Two-step jackknife bias reduction for logistic regression mles

References

• Albert , A. and Anderson , J.A. 1984 . On the existence of maximum likelihood estimates in logistic regression models . Biometrika , 71 : 1 – 10 .
   Web of Science ®Google Scholar
• Albert , A. and Harris , E.K. 1987 . Multivariate Interpretation of Clinical Laboratory Data , New York : Dekker .
   Google Scholar
• Anderson , J.A. and Richardson , S.C. 1979 . Logistic discrimination and bias correction in maximum likelihood estimation . Technometrics , 21 : 71 – 78 .
   Web of Science ®Google Scholar
• Breslow , N. 1981 . Odds ratio estimators when the data are sparse . Biometrika , 68 : 73 – 84 .
   Web of Science ®Google Scholar
• Byth , K. and Mclachlan , G.J. 1978 . The biases associated with maximum likelihood methods of estimation of the multivariate logistic risk function . Communications in Statistics - Theory and Methods , 7 : 877 – 890 .
   Web of Science ®Google Scholar
• Copas , J.B. 1988 . Binary regression models for contaminated data, with discussion . Journal of the Royal Statistical Society , 50 : 225 – 265 .
   Google Scholar
• Cordeiro , G.M. and Mccullagh , P. 1991 . Bias correction in generalized linear models . Journal of the Royal Statistical Society , 53 : 629 – 643 .
   Google Scholar
• Cox , D.R. and Snell , E.J. 1968 . A general definition of residuals . Journal of the Royal Statistical Society , 30 : 248 – 275 .
   Google Scholar
• Efron, B. (1982). The Jackknife, the Bootstrap and other Resampling Plans, Society for Industrial and Applied Mathematics,Philadelphia, Pennsylvania
   Google Scholar
• Efron , B. and Gong , G. 1983 . A leisurely look at the bootstrap, the jackknife, and cross-validation . The American Statistician , 37 : 36 – 48 .
   Web of Science ®Google Scholar
• Farewell , V.T. 1978 . Jackknife estimation with structured data . Biometrika , 65 : 444 – 447 .
   Google Scholar
• Fleiss , J.L. and Davies , M. 1982 . Jackknifing functions of multinomial frequencies, with an application to a measure of concordance . American Journal of Epidemiology , 115 : 841 – 845 .
   PubMedGoogle Scholar
• Gong , G. 1986 . Cross-validation, the jackknife, and the bootstrap: Excess error estimation in forward logistic regression . Journal of the American Statistical Association , 81 : 108 – 113 .
   Web of Science ®Google Scholar
• Haldane , J.B.S. 1956 . The estimation and significance of the logarithm of a ratio of frequencies . Annals of Human Genetics , 20 : 309 – 311 .
   PubMed Web of Science ®Google Scholar
• Hauck , W.W. 1984 . A comparative study of conditional maximum likelihood estimation of a common odds ratio . Biometrics , 40 : 1117 – 1123 .
   PubMed Web of Science ®Google Scholar
• Hauck , W.W. 1989 . Odds ratio inference from stratified samples . Communications in Statistics - Theory and Methods , 18 : 767 – 800 .
   Web of Science ®Google Scholar
• Hirji , K.F. , Mehta , C.R. and Patel , N.R. 1987 . Computing distributions for exact logistic regression . Journal of the American Statistical Association , 82 : 1110 – 1117 .
   Web of Science ®Google Scholar
• Hirji , K.F. , Tsiatis , A. and Mehta , C.R. 1989 . Median unbiased estimation for binary data . The American Statistician , 43 : 7 – 11 .
   Web of Science ®Google Scholar
• Jennings , D.E. 1986 . Judging inference adequacy in logistic regression . Journal of the American Statistical Association , 81 : 471 – 476 .
   Web of Science ®Google Scholar
• Jewell , N.P. 1984 . Small-sample bias of point estimators of the odds ratio from matched sets . Biometrics , 40 : 421 – 435 .
   PubMedGoogle Scholar
• Jewell , N.P. 1986 . On the bias of commonly used measures of association for 2 times & 2 tables . Biometrics , 42 : 351 – 358 .
   Web of Science ®Google Scholar
• Jorgensen , M.A. 1987 . Jackknifing fixed points of iterations . Biometrika , 74 : 207 – 211 .
   Web of Science ®Google Scholar
• Lesaffre , E. and Albert , A. 1989a . Partial separation in logistic discrimination . Journal of the Royal Statistical Society , 51 : 109 – 116 .
   Google Scholar
• Lesaffre , E. and Albert , A. 1989b . Multiple-group logistic regression diagnostics . Applied Statistics , 38 : 425 – 440 .
   Web of Science ®Google Scholar
• Lesaffre , E. , Willems , J.L. and Albert , A. 1989 . Estimation of error rate in multiple group logistic discrimination: The approximate leaving-one-out method . Communications in Statistics-Theory and Methods , 18 : 2989 – 3007 .
   Web of Science ®Google Scholar
• Mclachlan , G.J. 1980 . A note on bias correction in maximum likelihood estimation with logistic discrimination . Technometrics , 22 : 621 – 627 .
   Web of Science ®Google Scholar
• Parr , W.C. and Tolley , H.D. 1982 . Jackknifing in categorical data analysis . Australian Journal of Statistics , 24 : 67 – 79 .
   Google Scholar
• Pigeot , I. 1991 . A simulation study of estimators of a common odds ratio in several times& tables . Journal of Statistical Computation and Simulation , 38 : 65 – 82 .
   Google Scholar
• Pike , M.C. , Hill , A.P. and Smith , P.G. 1980 . Bias and efficiency in logistic analyses of stratified case control studies . International Journal of Epidemiologye , 9 : 89 – 95 .
   PubMed Web of Science ®Google Scholar
• Pregibon , D. 1981 . Logistic regression diagnostics . The Annals of Statistics , 9 : 705 – 724 .
   Web of Science ®Google Scholar
• Plomteux , G. 1980 . Multivariate analysis of an enzyme profile for the differential diagnosis of viral hepatitis . Clinical Chemistry , 26 : 1897 – 1899 .
   PubMedGoogle Scholar
• Santner , T.J. and Duffy , D.E. 1986 . A note on A. Albert and J.A. Anderson's conditions for the existence of maximum likelihood estimates in logistic regression models . Biometrika , 73 : 755 – 758 .
   Web of Science ®Google Scholar
• Schaefer , R.L. 1983 . Bias correction in maximum likelihood logistic regression . Statistics in Medicine , 2 : 71 – 78 .
   PubMedGoogle Scholar
• Silvapulle , M.J. 1981 . On the existence of maximum likelihood estimators for the binomial response models . Journal of the Royal Statistical Society , 43 : 310 – 313 .
   Google Scholar
• Tritchler , D. 1984 . An algorithm for exact logistic regression . Journal of the American Statistical Association , 79 : 709 – 711 .
   Web of Science ®Google Scholar
• Walter , S.D. 1985 . Small sample estimation of log odds ratios from logistic regression and fourfold tables . Statistics in Medicine , 4 : 437 – 444 .
   PubMedGoogle Scholar
• Walter , S.D. and Cook , R.J. 1991 . A comparison of several point estimators of the odds ratio in a single 2x2 contingency table . Biometrics , 47 : 795 – 811 .
   PubMedGoogle Scholar
• Whaley , F.S. 1991 . Comparison of different maximum likelihood estimators in a small sample logistic regression with two independent binary variables . Statistics in Medicine , 10 : 723 – 731 .
   PubMedGoogle Scholar