A CUSUM test for change point in quantile regression for longitudinal data

In regression analysis a single parametric form is assumed, over the whole domain of interest. However, this assumption might not be valid in some applications, such as existence of a change point in the functional form. In this case we need to detect and estimate such change point. Also, it is common to assume normality of the response variable when dealing with the change point problem. The normality assumption can be violated in many cases, such as heavy-tailed data or in the presence of outliers. In such cases, the quantile regression is a good candidate. It is known that the quantile regression is distribution free and robust to outliers. The CUSUM test has been used to detect the existence of a threshold effect (change point) to the quantile regression model in cross-sectional data. This article proposes and develops the CUSUM test, in longitudinal data setting, to investigate the existence of a change point in quantile regression model. Simulation study is used to assess the performance of the proposed test. Finally, the proposed test is used to detect any possible change points in a COVID-19 data.