Bent Line Quantile Regression with Application to an Allometric Study of Land Mammals' Speed and Mass
Article first published online: 28 MAY 2010
© 2010, The International Biometric Society
Volume 67, Issue 1, pages 242–249, March 2011
How to Cite
Li, C., Wei, Y., Chappell, R. and He, X. (2011), Bent Line Quantile Regression with Application to an Allometric Study of Land Mammals' Speed and Mass. Biometrics, 67: 242–249. doi: 10.1111/j.1541-0420.2010.01436.x
- Issue published online: 14 MAR 2011
- Article first published online: 28 MAY 2010
- Received June 2009. Revised March 2010. Accepted March 2010.
- Bahadur representation;
- Piecewise linear;
- Profile estimation
Summary 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.