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Bias reduction in exponential family nonlinear models

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  • Ioannis Kosmidis
  • David Firth

Abstract

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 generalized linear models the method is equivalent to maximizing a penalized likelihood that is easily implemented via iterative adjustment of the data. Here a more general family of bias-reducing adjustments is developed for a broad class of univariate and multivariate generalized nonlinear models. The resulting formulae for the adjusted score vector are computationally convenient, and in univariate models they directly suggest implementation through an iterative scheme of data adjustment. For generalized linear models a necessary and sufficient condition is given for the existence of a penalized likelihood interpretation of the method. An illustrative application to the Goodman row-column association model shows how the computational simplicity and statistical benefits of bias reduction extend beyond generalized linear models. Copyright 2009, Oxford University Press.

Suggested Citation

  • Ioannis Kosmidis & David Firth, 2009. "Bias reduction in exponential family nonlinear models," Biometrika, Biometrika Trust, vol. 96(4), pages 793-804.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:4:p:793-804
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    File URL: http://hdl.handle.net/10.1093/biomet/asp055
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    4. Kunz, J.S.; & Staub, K.E.; & Winkelmann, R.;, 2018. "Predicting fixed effects in panel probit models," Health, Econometrics and Data Group (HEDG) Working Papers 18/23, HEDG, c/o Department of Economics, University of York.
    5. Johannes S. Kunz & Kevin E. Staub & Rainer Winkelmann, 2021. "Predicting individual effects in fixed effects panel probit models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 1109-1145, July.
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    8. Tariq Maqsood & Mark Edwards & Ioanna Ioannou & Ioannis Kosmidis & Tiziana Rossetto & Neil Corby, 2016. "Seismic vulnerability functions for Australian buildings by using GEM empirical vulnerability assessment guidelines," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 80(3), pages 1625-1650, February.
    9. Mani Suleiman & Haydar Demirhan & Leanne Boyd & Federico Girosi & Vural Aksakalli, 2019. "Bayesian logistic regression approaches to predict incorrect DRG assignment," Health Care Management Science, Springer, vol. 22(2), pages 364-375, June.
    10. Yiyun Shou & Michael Smithson, 2015. "Evaluating Predictors of Dispersion: A Comparison of Dominance Analysis and Bayesian Model Averaging," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 236-256, March.
    11. Nicole Black & Johannes S. Kunz, 2019. "The Intergenerational Effects of Language Proficiency on Child Health Outcomes," Monash Economics Working Papers 05-19, Monash University, Department of Economics.
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    13. Buchmueller, Thomas C. & Cheng, Terence C. & Pham, Ngoc T.A. & Staub, Kevin E., 2021. "The effect of income-based mandates on the demand for private hospital insurance and its dynamics," Journal of Health Economics, Elsevier, vol. 75(C).
    14. Johannes S. Kunz & Carol Propper & Kevin E. Staub & Rainer Winkelmann, 2024. "Assessing the quality of public services: For‐profits, chains, and concentration in the hospital market," Health Economics, John Wiley & Sons, Ltd., vol. 33(9), pages 2162-2181, September.
    15. Patrick O. Perry, 2017. "Fast moment-based estimation for hierarchical models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 267-291, January.
    16. Woods, David C. & McGree, James M. & Lewis, Susan M., 2017. "Model selection via Bayesian information capacity designs for generalised linear models," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 226-238.
    17. Michela Battauz & Ruggero Bellio, 2011. "Structural Modeling of Measurement Error in Generalized Linear Models with Rasch Measures as Covariates," Psychometrika, Springer;The Psychometric Society, vol. 76(1), pages 40-56, January.
    18. Yee, Thomas W., 2010. "The VGAM Package for Categorical Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i10).
    19. Tariq Maqsood & Mark Edwards & Ioanna Ioannou & Ioannis Kosmidis & Tiziana Rossetto & Neil Corby, 2016. "Seismic vulnerability functions for Australian buildings by using GEM empirical vulnerability assessment guidelines," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 80(3), pages 1625-1650, February.
    20. Propper, Carol & Kunz, Johannes & Staub, Kevin & Winkelmann, Rainer, 2020. "Assessing the Quality of Public Services: Does Hospital Competition Crowd Out the For-Profit Quality Gap?," CEPR Discussion Papers 15045, C.E.P.R. Discussion Papers.
    21. Oscar Melo & Carlos Melo & Jorge Mateu, 2015. "Distance-based beta regression for prediction of mutual funds," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 83-106, January.
    22. Veflen, Nina & Scholderer, Joachim & Elvekrok, Ingunn, 2019. "Composition of Collaborative Innovation Networks: An Investigation of Process Characteristics and Outcomes," International Journal on Food System Dynamics, International Center for Management, Communication, and Research, vol. 10(1), January.
    23. Rahmouni, Mohieddine, 2023. "Corruption and corporate innovation in Tunisia during an economic downturn," Structural Change and Economic Dynamics, Elsevier, vol. 66(C), pages 314-326.

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