百分位数回归及其应用

Quantile Regression Model And it's Application

目的：传统的直线回归中，用最小二乘法估计回归系数，要求数据的独立性、方差齐性及正态性。但医学研究中，很多资料不满足上述要求，特别是ｙ的条件分布不是正态，或方差不为常数。这类资料显然不能用传统的最小二乘法估计回归系数。方法：采用一种适合于当资料不满足上述方差齐性或正态性条件时的直线回归方法——百分位数回归。结果：该模型采用加权最小一乘法估计回归系数，能有效地估计给定自变量ｘ时，因变量ｙ的中位数、百分位数，及容许区间等。结论：当资料的方差齐性及正态性不满足时，用中位数回归估计给定ｘ时ｙ的中位数，用百分位数回归估计给定ｘ时ｙ的百分位数，由此可得相应的容许区间。

Objective:To estimate the coefficients of linear regression by means of traditional least squares method,the dependence,normality and homogeneity of data are required.But departure from these conditions occurs frequently in medical research.Especially the distribution of y on x is nonnormal,the variance of y on x is heteroscedastic.Methods:In this paper,the authors introduced quantile regression(include median regression)models,the weighted least absolute method is used to estimate the coefficients of quantile regression.Result:The methods perfectly suited to model the data when the variance of y on x is heteroscedastic,and/or the distribution of y on x is non-normal.Conclusion:When data is non-normality and/or heteroscedastic,the median regression can be used to estimate the median of y on x,and quantile regression can be used to estimate the percentile and tolerance of y on x,an expample was illustrated.