Journal ArticleDOI
A solution to the problem of separation in logistic regression
Georg Heinze,Michael Schemper +1 more
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A procedure by Firth originally developed to reduce the bias of maximum likelihood estimates is shown to provide an ideal solution to separation and produces finite parameter estimates by means of penalized maximum likelihood estimation.Abstract:
The phenomenon of separation or monotone likelihood is observed in the fitting process of a logistic model if the likelihood converges while at least one parameter estimate diverges to +/- infinity. Separation primarily occurs in small samples with several unbalanced and highly predictive risk factors. A procedure by Firth originally developed to reduce the bias of maximum likelihood estimates is shown to provide an ideal solution to separation. It produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald tests and confidence intervals are available but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. The clear advantage of the procedure over previous options of analysis is impressively demonstrated by the statistical analysis of two cancer studies.read more
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References
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Journal ArticleDOI
Computing Extended Maximum Likelihood Estimates for Linear Parameter Models
Journal ArticleDOI
Infinite Parameter Estimates in Logistic Regression, with Application to Approximate Conditional Inference
TL;DR: In this article, the authors discuss recovery of information regarding logistic regression parameters in cases when maximum likelihood estimates of some parameters are infinite and present an algorithm for detecting such cases and characterizing the divergence of the parameter estimates.
Book ChapterDOI
Generalized Linear Models and Jeffreys Priors: An Iterative Weighted Least-Squares Approach
TL;DR: A new algorithm for calculation of the posterior mode of the Jeffreys invariant prior in generalized linear models makes use of the iterative weighted least-squares method commonly used for maximum likelihood calculations, so that implementation is possible in standard regression software, such as GLIM.
The application of Firth's procedure to Cox and logistic regression
TL;DR: In this paper, the authors present the results of an extensive simulation study exploring the properties of Firth's procedure in logistic and Cox regression, and the empirical bias of parameter estimates obtained by Firth-type parameter estimates is compared to that resulting from ordinary maximum likelihood estimation in logistically and Cox regressions.
Journal ArticleDOI
Jackknife bias reduction for polychotomous logistic regression.
TL;DR: A Monte Carlo comparison of the jackknife and Taylor series estimates in moderate sample sizes in a general logistic regression setting, to investigate dichotomous and trichotomous responses and a mixture of correlated and uncorrelated binary and normal covariates.