the Event of Hurricanes," Risk Analysis, John Wiley & Sons, vol. 31(12), pages 1897-1906, December.
    7. King, Gary & Zeng, Langche, 2001. "Logistic Regression in Rare Events Data," Political Analysis, Cambridge University Press, vol. 9(2), pages 137-163, January.
    8. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, September.
    9. Matthew W. Wheeler & A. John Bailer, 2007. "Properties of Model‐Averaged BMDLs: A Study of Model Averaging in Dichotomous Response Risk Estimation," Risk Analysis, John Wiley & Sons, vol. 27(3), pages 659-670, June.
    10. John Quigley & Matthew Revie, 2011. "Estimating the Probability of Rare Events: Addressing Zero Failure Data," Risk Analysis, John Wiley & Sons, vol. 31(7), pages 1120-1132, July.
    11. Roshanak Nateghi & Seth Guikema & Steven Quiring, 2014. "Forecasting hurricane-induced power outage durations," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 74(3), pages 1795-1811, December.
    12. Shen X. & Ye J., 2002. "Adaptive Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 210-221, March.
    13. Guikema, S.D. & Quiring, S.M., 2012. "Hybrid data mining-regression for infrastructure risk assessment based on zero-inflated data," Reliability Engineering and System Safety, Elsevier, vol. 99(C), pages 178-182.
    14. Hojin Moon & Hyun‐Joo Kim & James J. Chen & Ralph L. Kodell, 2005. "Model Averaging Using the Kullback Information Criterion in Estimating Effective Doses for Microbial Infection and Illness," Risk Analysis, John Wiley & Sons, vol. 25(5), pages 1147-1159, October.
    15. Ghosh, D. & Yuan, Z., 2009. "An improved model averaging scheme for logistic regression," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1670-1681, September.
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