对医学领域层次结构数据拟合线性回归模型时几个问题的探讨

在医学领域存在大量具有层次结构特征的资料，但通常仍采用各类传统线性回归模型分析这类数据。作者探讨了层次结构数据拟合常见的三类线性回归模型所存在的问题，三类模型参数估计间的相互关系以及参数估计精度的校正。结果显示，参数估计及其精度取决于自变量在水平２单位间和水平２单位内的变异大小，残差估计的差别与参数估计的差别有关；当数据具有层次结构时，三类常见的线性回归模型均不适宜，在一定条件下，可采用方差膨胀因子对水平１合并模型的标准误进行校正。

On the Problems of Fitting Linear Regression Models for Hierachically Structured Data in Medical Research

There are a large number of the hierarchically structured data in the field of medical sciences, which have been analyzed usually by conventional linear regression models. The objective of this paper is to explore the problems and the relationship of parameter estimates of the three common linear regression models in fitting the hierarchically structured date, and the correction of the precision of parameter estimates. It is shown that theestimate of parameter and it's precision of linear regression models is related to the variation of independent variable between and within level 2 units, and the difference of residual estimates is associated with the difference of parameter estimates. The three common linear regression models are all inappropriate for the hierarchically structured data, but the standard error of the level 1 combined model can be corrected by variance inflation factor in conditions.