Abstract
Common binary regression models such as logistic or probit regression have been extended to include parametric link transformation families. These binary regression models with parametric link are designed to avoid possible link misspecification and improve fit in some data sets. One and two parameter link families have been proposed in the literature (for a review see Stukel (1988)). However in real data examples published so far only one parameter link families have found to improve the fit significantly. This paper introduces a two parameter link family involving the modification of both tails of the link. An analysis based on computationally tractable Bayesian inference involving Monte Carlo sampling algorithms is presented extending earlier work of Czado (1992, 1993b). Finally, the usefulness of the two tailed link modification will be demonstrated in an example where single tail modification can be significantly improved upon by using a two tailed modification.
Similar content being viewed by others
References
Albert, J. and Chib, S. (1993) Bayesian Analysis of Binary and Polytomous Response Data.J. Amer. Statist. Assoc. 88 669–679.
Cox, D.R. and Reid, N. (1987). Parameter Orthogonality and Approximate Conditional Inference.J. Roy. Statist. Soc. (B) 49 1–39.
Collett, D. (1991)Modelling Binary Data. Chapman and Hall, London.
Czado, C. (1992) On Link Selection in Generalized Linear Models, inAdvances in GLIM and Statistical Modelling, Proceedings of the GLIM92 conference and the 7th International Workshop on Statistical Modelling, Munich, 13–17 July, 1992, L. Fahrmeir, B. Francis, R. Gilchrist, G. Tutz (eds), 60–65, Lecture Notes in Statistics78, Springer Verlag, New York.
Czado, C. (1993b) Norm Restricted Maximum Likelihood Estimators for Binary Regression Models with Parametric Link.Comm. Statist.—Theor. Meth. 22, No. 8, 2259–2274.
Czado, C. (1993b) Bayesian Inference of Binary Regression Models with Parametric Link. to appear inJ. Statist. Plann. Inf..
Czado, C. and Santner, T. J. (1992a) The Effect of Link Misspecification on Binary Regression Analysis.J. Statist. Plann. Inf. 33, 213–231.
Czado, C. and Santner, T. J. (1992b). Orthogonalizing Link Transformation Families in Binary Regression Analysis.Canad. J. Statist. 20, No. 1, 51–62.
Duffy, D. E. and Santner, T. J. (1988). Estimating logistic regression probabilities, inStatistical Decision Theory and Related Topics IV 1, S. S. Gupta, J. O. Berger (eds), 177–195, Springer Verlag, New York
Duffy, D. E. and Santner, T. J. (1989). On the small sample properties of restricted maximum likelihood estimators for logistic regression models.Comm. Statist.-Theor. Meth. 18, 959–989.
Gelfand, A.E. and Smith, A.F.M. (1990) Sampling based approaches to calculating marginal densities.J. Amer. Statist. Assoc. 85, 398–409.
Härdle, W. K. and Turlach, B. A. (1992). Nonparametric Approaches to Generalized Linear Models inAdvances in GLIM and Statistical Modelling, Proceedings of the GLIM92 conference and the 7th International Workshop on Statistical Modelling, Munich, 13–17 July, 1992, L. Fahrmeir, B. Francis, R. Gilchrist, G. Tutz (eds), 213–225, Lecture Notes in Statistics78, Springer Verlag, New York.
Newton, M.A., Czado, C. and Chappell, R. (1993) Semiparametric Bayesian Inference for Binary Regression. submitted.
Stukel, T. (1988). Generalized Logistic Models.J. Amer. Statist. Assoc. 83 426–431.
Tanner, T.A. and Wong W.H. (1987) The calculation of posterior distributions by data augmentation.J. Amer. Statist. Assoc. 82, 528–549.
Tierney, L. (1991) Markov Chains for Exploring Posterior DistributionsTechnical Report No. 560, School of Statistics, University of Minnesota.
Zeger, S.L. and Karim, M.R. (1991) Generalized linear models with random effects: A Gibb's sampling approach.J. Amer. Statist. Assoc. 86, 79–86.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Czado, C. Parametric link modification of both tails in binary regression. Statistical Papers 35, 189–201 (1994). https://doi.org/10.1007/BF02926413
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02926413