Logistic模型的系数比较问题及解决策略:一个综述

On the Coefficients Comparison between Logistic Regressions and the Solutions:A Brief Review

本文介绍了Logistic模型中经常被忽视的系数比较问题,包括同一样本在不同模型间的系数比较和在不同样本或子群体间的模型系数比较。研究者往往会沿袭线性回归模型的系数比较方法,但这是不恰当的,因为Logistic模型存在未被观测到的异质性(残差变异)问题,所以模型间系数不能进行简单的直接比较。根据已有研究,本文总结了解决这一问题的五种策略,分别是"y*标准化"、KHB分解、异质选择模型、平均偏效应(APE)和线性概率模型(LPM),然后利用CGSS2006数据,以教育递进率模型为例,比较这些解决策略的异同,最后总结这些策略的特征及适用情况。

This paper introduced the coefficients comparison between Logistic regression,which includes comparison between models within sample and that between samples or subsamples. Due to the unobserved heterogeneity （residual variation） problem in Logistic models, it is inappropriate to follow the OLS coefficients comparison in a naive simple way. With the same dependent variable, the total variance of OLS regression function is always fixed, which is irrelevant to the number of independent variables. However, the total variance of Logistic regression function will change as the independent variables increase or decrease,because the variance of error in Logistic regression is assumed to be constant,equals π2/3. Previous researchers proposed many solutions to this comparison problem. Based on the literature, this paper introduced five solutions： y＂ -standardization, KHB decomposition, heterogeneous choice model, average partial effect （APE）, and linear probability model （LPM）. Y＇- standardization and KHB only work in comparison between models within sample, heterogeneous choice model only works in comparison between samples or subsamples,and APE and LPM work in both situations. Drawing up on CGSS 2006 data, using educational transition model as an example, the author then showed the use and the differences between the five solutions through examining the cohort differences in school transition and whether the effects of parental ISEI differ in two cohorts＇ school transition. The final part summarized the characteristics and contexts of the five solutions.