Quantile Regression in Space-Time Varying Coefficient Model of Upper Respiratory Tract Infections Data

Abstract

Space-time varying coefficient models, which are used to identify the effects of covariates that change over time and spatial location, have been widely studied in recent years. One such model, called the quantile regression model, is particularly useful when dealing with outliers or non-standard conditional distributions in the data. However, when the functions of the covariates are not easily specified in a parametric manner, a nonparametric regression technique is often employed. One such technique is the use of B-splines, a nonparametric approach used to estimate the parameters of the unspecified functions in the model. B-splines smoothing has potential to overfit when the number of knots is increased, and thus, a penalty is added to the quantile objective function known as P-splines. The estimation procedure involves minimizing the quantile loss function using an LP-Problem technique. This method was applied to upper respiratory tract infection data in the city of Bandung, Indonesia, which were measured monthly across 30 districts. The results of the study indicate that there are differences in the effect of covariates between quantile levels for both space and time coefficients. The quantile curve estimates also demonstrate robustness with respect to outliers. However, the simultaneous estimation of the quantile curves produced estimates that were relatively close to one another, meaning that some quantile curves did not depict the actual data pattern as precisely. This suggests that each district in Bandung City not only has different categories of incidence rates but also has a heterogeneous incidence rate based on three quantile levels, due to the difference in the effects of covariates over time and space.

Keywords

• longitudinal data
• P-splines
• quantile regression
• space-time varying coefficient model