解释变量非正交时logistic回归系数的估计

Estimate of logistic Regression Coefficients for Nonorthogonal Explainary Variables

ｌｏｇｉｓｔｉｃ回归模型的目的是描述因变元与自变元之间的关系，回归系数有明确的实际意义。一旦回归系数的估计受非典型数的干扰，就难于获得对实际问题的解释。文中讨论了解释变量多元共线对ｌｏｇｉｓｔｉｃ回归系数影响，在此基础上引用线性回归系数主成分估计的思想，改进了ｌｏｇｉｓｔｉｃ回归系数的加权最小二乘估计，使之能克服多元共线引起的一般ｌｏｇｉｓｔｉｃ回归系数加权最小二乘估计方差扩大现象。

ogistic regression model was generally used to discribe the contributions of explainary variables to response variable.The scales of regression coefficients have their own medical background in case control studies.Once the estimates of the coefficients were perturbated,the interpretation of these is meaningless.In this paper,we found that multicollinearity affected the ordinary estimation of regression coefficients dramatically.We modified the weighted LS estimate by principle of principal components and got biased logistic regression coefficient estimations which cut down the variance inflation of estimations due to the nonoptimality and are more robust than ordinaryones. 