复杂随机抽样数据的多重线性回归分析方法及其应用

Multiple linear regression analysis methods for complex random sampled data and their application

目的探讨综合权重在复杂随机抽样数据线性回归分析中的意义和作用。方法基于蒙特卡洛随机模拟思想,采用SAS中REG和SURVEYREG两个不同的多重线性回归分析过程,分别对同一批复杂随机抽样数据(n=6756)在不同随机抽样率条件下进行回归建模,对所得结果进行比较。结果在未考虑和考虑观测权重与抽样权重的多重线性回归模型拟合的结果中,自变量的偏回归系数、标准误及P值的大小均有所不同。结论在对基于不同抽样率的复杂随机抽样资料,尤其是分层随机抽样调查资料的回归建模中,采用多重线性回归模型拟合资料时,将调查数据的综合权重纳入统计分析,方能更准确、灵敏地进行回归系数的参数估计和对结果变量的统计预测。

Objective To study the significance and function of the comprehensive weight in multiple linear regression analysis of complex random sampled data .Methods Based on the concept of Monte Carlo random simulation , two different multiple linear regression analysis procedures in SAS-REG and SURVEYREG were used to perform regression modeling for the same batch of complex random sampled data （ n=6756 ） at different random sampling proportions .The results were compared.Results In the results of the fitting multiple linear regression model when observation weight and sampling weight were considered or not , it was found that the size of the partial regression coefficient , standard error and P value of independent variables varied .Conclusion In complex random sampled data based on different proportions ,especially in regression modeling of stratified random sampling survey information , the multiple linear regression model makes it possible to more accurately and sensitively perform parameter estimates of regression coefficients and statistical prediction of outcome variables if the comprehensive weight of the survey data is incorporated into the statistical analysis .