1,458
Views
51
CrossRef citations to date
0
Altmetric
Regression Analysis

Determination of the Selection Statistics and Best Significance Level in Backward Stepwise Logistic Regression

, , &
Pages 62-72 | Received 06 Nov 2006, Accepted 27 Apr 2007, Published online: 03 Jan 2008

References

  • Ambler , G. , Brady , A. R. , Royston , P. ( 2002 ). Simplifying a prognostic model: a simulation study based on clinical data . Statistics in Medicine 21 : 3803 – 3822 .
  • Bendel , R. B. , Afifi , A. A. ( 1977 ). Comparison of stopping rules in forward stepwise regression . Journal of the American Statistical Association 72 ( 357 ): 46 – 53 .
  • Cochran , W. G. , Cox , G. M. ( 1957 ). Experimental Designs . New York : Wiley .
  • Costanza , M. C. , Afifi , A. A. ( 1979 ). Comparison of stopping rules in forward stepwise discriminant analysis . Journal of the American Statistical Association 74 ( 368 ): 777 – 785 .
  • Derksen , S. , Keselman , H. J. ( 1992 ). Backward, forward and stepwise automated subset selection algorithms: frequency of obtaining authentic and noise variables . British Journal of Mathematical and Statistical Psychology 45 : 265 – 282 .
  • Draper , N. R. , Smith , H. ( 1998 ). Applied Regression Analysis . New York : Wiley .
  • Efron , B. ( 1983 ). Estimating the error rate of a prediction rule: improvement on cross-validation . Journal of the American Statistics Association 78 : 316 – 331 .
  • Efron , B. ( 1986 ). How biased is the apparent error rate of a prediction rule? Journal of the American Statistical Association 81 ( 394 ): 461 – 470 .
  • Efroymson , M. A. ( 1960 ). Mathematical methods for digital computers . In: Ralston , A. , Wilf , H. S. , eds. Multiple Regression Analysis . New York : Wiley .
  • Glick , N. ( 1972 ). Sampled-based classification procedures derived from density estimators . Journal of the American Statistics Association 67 : 116 – 122 .
  • Glick , N. ( 1973 ). Sampled-based multinomial classification . Biometrics 29 ( 1 ): 241 – 256 .
  • Gong , G. ( 1986 ). Cross-validation, the jackknife, and the bootstrap: excess error estimation in forward logistic regression . Journal of the American Statistical Association 81 ( 393 ): 108 – 113 .
  • Harrell , F. E. , Lee , K. L. , Califf , R. M. , Pryor , D. B. , Rosati , R. A. ( 1984 ). Regression modelling strategies for improved prognostic prediction . Statistics in Medicine 3 : 143 – 152 .
  • Hauck , W. W. , Donner , A. ( 1977 ). Wald's test as applied to hypotheses in logit analysis . Journal of the American Statistical Association 72 ( 360 ): 851 – 853 .
  • Hills , M. ( 1966 ). Allocation rules and their error rates . Journal of the Royal Statistical Society Series B 28 : 1 – 20 .
  • Hosmer , D. W. , Lemeshow , S. ( 2000 ). Applied Logistic Regression. , 2nd ed. New York : Wiley .
  • Lee , K. I. , Koval , J. J. ( 1997 ). Determination of the best significance level in forward step-wise logistic regression . Communications in Statistics—Simulation and Computation 26 ( 2 ): 559 – 575 .
  • Montgomery , D. C. ( 2005 ). Design and Analysis of Experiments. , 6th ed. New York : Wiley .
  • Peduzzi , P. , Concato , J. , Kemper , E. , Holford , T. R. , Feinstein , A. R. ( 1996 ). A simulation study of the number of events per variable in logistic regression analysis . Journal of Clinical Epidemiology 49 : 1503 – 1510 .
  • Qaqish , B. F. ( 2003 ). A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations . Biometrika 90 : 455 – 463 .
  • Rao , C. R. ( 1973 ). Linear Statistical Inference and Its Applications. , 2nd ed. New York : Wiley .
  • Roecker , E. B. ( 1991 ). Prediction error and its estimation for subset-selected models . Technometrics 33 : 459 – 468 .
  • SAS/IML Software . ( 2004 ). User's Guide, SAS Institute Inc. Version 9.1, Cary , NC , USA .
  • SAS/STAT . ( 2004 ). User's Guide, SAS Institute Inc. Version 9.1 Cary , NC , USA .
  • Steyerberg , E. W. , Eijkemans , M. J. C. , Harrell , J. , F. E. , Habbema , J. D. F. ( 2000 ). Prognostic modeling with logistic regression analysis: a comparison of selection and estimation methods in small data sets . Statistics in Medicine 19 : 1059 – 1079 .
  • Steyerberg , E. W. , Eijkemans , M. J. C. , Harrell , J. , F. E. , Habbema , J. D. F. ( 2001 ). Prognostic modeling with logistic regression analysis: in search of a sensible strategy in small data sets . Medical Decision Making 21 : 45 – 56 .
  • Wald , A. ( 1943 ). Tests of statistical hypotheses concerning several parameters when the number of observations is large . Transactions of the American Mathematical Society 54 : 426 – 482 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.