2009
DOI: 10.1093/biomet/asp055
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Bias reduction in exponential family nonlinear models

Abstract: In Firth (1993, Biometrika) it was shown how the leading term in the asymptotic bias of the maximum likelihood estimator is removed by adjusting the score vector, and that in canonical-link generalized linear models the method is equivalent to maximizing a penalized likelihood which is easily implemented via iterative adjustment of the data. Here a more general family of bias-reducing adjustments is developed, for a broad class of univariate and multivariate generalized nonlinear models. The resulting formula… Show more

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Cited by 157 publications
(221 citation statements)
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“…Regression analyses were performed using the brglm package (Kosmidis 2013), which addresses issues of near perfect separation in logistic regressions (i.e., when there is perfect correspondence of the response variable for most values of the predictors, but not for all) (Heinze and Schemper 2002). All statistical analyses were performed in R (R Development Core Team 2015).…”
Section: Discussionmentioning
confidence: 99%
“…Regression analyses were performed using the brglm package (Kosmidis 2013), which addresses issues of near perfect separation in logistic regressions (i.e., when there is perfect correspondence of the response variable for most values of the predictors, but not for all) (Heinze and Schemper 2002). All statistical analyses were performed in R (R Development Core Team 2015).…”
Section: Discussionmentioning
confidence: 99%
“…This can potentially have a big impact on the reported significance of the explanatory variables. In order to get more realistic estimates of the standard errors of the model parameters, we use the bias reduction method that is supplied in the 'betareg' package (Firth 1993;Kosmidis and Firth 2009).…”
Section: Statistical Model Fitting Techniquementioning
confidence: 99%
“…Hence, expression (13) in Kosmidis & Firth (2009) gives that the bias-reducing adjusted score equations using adjustments based on the expected information matrix take the form…”
Section: Bias Reduction Via the Log-linear Modelmentioning
confidence: 99%