Nonlinear Quantile Regression Estimation of Longitudinal Data

Abstract

This article examines a weighted version of the quantile regression estimator as defined by Koenker and Bassett (1978), adjusted to the case of nonlinear longitudinal data. Using a four-parameter logistic growth function and error terms following an AR(1) model, different weights are used and compared in a simulation study. The findings indicate that the nonlinear quantile regression estimator is performing well, especially for the median regression case, that the differences between the weights are small, and that the estimator performs better when the correlation in the AR(1) model increases. A comparison is also made with the corresponding mean regression estimator, which is found to be less robust. Finally, the estimator is applied to a data set with growth patterns of two genotypes of soybean, which gives some insights into how the quantile regressions provide a more complete picture of the data than the mean regression.

Keywords:

• Dependent errors
• Median regression
• Repeated measures
• Simulation study

Mathematics Subject Classification:

• Primary 62G30, 62M10
• Secondary 62J02, 62P10

Acknowledgments

Thanks to Dr. Johan Lyhagen, Professor Rolf Larsson, Dr. Jonas Andersson, and the anonymous referees for their valuable comments and suggestions. This work was mainly performed as a part of the author's graduate studies at the Division of Statistics, Department of Information Sciences, Uppsala University during the years 2001–2006.