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

@inproceedings{Kosmidis2021MeanAM, title={Mean and median bias reduction: A concise review and application to adjacent-categories logit models}, author={Ioannis Kosmidis}, year={2021} }

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…

## One Citation

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

- MedicineInternational Journal of Life Science and Pharma Research
- 2022

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.

## References

SHOWING 1-10 OF 44 REFERENCES

### Mean and median bias reduction in generalized linear models

- MathematicsStat. Comput.
- 2020

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.

### Reducing Bias and Mean Squared Error Associated With Regression-Based Odds Ratio Estimators.

- MathematicsJournal of statistical planning and inference
- 2012

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

- MathematicsBiometrika
- 2020

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

- Mathematics
- 2020

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

- Mathematics
- 2016

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

- Mathematics
- 2009

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 modified score function estimator for multinomial logistic regression in small samples

- Mathematics
- 2002

### A solution to the problem of separation in logistic regression

- MathematicsStatistics in medicine
- 2002

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

- Mathematics
- 1986

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

- MathematicsBiometrics
- 2017

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.