Profile Likelihood Confidence Interval for the Probability of a Success in the Firth’s Logistic Regression

Kamil Fijorek

doi:https://doi.org/10.59139/ps.2012.04.1

Kamil Fijorek Uniwersytet Ekonomiczny w Krakowie Przegląd Statystyczny. Statistical Review, vol. 59, 2012, 4, pages: 355-368 Published online: 31 December 2012 DOI https://doi.org/10.59139/ps.2012.04.1

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ARTICLE

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ABSTRACT

In the first part of the paper the results of the simulation study, comparing the coverage properties of Wald’s and the profile likelihood confidence intervals for the probability of a success in the Firth’s logistic regression, are described. The efficient algorithm for computing profile likelihood confidence intervals is proposed. In the second part of the paper the theoretical results are applied to the bankruptcy model.

KEYWORDS

logistic regression, confidence intervals, profile likelihood

REFERENCES

[1] DiCiccio T., Tibshirani R., (1991), Technical Report No. 9107: On the Implementation of Profile Likelihood, Department of Statistics, University of Toronto.

[2] Fijorek K., Fijorek D., (2011), Dobór zmiennych objasniajacych metoda najlepszego podzbioru do modelu regresji logistycznej Firtha, Metody Informatyki Stosowanej, 2, 15-23.

[3] Fijorek K., Fijorek D., Wisniowska B., Polak S., (2011), BDTcomparator: A Program for Comparing Binary Classifiers, Bioinformatics, 27 (24), 3439-3440.

[4] Fijorek K., Grotowski M., (2012), Bankruptcy Prediction: Some Results From a Large Sample of Polish Companies, International Business Research, 5 (9).

[5] Fijorek K., Sokołowski A., (2012), Separation-Resistant and Bias-Reduced Logistic Regression: STATISTICA macro, Journal of Statistical Software, 47, 1-12.

[6] Firth D., (1993), Bias Reduction of Maximum Likelihood Estimates, Biometrika, 80, 27-38.

[7] Heinze G., (1999), Technical Report 10: The Application of Firth’s Procedure to Cox and Logistic Regression, Department of Medical Computer Sciences, Section of Clinical Biometrics, Vienna University, Vienna.

[8] Heinze G., (2006), A Comparative Investigation of Methods for Logistic Regression with Separated or Nearly Separated Data, Statistics in Medicine, 25, 4216-4226.

[9] Heinze G., Ploner M., (2004), Technical Report 2/2004: A SAS Macro, S-PLUS Library and R Package to Perform Logistic Regression without Convergence Problems, Section of Clinical Biometrics, Department of Medical Computer Sciences, Medical University of Vienna, Vienna.

[10] Heinze G., Schemper M., (2002), A Solution to the Problem of Separation in Logistic Regression, Statistics in Medicine, 21, 2409-2419.

[11] Hosmer D.W., Lemeshow S., (1989), Applied Logistic Regression, Wiley, New York.

[12] Long J.S., (1997), Regression Models for Categorical and Limited Dependent Variables, SAGE.

[13] R Development Core Team, (2011), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, ISBN 3-900051-07-0, http://www.Rproject.org.

[14] Stryhn H., Christensen J., (2003), Confidence Intervals by the Profile Likelihood Method, with Applications in Veterinary Epidemiology, ISVEE X, Chile.

[15] Venzon D.J., Moolgavkar S.H., (1988), A Method for Computing Profile-Likelihood Based Confidence Intervals, Applied Statistics, 37, 87-94.