Alpha-Stable Distribution Based Regression for Binary Response Data

Logit model is the most popular binary regression models for modelling binary response data.When dealing with unbalanced data,Logit model will cause link misspecification.A more flexible model of alpha-stable model,is introduced to fit unbalanced data by setting alpha-stable distribution as the link function.For model estimation,since alpha-stable distribution admits no closed-form expression for the density,we employ expectation propagation with approximate Bayesian computation (EP-ABC) algorithm.It overcomes the difficulties that high dimensionality results in low acceptance rate through data partitioning.According to the simulation results,alpha-stable model performs better than Logit,Probit,Cloglog or GEV model in fitting both balanced and unbalanced data.