Logistic回归模型的统计诊断

统计诊断的主要任务就是通过诊断统计量检测已知观测数据在用既定模型拟合时的合理性,主要是找出数据当中的异常点或强影响点。本文主要研究Logostic回归模型的诊断统计量和诊断统计图。用牛顿迭代法给出Logistic回归模型的极大似然估计值,根据扰动模型得到传统的诊断统计量,结合残差、杠杆值和系数变化三者构造新的诊断统计量,绘制新的诊断统计图,通过模拟研究说明新的诊断统计量的有效性,最后用一个实际案例说明新的诊断方法的应用并进一步验证其优越性。

Statistical Diagnostics for Logistic Regression Model

The main task of statistical diagnostics is using the diagnosis statistics to detect the rationality of fitting the data with established model,the most important is identifying outliers or influential points.In this paper,we focus on the diagnosis statistics and diagnosis graph of Logistic regression model.We discuss how to obtain the maximum likelihood estimates by Newton iterative method,then we can get the traditional diagnostic statistics based on perturbation model.In addition,we combine residuals,leverage value and the change in the value of the estimated coefficients to construct new diagnosis statistics and plot new diagnosis graph.Through simulation the effectiveness of the new diagnosis statistics can be verified.Finally,we cite an example to illustrate the application of new diagnostic method and to further validate its superiority.