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Equivalence of several methods for efficient best subsets selection in generalized linear models. (English) Zbl 0875.62337

Summary: In the recent past, five methods for reducing computational intensity in best subset selection for Generalized Linear Models (GLM) have been proposed. We review these methods and explicitly show their mutual equivalence. Further, we show how the existing linear regression software can be used for such efficient best subset selection. Using the summary results presented in this paper, efficient best subset selection can easily be made available for all nonlinear GLM already present in statistical packages. This is of special importance for computing environments where computational efficiency has a high priority.

MSC:

62J12 Generalized linear models (logistic models)
62F07 Statistical ranking and selection procedures
65C99 Probabilistic methods, stochastic differential equations

Software:

SAS/STAT
Full Text: DOI

References:

[1] Fahrmeir, L.; Kaufmann, H.: Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear model. The annals of statistics 13, No. 1, 342-368 (1985) · Zbl 0594.62058
[2] Gilks, W. R.: A rapid two-stage modelling technique for exploring large data sets. Applied statistics 35, No. 2, 183-194 (1986)
[3] Hosmer, D.; Lemeshow, S.: Applied logistic regression. (1989) · Zbl 0715.62125
[4] Hosmer, D.; Jovanovic, B.; Lemeshow, S.: Best subsets logistic regression. Biometrics 45, 1265-1270 (1989) · Zbl 0715.62125
[5] Jovanovic, B.: Linearization, variable selection and diagnostics in generalized linear models. Doctoral dissertation (1991)
[6] Kuk, A. Y. C.: All subsets regression in a proportional hazards model. Biometrika 71, No. 3, 587-592 (1984)
[7] Lawless, J. F.; Singhal, K.: Efficient screening of non-normal models. Biometrics 34, 318-327 (1978)
[8] Lawless, J. F.; Singhal, K.: ISMOD: an all-subsets regression program for generalized linear models. I. statistical and computational background. Computer methods and programs in biomedicine 24, 117-124 (1987)
[9] Lawless, J. F.; Singhal, K.: ISMOD: an all-subsets regression program for generalized linear models. I. statistical and computational background. Computer methods and programs in biomedicine 24, 125-134 (1987)
[10] Mallows, C. L.: Some comments on cp. Technometrics 15, 661-676 (1973) · Zbl 0269.62061
[11] Mccullagh, P.; Nelder, J. A.: Generalized linear models. (1989) · Zbl 0744.62098
[12] Nordberg, L., Stepwise selection of explanatory variables in the binary logit model, Scandinavian J. Statistics, 8 17–26. · Zbl 0459.62054
[13] Nordberg, L.: On variable selection in generalized and related linear models. Communications in statistics, theory and methods 11, No. 21, 2427-2449 (1982) · Zbl 0502.62060
[14] . SAS/STAT user’s guide 2 (1992)
[15] Wedderburn, R. W. M.: Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika 61, No. 3, 439-447 (1974) · Zbl 0292.62050
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