Logistic回归中不同Pearson残差估计方法的探讨

目的 探讨logistic回归中不同Pearson残差估计方法的差异，为回归诊断时残差估计方法及软件的选择提供参考。方法 通过对代表不同数据类型的两个实例构建logistic回归模型，并使用分别代表不同估计方法的SPSS与STATA软件计算其Pearson残差值，分析比较二者的异同。结果 Logistic回归模型的两种Pearson残差估计方法对协变量组数等于或近似等于研究对象个体数的数据的计算结果一致，而对协变量组数远小于研究对象个体数的数据的计算结果差异较大。结论 Logistic回归的两种Pearson残差估计方法在理论和应用上均有一定差异，针对协变量组数远小于研究对象个体数的数据，如何选择适当的Pearson残差估计方法，值得进一步深入研究。

Calculating Pearson Residual in Logistic Regressions: a Comparison Between SPSS and SAS

Objective To compare the results of Pearson residual calculations in logistic regression models using SPSS and SAS. Methods We reviewed Pearson residual calculation methods, and used two sets of data to test logistic models constructed by SPSS and STATA. One model contained a small number of covariates compared to the number of observed. The other contained a similar number of covariates as the number of observed. Results The two software packages produced similar Pearson residual estimates when the models contained a similar number of covariates as the number of observed, but the results differed when the number of observed was much greater than the number of covariates. Conclusion The two software packages produce different results of Pearson residuals, especially when the models contain a small number of covariates. Further studies are warranted.