Kosmidis, Ioannis (2009) On iterative adjustment of responses for the reduction of bias in binary regression models. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2009 (No.36).

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Abstract

The adjustment of the binomial data by small constants is a common practice in statistical
modelling, for avoiding sparseness issues and, historically, for improving the asymptotic properties
of the estimators. However, there are two main disadvantages with such practice: i) there
is not a universal constant adjustment that results estimators with optimal asymptotic properties
for all possible modelling settings, and ii) the resultant estimators are not invariant to the
representation of the binomial data. In the current work, we present a parameter-dependent
adjustment scheme which is applicable to binomial-response generalized linear models with arbitrary
link functions. The adjustment scheme results by the expressions for the bias-reducing
adjusted score functions in Kosmidis & Firth (2008, Biometrika) and thus its use guarantees
estimators with second-order bias. Based on an appropriate expression of the adjusted data,
a procedure for obtaining the bias-reduced estimates is developed which relies on the iterative
adjustment of the binomial responses and totals using existing maximum likelihood implementations.
Furthermore, it is shown that the bias-reduced estimator, like the maximum likelihood
estimator, is invariant to the representation of the binomial data. A complete enumeration
study is used to demonstrate the superior statistical properties of the bias-reduced estimator to
the maximum likelihood estimator.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Regression analysis, Mathematical models
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Official Date:	2009
Dates:	Date Event 2009 Published
Volume:	Vol.2009
Number:	No.36
Number of Pages:	8
Institution:	University of Warwick
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access

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