基于选择抽样下的Logistic回归

Logistic Regression in Choice-based Samples

传统的Logistic回归参数估计(如极大似然估计)是在随机抽样的假设下做出的.但是,在基于选择(Choice-based)抽样条件下,传统的回归系数估计是有偏的.本文利用随机模拟的方法,比较了Logistic回归参数估计的3种方法,即先验概率法、加权法和传统的极大似然估计法,并列举了两种修改Logistic回归参数估计的方法.

The traditional parameters estimation （maximum likelihood estimation for example） of logistic regression is based on mode-based inference which involves some hypotheses including infinite population, correct mode specification, etc. Under these hypotheses, if the sample is choicebased, the intercept is the only parameter estimate affected by a sample design that depends on the response variables, if these hypotheses are not satisfied as is often the case in practice, the inference method should be design-based. In this case, all the maximum likelihood estimations of logistic coefficients are biased if the sample is choice-based. The paper presents two methods to fit the logistic regression in choice-based samples and compares their effects on the computer.