Power and reversal power links for binary regressions

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  • Author: J.L. Bazán, F. Torres-Avilés, A.K. Suzuki and F. Louzada
  • Date: 12 January 2018

Authors of a recent article published in Applied Stochastic Models in Business and Industry discuss how, in binary regression, symmetric links such as logit and probit are usually considered as standard. However, in the presence of unbalancing of ones and zeros, these links can be inappropriate and inflexible to fit the skewness in the response curve and likely to lead to misspecification. This is the case of covering some type of insurance, where it can be observed that the probability of a given binary response variable approaches zero at different rates than it approaches one. Furthermore, when usual links are considered, there is not a skewness parameter associated with the distribution chosen that, regardless of the linear predictor, is easily interpreted. In order to overcome such problems, a proposal for the construction of a set of new skew links is developed in this paper, where some of their properties are discussed. In this context, power links and their reversal versions are presented.

Power and reversal power links for binary regressions: An application for motor insurance policyholders

J.L. Bazán, F. Torres-Avilés, A.K. Suzuki and F. Louzada

Applied Stochastic Models in Business and Industry, Volume 33, Issue 1, pages 22–34, January/February 2017

DOI: 10.1002/asmb.2215

The article is available to view for free and the authors explain their findings further below.

thumbnail image: Power and reversal power links for binary regressions

Unbalanced binary response are commonly observed in financial and insurance data, such as good or bad credit borrowers, use or no use of a motor insurance, fraudulent or legitimate operations and so on. In this cases, a higher or lower proportion of success is modelled by using binary regression models with symmetric links, these procedures are standard and can be performed by using software. However they can be inadequate in the case of great unbalances.

We overcome such a problem by introducing a set of new skew links, using power and reversal versions of symmetric links. A direct advantage is to have a skewness parameter associated with the chosen distribution, which is easily interpreted as a penalty or a bonus parameter. Some properties of the new links are discussed. A Bayesian inference estimation method is developed for the presented models by using the SAS software. The methodology is illustrated on a sample of motor insurance policyholders, selected randomly by gender. Results suggest that the proposed link functions are more appropriate than other alternative link functions commonly used in the literature.

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