Li Chenxi, Wei Ying, Chappell Rick, He Xuming
Department of Statistics, University of Wisconsin, Madison, Wisconsin 53706, USA.
Biometrics. 2011 Mar;67(1):242-9. doi: 10.1111/j.1541-0420.2010.01436.x.
Quantile regression, which models the conditional quantiles of the response variable given covariates, usually assumes a linear model. However, this kind of linearity is often unrealistic in real life. One situation where linear quantile regression is not appropriate is when the response variable is piecewise linear but still continuous in covariates. To analyze such data, we propose a bent line quantile regression model. We derive its parameter estimates, prove that they are asymptotically valid given the existence of a change-point, and discuss several methods for testing the existence of a change-point in bent line quantile regression together with a power comparison by simulation. An example of land mammal maximal running speeds is given to illustrate an application of bent line quantile regression in which this model is theoretically justified and its parameters are of direct biological interests.
分位数回归对给定协变量的响应变量的条件分位数进行建模，通常假定为线性模型。然而，这种线性在现实生活中往往不切实际。线性分位数回归不适用的一种情况是，响应变量在协变量方面是分段线性但仍连续的。为了分析此类数据，我们提出了一种折线分位数回归模型。我们推导了其参数估计值，证明了在存在变化点的情况下它们是渐近有效的，并讨论了几种用于检验折线分位数回归中变化点存在性的方法以及通过模拟进行的功效比较。给出了陆地哺乳动物最大奔跑速度的一个例子，以说明折线分位数回归的应用，在该应用中此模型在理论上是合理的，并且其参数具有直接的生物学意义。
