Abstract
We study new logistic model selection criteria based on p-values. The rules are proved to be consistent provided suitable assumptions on design matrix and scaling constants are satisfied and the search is performed over the family of all submodels. Moreover, we investigate practical performance of the introduced criteria in conjunction with greedy search methods such as initial ordering, forward and backward search and genetic algorithm which restrict the range of family of models over which an optimal value of the respective criterion is sought. Scaled minimal p-value criterion with initial ordering turns out to be a promising alternative to BIC.
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References
Broman, K.W., Speed, T.P.: A model selection approach for the identification of quantitative trait loci in experimental crosses (with discussion). J. Roy Stat. Soc. B 64, 641–656, 731–775 (2002)
Chen, J., Chen, Z.: Extended Bayesian criteria for model selection with large model spaces. Biometrika 95(3), 759–771 (1995)
Davison, A., Hinkley, D.: Bootstrap Methods and Their Applications. Cambridge University Press (1997)
Fahrmeir, L.: Asymptotic testing theory for generalized linear models. Statistics 1, 65–76 (1987)
Fahrmeir, L., Kaufmann, H.: Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. The Annals of Statistics 1(13), 342–368 (1985)
Harrell, F.E.: Regression Modelling Strategies: with Applications to Linear Models. Logistic Regression and Survival Analysis. Springer, New York (2001)
Hastie, T.J., Pregibon, D.: Generalized Linear Models. Wadsworth and Brooks/Cole (1992)
Mühlenbein, H., Schlierkamp-Voosen, D.: Predictive Models for the Breeder Genetic Algorithm, I: Continuous Parameter Optimization. Evolutionary Computation 1(1), 25–49 (1993)
Pokarowski, P., Mielniczuk, J.: P-values of likelihood ratio statistic for consistent model selection and testing (2011) (in preparation)
SAS datasets, http://ftp.sas.com/samples/A56902
Qian, G., Field, C.: Law of iterated logarithm and consistent model selection criterion in logistic regression. Statistics and Probability Letters 56, 101–112 (2002)
Tolvi, J.: Genetic algorithms for outlier detection and variable selection in linear regression models. Soft Comput. 8(8), 527–533 (2004)
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Mielniczuk, J., Teisseyre, P. (2012). Model Selection in Logistic Regression Using p-Values and Greedy Search. In: Bouvry, P., Kłopotek, M.A., Leprévost, F., Marciniak, M., Mykowiecka, A., Rybiński, H. (eds) Security and Intelligent Information Systems. SIIS 2011. Lecture Notes in Computer Science, vol 7053. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25261-7_10
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DOI: https://doi.org/10.1007/978-3-642-25261-7_10
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