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Journal of Statistical Theory and Practice

, Volume 5, Issue 2, pp 207–219 | Cite as

Subset Selection in Poisson Regression

Article

Abstract

In this article, we propose a criterion for subset selection in Poisson regression called Dp criterion. This criterion uses the deviance of the full model and subset model to arrive at a decision. Based on the same criterion a stepwise procedure is also developed to select the appropriate subset. The procedure is useful even when the number of regressors is large. The proposed stepwise method is operationally simple to implement. The method is illustrated with examples.

AMS Subject Classification

62J12 

Key-words

Deviance Poisson regression Stepwise procedure Subset selection 

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References

  1. Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, AC-19, 716–723.MathSciNetCrossRefGoogle Scholar
  2. D’ Agostino, R.B., Stephens, M.A., 1986. Goodness of Fit Ttechniques. Marcel Decker, Inc.Google Scholar
  3. Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., 2004. Least angle regression. Annals of Statistics, 32(2), 407–499.MathSciNetCrossRefGoogle Scholar
  4. Efroymson, M.A., 1960. Multiple regression analysis. In Mathematical Methods for Digital Computers, Ralston, A. and Wilf, H.S. (Editors), Wiley, New York.Google Scholar
  5. Guo, Jie Q., Li, Tong, 2002. Poisson regression models with errors-in-variables: implementation and treatment. Journal of Statistical Planning and Inference, 104(2), 391–401.MathSciNetCrossRefGoogle Scholar
  6. Mallows, C.L., 1973. Some comments on Cp. Technometrics, 15, 661–675.MATHGoogle Scholar
  7. Meier, L., Sara van de Geer, Bühlmann, P., 2008. Group LASSO for logistic regression. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70(1), 53–71.MathSciNetCrossRefGoogle Scholar
  8. Miller, A.J., 2002. Subset Selection in Regression. Chapman and Hall.CrossRefGoogle Scholar
  9. Montgomery, D.C., Peck, E.A., Vining, G.G., 2006. Introduction to Linear Regression Analysis. John Wiley and Sons, New York.MATHGoogle Scholar
  10. Myers, R.H., Montgomery, D.C., Vining G.G., 2002. Generalized Linear Models: with Applications in Engineering and the Sciences. John Wiley and Sons, New York.MATHGoogle Scholar
  11. Thompson, M.L., 1978a. Selection of variables in multiple linear regression part I: A review and evaluation. Inter. Stat. Review., 46, 1–9.CrossRefGoogle Scholar
  12. Thompson, M.L., 1978b. Selection of variables in multiple linear regression part II: Chosen predictors, computation and examples. Inter. Stat. Review., 46, 129–146.CrossRefGoogle Scholar
  13. Yamashita, T., Yamashita, K., Kamimura, R., 2007. A stepwise AIC method for variable selection in linear regression. Communications in Statistics-Theory and methods, 36, 2395–2403.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.Department of StatisticsShivaji UniversityKolhapurIndia

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