IDEAS home Printed from https://ideas.repec.org/a/wly/riskan/v36y2016i10p1855-1870.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/risa.12558
    Download Restriction: no
    File URL: https://libkey.io/10.1111/risa.12558?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hou, Hui & Liu, Chao & Wei, Ruizeng & He, Huan & Wang, Lei & Li, Weibo, 2023. "Outage duration prediction under typhoon disaster with stacking ensemble learning," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    2. Walter W. Piegorsch & Hui Xiong & Rabi N. Bhattacharya & Lizhen Lin, 2014. "Benchmark Dose Analysis via Nonparametric Regression Modeling," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 135-151, January.
    3. Signe M. Jensen & Felix M. Kluxen & Christian Ritz, 2019. "A Review of Recent Advances in Benchmark Dose Methodology," Risk Analysis, John Wiley & Sons, vol. 39(10), pages 2295-2315, October.
    4. Jichao He & David W. Wanik & Brian M. Hartman & Emmanouil N. Anagnostou & Marina Astitha & Maria E. B. Frediani, 2017. "Nonparametric Tree‐Based Predictive Modeling of Storm Outages on an Electric Distribution Network," Risk Analysis, John Wiley & Sons, vol. 37(3), pages 441-458, March.
    5. Harriet Namata & Marc Aerts & Christel Faes & Peter Teunis, 2008. "Model Averaging in Microbial Risk Assessment Using Fractional Polynomials," Risk Analysis, John Wiley & Sons, vol. 28(4), pages 891-905, August.
    6. Walter W. Piegorsch, 2010. "Translational benchmark risk analysis," Journal of Risk Research, Taylor & Francis Journals, vol. 13(5), pages 653-667, July.
    7. Edsel A. Peña & Wensong Wu & Walter Piegorsch & Ronald W. West & LingLing An, 2017. "Model Selection and Estimation with Quantal‐Response Data in Benchmark Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 37(4), pages 716-732, April.
    8. Matthew W. Wheeler & Todd Blessinger & Kan Shao & Bruce C. Allen & Louis Olszyk & J. Allen Davis & Jeffrey S Gift, 2020. "Quantitative Risk Assessment: Developing a Bayesian Approach to Dichotomous Dose–Response Uncertainty," Risk Analysis, John Wiley & Sons, vol. 40(9), pages 1706-1722, September.
    9. Hui Hou & Hao Geng & Yong Huang & Hao Wu & Xixiu Wu & Shiwen Yu, 2019. "Damage Probability Assessment of Transmission Line-Tower System Under Typhoon Disaster, Based on Model-Driven and Data-Driven Views," Energies, MDPI, vol. 12(8), pages 1-17, April.
    10. Zhang, Bo & Shen, Xiaotong & Mumford, Sunni L., 2012. "Generalized degrees of freedom and adaptive model selection in linear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 574-586.
    11. Steven B. Kim & Ralph L. Kodell & Hojin Moon, 2014. "A Diversity Index for Model Space Selection in the Estimation of Benchmark and Infectious Doses via Model Averaging," Risk Analysis, John Wiley & Sons, vol. 34(3), pages 453-464, March.
    12. Steven B. Kim & Scott M. Bartell & Daniel L. Gillen, 2015. "Estimation of a Benchmark Dose in the Presence or Absence of Hormesis Using Posterior Averaging," Risk Analysis, John Wiley & Sons, vol. 35(3), pages 396-408, March.
    13. Enrique López Droguett & Ali Mosleh, 2014. "Bayesian Treatment of Model Uncertainty for Partially Applicable Models," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 252-270, February.
    14. Berk A. Alpay & David Wanik & Peter Watson & Diego Cerrai & Guannan Liang & Emmanouil Anagnostou, 2020. "Dynamic Modeling of Power Outages Caused by Thunderstorms," Forecasting, MDPI, vol. 2(2), pages 1-12, May.
    15. Matthew W. Wheeler & Jose Cortiñas Abrahantes & Marc Aerts & Jeffery S. Gift & Jerry Allen Davis, 2022. "Continuous model averaging for benchmark dose analysis: Averaging over distributional forms," Environmetrics, John Wiley & Sons, Ltd., vol. 33(5), August.
    16. Mukherjee, Sayanti & Nateghi, Roshanak & Hastak, Makarand, 2018. "A multi-hazard approach to assess severe weather-induced major power outage risks in the U.S," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 283-305.
    17. Signe M. Jensen & Christian Ritz, 2015. "Simultaneous Inference for Model Averaging of Derived Parameters," Risk Analysis, John Wiley & Sons, vol. 35(1), pages 68-76, January.
    18. Hojin Moon & Steven B. Kim & James J. Chen & Nysia I. George & Ralph L. Kodell, 2013. "Model Uncertainty and Model Averaging in the Estimation of Infectious Doses for Microbial Pathogens," Risk Analysis, John Wiley & Sons, vol. 33(2), pages 220-231, February.
    19. Enrique López Droguett & Ali Mosleh, 2008. "Bayesian Methodology for Model Uncertainty Using Model Performance Data," Risk Analysis, John Wiley & Sons, vol. 28(5), pages 1457-1476, October.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:riskan:v:36:y:2016:i:10:p:1855-1870. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1111/(ISSN)1539-6924 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.