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Properties of the Maximum Likelihood Estimates and Bias Reduction for Logistic Regression Model

DOI: 10.4236/oalib.1103625, PP. 1-12

Subject Areas: Applied Statistical Mathematics

Keywords: Logistic Regression Model, Maximum Likelihood Method, Convergence Problems, Bias Reduction Technique

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Abstract

A frequent problem in estimating logistic regression models is a failure of the likelihood maximization algorithm to converge. Although popular and extremely well established in bias correction for maximum likelihood estimates of the parameters for logistic regression, the behaviour and properties of the maximum likelihood method are less investigated. The main aim of this paper is to examine the behaviour and properties of the parameters estimates methods with reduction technique. We will focus on a method used a modified score function to reduce the bias of the maximum likelihood estimates. We also present new and interesting examples by simulation data with different cases of sample size and percentage of the probability of outcome variable.

Cite this paper

Badi, N. H. S. (2017). Properties of the Maximum Likelihood Estimates and Bias Reduction for Logistic Regression Model. Open Access Library Journal, 4, e3625. doi: http://dx.doi.org/10.4236/oalib.1103625.

References

[1]  Cox, D.R. and Hinkley, D.V. (1974) Theoretical Statistics. Chapman and Hall, London.
[2]  Firth, D. (1993) Bias Reduction of Maximum Likelihood Estimates. Biometrika, 80, 27-38.
https://doi.org/10.1093/biomet/80.1.27
[3]  Anderson, J.A. and Richardson, C. (1979) Logistic Discrimination and Bias Correction in Maximum Likelihood Estimation. Technometrics, 21, 71-78.
[4]  McCullagh, P. (1986) The Conditional Distribution of Goodness-of-Fit Statistics for Discrete Data. Journal of the American Statistical Association, 81, 104-107.
https://doi.org/10.1080/01621459.1986.10478244
[5]  Shenton, L.R. and Bowman, K.O. (1977) Maximum Likelihood Estimation in Small Samples. Griffins Statistical Monograph No. 38, London.
[6]  Nelder, J.A. and Wedderburn, R.W.M. (1972) Generalized Linear Models. Journal of the Royal Statistical Society, Series A, 135, 370-384.
https://doi.org/10.2307/2344614
[7]  Dobson, A. (1990) An Introduction to Generalized Linear Models. Chapman and Hall, London.
[8]  Dobson, A.J. and Barnett, A.G. (2008) An Introduction to Generalized Linear Models. 3rd Edition, Chapman and Hall, New York.
[9]  Kleinbaum, D.G. (1994) Logistic Regression: A Self-Learning Text. Springer-Verlag, New York.
https://doi.org/10.1007/978-1-4757-4108-7
[10]  Hilbe, J.M. (2009) Logistic Regression Model. Chapman and Hall, New York.
[11]  Hosmer, D.W. and Lemeshow, S. (2000) Applied Logistic Regression. Wiley, Chi- chester.
https://doi.org/10.1002/0471722146
[12]  Hosmer, D., Lemeshow, S. and Sturdivant, R.X. (2013) Applied Logistic Regression. 3rd Edition, Wiley, Chichester.
https://doi.org/10.1002/9781118548387
[13]  Quenouille, M.H. (1949) Approximate Tests of Correlation in Time-Series. Journal of the Royal Statistical Society: Series B, 11, 68-84.
[14]  Quenouille, M.H. (1956) Notes on Bias in Estimation. Biometrika, 43, 353-360.
https://doi.org/10.1093/biomet/43.3-4.353
[15]  Albert, A. and Anderson, J.A. (1984) On the Existence of Maximum Likelihood Estimates in Logistic Regression Models. Biometrika, 71, 1-10.
https://doi.org/10.1093/biomet/71.1.1
[16]  Clogg, C.C., Rubin, D.B., Schenker, N., Schultz, B. and Weidman, L. (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.
https://doi.org/10.1080/01621459.1991.10475005
[17]  McCullagh, P. and Nelder, J.A. (1989) Linear Models. 2nd Edition, Chapman and Hall, London.

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