Bootstrap Methods for Bias Correction and Confidence Interval Estimation for Nonlinear Quantile Regression of Longitudinal Data

This paper examines the use of bootstrapping for bias correction and confidence interval calculations for a weighted nonlinear quantile regression estimator, adjusted to the case of longitudinal data. Different weights, bootstrap methods and types of confidence intervals are used and compared by computer simulation using a four-parameter logistic growth function and error terms following an AR(1) model. Finally the methods are applied to a data set with growth patterns of two genotypes of soybean. It is found that the bias correction reduces the bias, but has the disadvantage of increasing the risk of getting crossing quantile regression curves, and that the bootstrap percentile method and the normal approximation method perform well when used without bias correction. When increasing the autocorrelation in the AR(1) model, the length of the confidence intervals decrease