Kosmidis, Ioannis (2009) On iterative adjustment of responses for the reduction of bias in binary regression models. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

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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
Date:	2009
Volume:	Vol.2009
Number:	No.36
Number of Pages:	8
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
References:	Agresti, A. (2002). Categorical Data Analysis. New York: Wiley. Anscombe (1956). On estimating binomial response relations. Biometrika 43 (3), 461{464. Clogg, C. C., D. B. Rubin, N. Schenker, B. Schultz, and L. Weidman (1991). Multiple imputation of industry and occupation codes in census public-use samples using Bayesian logistic regression. Journal of the American Statistical Association 86, 68{78. Cordeiro, G. M. and P. McCullagh (1991). Bias correction in generalized linear models. Journal of the Royal Statistical Society, Series B: Methodological 53 (3), 629{643. Firth, D. (1993). Bias reduction of maximum likelihood estimates. Biometrika 80 (1), 27{38. Gart, J. J., H. M. Pettigrew, and D. G. Thomas (1985). The e�ect of bias, variance estimation, skewness and kurtosis of the empirical logit on weighted least squares analyses. Biometrika 72, 179{190. Gart, J. J. and J. R. Zweifel (1967, June). On the bias of various estimators of the logit and its variance with application to quantal bioassay. Biometrika 54 (1), 181{187. Haldane, J. (1955). The estimation of the logarithm of a ratio of frequencies. Annals of Human Genetics 20, 309{311. Heinze, G. and M. Schemper (2002). A solution to the problem of separation in logistic regression. Statistics in Medicine 21, 2409{2419. Hitchcock, S. E. (1962, June). A note on the estimation of parameters of the logistic function using the minimum logit �2 method. Biometrika 49 (1), 250{252. Kosmidis, I. and D. Firth (2008). Bias reduction in exponential family non-linear models. Technical Report 8-5, CRiSM working paper series, University of Warwick. Rubin, D. B. and N. Schenker (1987). Logit-based interval estimation for binomial data using the Je�reys prior. Sociological Methodology 17, 131{144.
URI:	http://wrap.warwick.ac.uk/id/eprint/35223

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