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Volumn 187, Issue 4, 2018, Pages 864-870

Separation in Logistic Regression: Causes, Consequences, and Control

Author keywords

logistic regression; maximum likelihood; penalized likelihood; separation; small samples; sparse data

Indexed keywords

BAYESIAN ANALYSIS; DATA SET; MAXIMUM LIKELIHOOD ANALYSIS; NUMERICAL METHOD; NUMERICAL MODEL; REGRESSION ANALYSIS; URINARY TRACT DISEASE;

EID: 85045447736     PISSN: 00029262     EISSN: 14766256     Source Type: Journal    
DOI: 10.1093/aje/kwx299     Document Type: Article
Times cited : (190)

References (42)
  • 1
    • 0002347322 scopus 로고
    • Median unbiased estimation for binary data
    • Hirji KF, Tsiatis AA, Mehta CR. Median unbiased estimation for binary data. Am Stat. 1989;43(1):7-11.
    • (1989) Am Stat. , vol.43 , Issue.1 , pp. 7-11
    • Hirji, K.F.1    Tsiatis, A.A.2    Mehta, C.R.3
  • 2
    • 0002178053 scopus 로고
    • Bias reduction of maximum likelihood estimates
    • Firth D. Bias reduction of maximum likelihood estimates. Biometrika. 1993;80(1):27-38.
    • (1993) Biometrika. , vol.80 , Issue.1 , pp. 27-38
    • Firth, D.1
  • 3
    • 0020623772 scopus 로고
    • Bias correction in maximum likelihood logistic regression
    • Schaefer RL. Bias correction in maximum likelihood logistic regression. Stat Med. 1983;2(1):71-78.
    • (1983) Stat Med. , vol.2 , Issue.1 , pp. 71-78
    • Schaefer, R.L.1
  • 4
    • 0030890006 scopus 로고    scopus 로고
    • Jackknife bias reduction for polychotomous logistic regression
    • Bull SB, Greenwood CM, Hauck WW. Jackknife bias reduction for polychotomous logistic regression. Stat Med. 1997;16(5):545-560.
    • (1997) Stat Med. , vol.16 , Issue.5 , pp. 545-560
    • Bull, S.B.1    Greenwood, C.M.2    Hauck, W.W.3
  • 5
    • 0000551492 scopus 로고    scopus 로고
    • On bias reduction in exponential and non-exponential family regression models
    • Cordeiro GM, Cribari-Neto F. On bias reduction in exponential and non-exponential family regression models. Commun Stat Simul Comput. 1998;27(2):485-500.
    • (1998) Commun Stat Simul Comput. , vol.27 , Issue.2 , pp. 485-500
    • Cordeiro, G.M.1    Cribari-Neto, F.2
  • 6
    • 33845900763 scopus 로고    scopus 로고
    • A comparative investigation of methods for logistic regression with separated or nearly separated data
    • Heinze G. A comparative investigation of methods for logistic regression with separated or nearly separated data. Stat Med. 2006;25(24):4216-4226.
    • (2006) Stat Med. , vol.25 , Issue.24 , pp. 4216-4226
    • Heinze, G.1
  • 7
    • 0002662712 scopus 로고
    • On the existence of maximum likelihood estimates in logistic regression models
    • Albert A, Anderson JA. On the existence of maximum likelihood estimates in logistic regression models. Biometrika. 1984;71(1):1-10.
    • (1984) Biometrika. , vol.71 , Issue.1 , pp. 1-10
    • Albert, A.1    Anderson, J.A.2
  • 8
    • 70449700320 scopus 로고    scopus 로고
    • Convergence problems in logistic regression
    • In: Altman M, Gill G, McDonald MP, eds. Hoboken, NJ: John Wiley & Sons
    • Allison P. Convergence problems in logistic regression. In: Altman M, Gill G, McDonald MP, eds. Numerical Issues in Statistical Computing for the Social Scientist. Hoboken, NJ: John Wiley & Sons; 2004:238-252.
    • (2004) Numerical Issues in Statistical Computing for the Social Scientist , pp. 238-252
    • Allison, P.1
  • 9
    • 0030867224 scopus 로고    scopus 로고
    • Condom use and first time urinary tract infection
    • Foxman B, Marsh J, Gillespie B, et al. Condom use and first time urinary tract infection. Epidemiology. 1997;8(6):637-641.
    • (1997) Epidemiology. , vol.8 , Issue.6 , pp. 637-641
    • Foxman, B.1    Marsh, J.2    Gillespie, B.3
  • 10
    • 76949085987 scopus 로고    scopus 로고
    • Concomitant endothelin-1 overexpression in lung transplant donors and recipients predicts primary graft dysfunction
    • Salama M, Andrukhova O, Hoda MA, et al. Concomitant endothelin-1 overexpression in lung transplant donors and recipients predicts primary graft dysfunction. Am J Transplant. 2010;10(3):628-636.
    • (2010) Am J Transplant. , vol.10 , Issue.3 , pp. 628-636
    • Salama, M.1    Andrukhova, O.2    Hoda, M.A.3
  • 11
    • 14544305522 scopus 로고    scopus 로고
    • A permutation test for inference in logistic regression with small-and moderate-sized data sets
    • Potter DM. A permutation test for inference in logistic regression with small-and moderate-sized data sets. Stat Med. 2005;24(5):693-708.
    • (2005) Stat Med. , vol.24 , Issue.5 , pp. 693-708
    • Potter, D.M.1
  • 12
    • 84891552769 scopus 로고    scopus 로고
    • Maximum likelihood, profile likelihood, and penalized likelihood: A primer
    • Cole SR, Chu HT, Greenland S. Maximum likelihood, profile likelihood, and penalized likelihood: a primer. Am J Epidemiol. 2014;179(2):252-260.
    • (2014) Am J Epidemiol. , vol.179 , Issue.2 , pp. 252-260
    • Cole, S.R.1    Chu, H.T.2    Greenland, S.3
  • 13
    • 0005484509 scopus 로고
    • On the use of Wald's test in exponential-families
    • Vaeth M. On the use of Wald's test in exponential-families. Int Stat Rev. 1985;53(2):199-214.
    • (1985) Int Stat Rev. , vol.53 , Issue.2 , pp. 199-214
    • Vaeth, M.1
  • 14
    • 84964857173 scopus 로고    scopus 로고
    • Sparse data bias: A problem hiding in plain sight
    • Greenland S, Mansournia MA, Altman DG. Sparse data bias: a problem hiding in plain sight. BMJ. 2016;352:i1981.
    • (2016) BMJ. , vol.352 , pp. i1981
    • Greenland, S.1    Mansournia, M.A.2    Altman, D.G.3
  • 16
    • 0037199788 scopus 로고    scopus 로고
    • A solution to the problem of separation in logistic regression
    • Heinze G, Schemper M. A solution to the problem of separation in logistic regression. Stat Med. 2002;21(16): 2409-2419.
    • (2002) Stat Med. , vol.21 , Issue.16 , pp. 2409-2419
    • Heinze, G.1    Schemper, M.2
  • 17
    • 77949375519 scopus 로고    scopus 로고
    • Bias-reduced and separation-proof conditional logistic regression with small or sparse data sets
    • Heinze G, Puhr R. Bias-reduced and separation-proof conditional logistic regression with small or sparse data sets. Stat Med. 2010;29(7-8):770-777.
    • (2010) Stat Med. , vol.29 , Issue.7-8 , pp. 770-777
    • Heinze, G.1    Puhr, R.2
  • 19
    • 71249090906 scopus 로고    scopus 로고
    • Bias reduction in exponential family nonlinear models
    • Kosmidis I, Firth D. Bias reduction in exponential family nonlinear models. Biometrika. 2009;96(4):793-804.
    • (2009) Biometrika. , vol.96 , Issue.4 , pp. 793-804
    • Kosmidis, I.1    Firth, D.2
  • 21
    • 85015204988 scopus 로고    scopus 로고
    • Firth's logistic regression with rare events: Accurate effect estimates and predictions?
    • Puhr R, Heinze G, Nold M, et al. Firth's logistic regression with rare events: accurate effect estimates and predictions? Stat Med. 2017;36(14):2302-2317.
    • (2017) Stat Med , vol.36 , Issue.14 , pp. 2302-2317
    • Puhr, R.1    Heinze, G.2    Nold, M.3
  • 22
    • 85013747969 scopus 로고    scopus 로고
    • Performance of Firth-and logF-type penalized methods in risk prediction for small or sparse binary data
    • Rahman MS, Sultana M. Performance of Firth-and logF-type penalized methods in risk prediction for small or sparse binary data. BMC Med Res Methodol. 2017;17(1):33.
    • (2017) BMC Med Res Methodol. , vol.17 , Issue.1 , pp. 33
    • Rahman, M.S.1    Sultana, M.2
  • 23
    • 79955798239 scopus 로고    scopus 로고
    • Comment on "Bias reduction in conditional logistic regression"
    • Heinze G. Comment on "Bias reduction in conditional logistic regression". Stat Med. 2011;30(12):1466-1467.
    • (2011) Stat Med. , vol.30 , Issue.12 , pp. 1466-1467
    • Heinze, G.1
  • 24
    • 84870028341 scopus 로고    scopus 로고
    • Comment on "A comparative study of the bias corrected estimates in logistic regression"
    • Heinze G. Comment on "A comparative study of the bias corrected estimates in logistic regression". Stat Methods Med Res. 2012;21(6):660-661.
    • (2012) Stat Methods Med Res. , vol.21 , Issue.6 , pp. 660-661
    • Heinze, G.1
  • 25
    • 84865371361 scopus 로고    scopus 로고
    • A weakly informative default prior distribution for logistic and other regression models
    • Gelman A, Jakulin A, Pittau MG, et al. A weakly informative default prior distribution for logistic and other regression models. Ann Appl Stat. 2008;2(4):1360-1383.
    • (2008) Ann Appl Stat. , vol.2 , Issue.4 , pp. 1360-1383
    • Gelman, A.1    Jakulin, A.2    Pittau, M.G.3
  • 26
    • 0037366626 scopus 로고    scopus 로고
    • Generalized conjugate priors for Bayesian analysis of risk and survival regressions
    • Greenland S. Generalized conjugate priors for Bayesian analysis of risk and survival regressions. Biometrics. 2003;59(1):92-99.
    • (2003) Biometrics. , vol.59 , Issue.1 , pp. 92-99
    • Greenland, S.1
  • 27
    • 34447343362 scopus 로고    scopus 로고
    • Bayesian perspectives for epidemiological research. II. Regression analysis
    • Greenland S. Bayesian perspectives for epidemiological research. II. Regression analysis. Int J Epidemiol. 2007;36(1):195-202.
    • (2007) Int J Epidemiol. , vol.36 , Issue.1 , pp. 195-202
    • Greenland, S.1
  • 28
    • 84941024439 scopus 로고    scopus 로고
    • Penalization, bias reduction, and default priors in logistic and related categorical and survival regressions
    • Greenland S, Mansournia MA. Penalization, bias reduction, and default priors in logistic and related categorical and survival regressions. Stat Med. 2015;34(23):3133-3143.
    • (2015) Stat Med. , vol.34 , Issue.23 , pp. 3133-3143
    • Greenland, S.1    Mansournia, M.A.2
  • 29
    • 84875595678 scopus 로고    scopus 로고
    • Bayesian regression in SAS software
    • Sullivan SG, Greenland S. Bayesian regression in SAS software. Int J Epidemiol. 2013;42(1):308-317.
    • (2013) Int J Epidemiol. , vol.42 , Issue.1 , pp. 308-317
    • Sullivan, S.G.1    Greenland, S.2
  • 30
    • 85000991995 scopus 로고    scopus 로고
    • Approximate Bayesian logistic regression via penalized likelihood by data augmentation
    • Discacciati A, Orsini N, Greenland S. Approximate Bayesian logistic regression via penalized likelihood by data augmentation. Stata J. 2015;15(3):712-736.
    • (2015) Stata J. , vol.15 , Issue.3 , pp. 712-736
    • Discacciati, A.1    Orsini, N.2    Greenland, S.3
  • 32
    • 85194972808 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the lasso
    • Tibshirani R. Regression shrinkage and selection via the lasso. J R Stat Soc Series B Stat Methodol. 1996;58(1):267-288.
    • (1996) J R Stat Soc Series B Stat Methodol. , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 34
    • 77950537175 scopus 로고    scopus 로고
    • Regularization paths for generalized linear models via coordinate descent
    • Friedman J, Hastie T, Tibshirani R. Regularization paths for generalized linear models via coordinate descent. J Stat Softw. 2010;33(1):1-22.
    • (2010) J Stat Softw. , vol.33 , Issue.1 , pp. 1-22
    • Friedman, J.1    Hastie, T.2    Tibshirani, R.3
  • 35
    • 0034159815 scopus 로고    scopus 로고
    • Problems due to small samples and sparse data in conditional logistic regression analysis
    • Greenland S, Schwartzbaum JA, Finkle WD. Problems due to small samples and sparse data in conditional logistic regression analysis. Am J Epidemiol. 2000;151(5):531-539.
    • (2000) Am J Epidemiol. , vol.151 , Issue.5 , pp. 531-539
    • Greenland, S.1    Schwartzbaum, J.A.2    Finkle, W.D.3
  • 38
    • 78751611452 scopus 로고    scopus 로고
    • To explain or to predict?
    • Shmueli G. To explain or to predict? Stat Sci. 2010;25(3): 289-310.
    • (2010) Stat Sci , vol.25 , Issue.3 , pp. 289-310
    • Shmueli, G.1
  • 39
    • 0025944012 scopus 로고
    • Standardized regression-coefficients-a further critique and review of some alternatives
    • Greenland S, Maclure M, Schlesselman JJ, et al. Standardized regression-coefficients-a further critique and review of some alternatives. Epidemiology 1991;2(5):387-392.
    • (1991) Epidemiology , vol.2 , Issue.5 , pp. 387-392
    • Greenland, S.1    Maclure, M.2    Schlesselman, J.J.3
  • 40
    • 0022573786 scopus 로고
    • The fallacy of employing standardized regression coefficients and correlations as measures of effect
    • Greenland S, Schlesselman JJ, Criqui MH. The fallacy of employing standardized regression coefficients and correlations as measures of effect. Am J Epidemiol. 1986; 123(2):203-208.
    • (1986) Am J Epidemiol. , vol.123 , Issue.2 , pp. 203-208
    • Greenland, S.1    Schlesselman, J.J.2    Criqui, M.H.3
  • 41
    • 0035099124 scopus 로고    scopus 로고
    • A solution to the problem of monotone likelihood in Cox regression
    • Heinze G, Schemper L. A solution to the problem of monotone likelihood in Cox regression. Biometrics. 2001;57(1):114-119.
    • (2001) Biometrics. , vol.57 , Issue.1 , pp. 114-119
    • Heinze, G.1    Schemper, L.2
  • 42
    • 79960824854 scopus 로고    scopus 로고
    • Poisson: Some convergence issues
    • Santos Silva JMC, Tenreyro S. Poisson: some convergence issues. Stata J. 2011;11(2):207-212.
    • (2011) Stata J. , vol.11 , Issue.2 , pp. 207-212
    • Santos Silva, J.M.C.1    Tenreyro, S.2


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