摘要
目的 logistic回归模型中解释变量存在共线性的情形下,比较联合式偏最小二乘logistic回归(IPLSLR),耦合式偏最小二乘logistic回归(CPLSLR)和主成分logistic回归(PCLR)三种降维方法所得到的回归系数估计的偏差和稳定性。方法运用MonteCarlo随机法,采用SAS软件编程,模拟估算不同共线性情形下三种降维方法所得到的回归系数估计均值及标准差。结果简单共线性情形下,IPLSLR与CPLSLR回归系数估计的偏差较小,PCLR估计则相对稳定。多重共线性情形下,当样本量较大时,若共线性较高,IPLSLR,CPLSLR和PCLR均获得偏差较小、稳定性较好的回归系数估计;若共线性较低,PCLR回归系数估计的偏差明显大于IPLSLR和CPLSLR。当样本量较小时,IPLSLR与CPLSLR在回归系数估计偏差和稳定性方面互有优劣。结论应根据共线性的程度和样本量的大小决定使用相应的降维方法用于处理logistic回归模型中共线性情况。通过对三种降维方法不足的分析,提出了进一步改进的原则。
Objective：To compare integrated partial least squares logistic regression（IPLSLR）,coupled partial least squares logistic regression（CPLSLR） and principal component logistic regression（PCLR） for logistic regression models with colinearity in terms of deviation and robustness of coefficient estimate.Methods：A simulation was conducted in SAS software by using the three dimension-reduced methods to obtain means and standard deviations of coefficients in logistic regression model with various colinearity.Results：For logistic regression models with simple colinearity,coefficients estimated by IPLSLR and CPLSLR were closer to their true values.Moreover,coefficients estimated by PCLR had smaller standard deviations.For logistic regression models with multicolinearity,if sample size was large and colinearity was high,all three methods could offer better estimation of coefficients.And if sample size was large and colinearity was low,estimates of coefficients by using IPLSLR and CPLSLR were better than those by using PCLR.If sample size was small,IPLSLR was not consistently better than CPLSLR in terms of precision and stability of coefficients estimate.Conclusion：It suggests which of the three methods should be chosen according to colinearity and sample size.Moreover,three principles for improving the present dimension-reduced methods is derived from the analysis of drawbacks of these methods.
出处
《中国卫生统计》
CSCD
北大核心
2010年第6期562-566,共5页
Chinese Journal of Health Statistics
