基于Alpha稳定分布的二元响应变量回归模型

Alpha-Stable Distribution Based Regression for Binary Response Data

Logit模型是常用的针对二元响应变量的回归模型,当0-1响应变量不平衡时,Logit模型将会带来连接函数设定错误。为了更灵活地捕捉带偏和厚尾特征,提出了以Alpha稳定分布作为连接函数的二元响应变量回归模型,称之为稳定分布模型。借助期望传播-近似贝叶斯计算(EPABC)方法,克服了Alpha稳定分布由于没有概率密度函数解析表达式所带来的困难,同时也解决了高维运算所导致的低接收率的问题。结果表明该模型对平衡或不平衡二元响应变量数据拟合和预测的效果均明显优于Logit、Probit、Cloglog和GEV模型。

Logi t model is the most popular binary regression models for model ling 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 dimensional ity 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.