Journal of Statistical Theory and Practice

, Volume 5, Issue 2, pp 207–219

# Subset Selection in Poisson Regression

• D. M. Sakate
• D. N. Kashid
• D. T. Shirke
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.

62J12

## Key-words

Deviance Poisson regression Stepwise procedure Subset selection

## References

1. Akaike, H., 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control, AC-19, 716–723.
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.
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.
6. Mallows, C.L., 1973. Some comments on Cp. Technometrics, 15, 661–675.
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.
8. Miller, A.J., 2002. Subset Selection in Regression. Chapman and Hall.
9. Montgomery, D.C., Peck, E.A., Vining, G.G., 2006. Introduction to Linear Regression Analysis. John Wiley and Sons, New York.
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.
11. Thompson, M.L., 1978a. Selection of variables in multiple linear regression part I: A review and evaluation. Inter. Stat. Review., 46, 1–9.
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.
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.