Firth's Logistic Regression Approximation by Weighting Observations
DOI:
https://doi.org/10.15678/ZNUEK.2013.0923.07Keywords:
logistic regression, bias reduction, complete separation, approximate estimationAbstract
Firth's approach to a logistic regression is presented from the perspective of weighted data points. Hidden Logistic Model is reformulated accordingly and two approximations of Firth's procedure are introduced. A simulation study was conducted to investigate and compare the quality of the approximations.
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References
Albert A., Anderson J.A. [1984], On the Existence of Maximum Likelihood Estimates in Logistic Regression Models, „Biometrika", vol. 71.
Cordeiro G., Barroso L. [2007], A Third-order Bias Corrected Estimate in Generalized Linear Models, „Test", vol. 16, nr 1.
Fijorek K. [2012], Porównanie modeli regresji logistycznej odpornych na problem całkowitego rozdzielenia, Zeszyty Naukowe Uniwersytetu Ekonomicznego w Krakowie, nr 884, Kraków.
Finney D.J. [1947], The Estimation from Individual Records of the Relationship between Dose and Quantal Response, „Biometrika", vol. 34.
Firth D. [1993], Bias Reduction of Maximum Likelihood Estimates, „Biometrika", vol. 80.
Greene W.H. [2003], Econometric Analysis, Pearson Education, New Jersey.
Heinze G. [1999], The Application of Firth's Procedure to Cox and Logistic Regression, Technical Report 10, Department of Medical Computer Sciences, Section of Clinical Biometrics, Vienna University, Vienna.
Heinze G. [2006], A Comparative Investigation of Methods for Logistic Regression with Separated or Nearly Separated Data, „Statistics in Medicine", vol. 25.
Heinze G., Ploner M. [2004], A SAS Macro, S-PLUS Library and R Package to Perform Logistic Regression without Convergence Problems, Technical Report 2, Section of Clinical Biometrics, Department of Medical Computer Sciences, Medical University of Vienna, Vienna.
Heinze G., Schemper M. [2002], A Solution to the Problem of Separation in Logistic Regression, „Statistics in Medicine", vol. 21.
Hosmer D.W., Lemeshow S. [2000], Applied Logistic Regression, John Wiley and Sons.
Long J.S. [1997], Regression Models for Categorical and Limited Dependent Variables, Sage, Thousand Oaks.
R Development Core Team. R: A Language and Environment for Statistical Computing [2010], R Foundation for Statistical Computing, Vienna.
Rousseeuw P.J., Christmann A. [2003], Robustness against Separation and Outliers in Logistic Regression, „Computational Statistics and Data Analysis", vol. 43.
Tutz G., Leitenstorfer F. [2006], Response Shrinkage Estimators in Binary Regression, „Computational Statistics and Data Analysis", vol. 50.
