• Corpus ID: 244909384

Mean and median bias reduction: A concise review and application to adjacent-categories logit models

  title={Mean and median bias reduction: A concise review and application to adjacent-categories logit models},
  author={Ioannis Kosmidis},
The estimation of categorical response models using bias-reducing adjusted score equations has seen extensive theoretical research and applied use. The resulting estimates have been found to have superior frequentist properties to what maximum likelihood generally delivers and to be finite, even in cases where the maximum likelihood estimates are infinite. We briefly review mean and median bias reduction of maximum likelihood estimates via adjusted score equations in an illustration-driven way… 
1 Citations

Figures and Tables from this paper

The Severity of Covid-19 Infection and Vaccine Side Effects among the Saudi Population

There was no significant association between vaccinated and non-vaccinated individuals in terms of reporting COVID-19 severe infection, on the other hand, there were several significant predictors of reporting severe CO VID-19 infection level as number of symptoms, hospitalization, gender, marital status, and education attainment.



Mean and median bias reduction in generalized linear models

The estimates coming out from mean and median bias reduction are found to overcome practical issues related to infinite estimates that can occur with positive probability in generalized linear models with multinomial or discrete responses, and can result in valid inferences even in the presence of a high-dimensional nuisance parameter.

Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models

Penalization of the likelihood by Jeffreys’ invariant prior, or a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial

Median bias reduction in cumulative link models

This paper presents a novel estimation approach for cumulative link models, based on median bias reduction as developed in Kenne Pagui et al. (2017). The median bias reduced estimator is obtained as

Median bias reduction of maximum likelihood estimates

For regular parametric problems, we show how median centering of the maximum likelihood estimate can be achieved by a simple modification of the score equation. For a scalar parameter of interest,

Bias reduction in exponential family nonlinear models

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

A solution to the problem of separation in logistic regression

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.

Partial Proportional Odds Models for Ordinal Response Variables

SUMMARY The ordinal logistic regression model that McCullagh calls the proportional odds model is extended to models that allow non-proportional odds for a subset of the explanatory variables. The

Ordinal probability effect measures for group comparisons in multinomial cumulative link models

An "ordinal superiority" measure summarizes the probability that an observation from one distribution falls above an independent observation from the other distribution, adjusted for explanatory variables in a model.