A Bayesian dichotomous model with asymmetric link for fraud in insurance

Standard binary models have been developed to describe the behavior of consumers when they are faced with two choices. The classical logit model presents the feature of the symmetric link function. However, symmetric links do not provide good fits for data where one response is much more frequent than the other (as it happens in the insurance fraud context). In this paper, we use an asymmetric or skewed logit link, proposed by Chen et al. [Chen, M., Dey, D., Shao, Q., 1999. A new skewed link model for dichotomous quantal response data. J. Amer. Statist. Assoc. 94 (448), 1172-1186], to fit a fraud database from the Spanish insurance market. Bayesian analysis of this model is developed by using data augmentation and Gibbs sampling. The results show that the use of an asymmetric link notably improves the percentage of cases that are correctly classified after the model estimation.