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

12/05/2021
by   Ioannis Kosmidis, et al.
0

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, and discuss their particular equivariance properties under parameter transformations. We then apply mean and median bias reduction to adjacent-categories logit models for ordinal responses. We show how ready bias reduction procedures for Poisson log-linear models can be used for mean and median bias reduction in adjacent-categories logit models with proportional odds and mean bias-reduced estimation in models with non-proportional odds. As in binomial logistic regression, the reduced-bias estimates are found to be finite even in cases where the maximum likelihood estimates are infinite. We also use the approximation of the bias of transformations of mean bias-reduced estimators to correct for the mean bias of model-based ordinal superiority measures. All developments are motivated and illustrated using real-data case studies and simulations

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/11/2018

Mean and median bias reduction in generalized linear models

This paper presents an integrated framework for estimation and inference...
research
11/05/2020

Accurate inference in negative binomial regression

Negative binomial regression is commonly employed to analyze overdispers...
research
01/18/2021

Bias Reduction as a Remedy to the Consequences of Infinite Estimates in Poisson and Tobit Regression

Data separation is a well-studied phenomenon that can cause problems in ...
research
07/14/2023

Bounded-memory adjusted scores estimation in generalized linear models with large data sets

The widespread use of maximum Jeffreys'-prior penalized likelihood in bi...
research
05/27/2020

Median bias reduction in cumulative link models

This paper presents a novel estimation approach for cumulative link mode...
research
12/14/2018

Conditional bias reduction can be dangerous: a key example from sequential analysis

We present a key example from sequential analysis, which illustrates tha...
research
04/18/2020

Efficient implementation of median bias reduction

In numerous regular statistical models, median bias reduction (Kenne Pag...

Please sign up or login with your details

Forgot password? Click here to reset