Composite Estimation for Quantile Regression Kink Models with Longitudinal Data

Abstract

Kink model is developed to analyze the data where the regression function is twostage linear but intersects at an unknown threshold. In quantile regression with longitudinal data, previous work assumed that the unknown threshold parameters or kink points are heterogeneous across different quantiles. However, the location where kink effect happens tend to be the same across different quantiles, especially in a region of neighboring quantile levels. Ignoring such homogeneity information may lead to efficiency loss for estimation. In view of this, we propose a composite estimator for the common kink point by absorbing information from multiple quantiles. In addition, we also develop a sup-likelihood-ratio test to check the kink effect at a given quantile level. A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test. The simulation study shows that the proposed composite kink estimator is more competitive with the least square estimator and the single quantile estimator. We illustrate the practical value of this work through the analysis of a body mass index and blood pressure data set.