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Bayesian variable selection for Poisson regression with underreported responses

Author

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  • Powers, Stephanie
  • Gerlach, Richard
  • Stamey, James

Abstract

Variable selection for Poisson regression when the response variable is potentially underreported is considered. A logistic regression model is used to model the latent underreporting probabilities. An efficient MCMC sampling scheme is designed, incorporating uncertainty about which explanatory variables affect the dependent variable and which affect the underreporting probabilities. Validation data is required in order to identify and estimate all parameters. A simulation study illustrates favorable results both in terms of variable selection and parameter estimation. Finally, the procedure is applied to a real data example concerning deaths from cervical cancer.

Suggested Citation

  • Powers, Stephanie & Gerlach, Richard & Stamey, James, 2010. "Bayesian variable selection for Poisson regression with underreported responses," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3289-3299, December.
  • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3289-3299
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    References listed on IDEAS

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    1. Roldán Nofuentes, J.A. & Luna del Castillo, J.D. & Montero Alonso, M.A., 2009. "Determining sample size to evaluate and compare the accuracy of binary diagnostic tests in the presence of partial disease verification," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 742-755, January.
    2. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    3. Richard Gerlach & Ron Bird & Anthony D. Hall, 2000. "A Bayesian Approach to Variable Selection in Logistic Regression with Application to Predicting Earnings Direction from Accounting Information," Research Paper Series 47, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Leonhard Knorr-Held, 1999. "Conditional Prior Proposals in Dynamic Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 129-144.
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