A solution to the problem of separation in logistic regression

By Georg Heinze, M. Schemper. Statistics in Medicine, 2002

2,231 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/026f454047484c20cf0ad382e897a7a9eb06f8b7

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Citations in the corpus

Multinomial logit bias reduction via the Poisson log-linear model (2011, methodology): “…penalty to remove the O(n−1) asymptotic bias of the maximum likelihood estimator in full exponential family models was developed in Firth (1993) and has been found to be particularly effective in binomial and multinomial logistic regressions (e.g., Heinze & Schemper, 2002; Bull et al., 2002, 2007).”
L1‐regularization path algorithm for generalized linear models (2007, methodology): “As an alternative solution to the separation in logistic regression, one can apply the Jeffreys prior to the likelihood function as suggested in Firth (1993) and further demonstrated in Heinze and Schemper (2002).”
Restoring forest herb communities through landscape-level deer herd reductions: Is recovery limited by legacy effects? (2010, methodology): “For F. americana and P. serotina, maximum likelihood estimation was not feasible due to quasi-complete separation (i.e., in the year browse category table, all individuals in 2007 are unbrowsed); thus we employed penalized maximum likelihood methods (see Heinze and Schemper, 2002).”
Sample size for binary logistic prediction models: Beyond events per variable criteria (2018, background): “As a consequence of its penalty function, the regression coefficients remain finite in situations of separation (issue 3).(38) More recently, Puhr and colleagues(21) evaluated the Firth’s estimator for improving predictive performance (issue 1), warning that it introduced bias in predicted probabili”
Firth's logistic regression with rare events: accurate effect estimates and predictions? (2017, methodology): “Similarly as for Firth’s logistic regression, we suggest the use of profile (penalized) likelihood confidence intervals (CIs) for the coefficients estimated by FLIC except for the intercept [2].”
Bias in parametric estimation: reduction and useful side‐effects (2013, methodology): “ Albert and Anderson, 1984, for conditions that characterize when inﬁnite estimates occur in multinomial response models) and have been the subject of study in works like Mehrabi and Matthews (1995), Heinze and Schemper (2002), Bull et al. (2002), Kosmidis and Firth (2009), Kosmidis and Firth (2011)”
Developmental evidence for foraging traditions in wild bottlenose dolphins (2009, methodology): “…of complete separation (where explanatory variable(s) completely separate the response into yes or no), which was common in our data sets; and (2) it is appropriate for very small data sets in which the number of parameters is large relative to the sample size (Heinze & Schemper 2002; Heinze 2006).”
Bias reduction in exponential family nonlinear models (2009, positive): “1 Introduction Bias correction in logistic regression has attracted the attention of many authors, for example Anderson & Richardson (1979), Schaefer (1983), Copas (1988), Cordeiro & McCullagh (1991) and other references therein.”
On the Use of Cauchy Prior Distributions for Bayesian Logistic Regression (2015, background): “In the frequentist literature, various solutions based on penalized or modified likelihoods have been proposed to obtain finite parameter estimates (Firth, 1993; Heinze and Schemper, 2002; Heinze, 2006; Rousseeuw and Christmann, 2003).”