Alpha-stable Distribution Based Regression Model For Binary Response Data

Logit model is the most popular binary regression model for modelling binary response data, but when dealing with unbalanced data, logit model will cause link misspecification. Alpha-stable model, a more flexible model, is introduced to fit unbalanced data by setting alpha-stable distribution as the link function. The model contains two shape parameters to detect skewness and fat tails separately, it also has reflection property, which brings abundant shapes in the response curve between the covariates and probabilities. 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 or GEV model in fitting both balanced and unbalanced data. Finally, alpha-stable model is applied in player churn prediction of Massive Multiplayer Online Role-Playing Game (MMORPG), achieved the accuracy as high as of 86%.