Quantile regression in varying coefficient model of upper respiratory tract infections in Bandung City

Abstract

Abstract Varying coefficient models are commonly used to obtain effects of covariates that vary over other variables. A special case of varying coefficient model is applied to longitudinal data where the covariates may vary over time. When the function is not easy to specify parametrically, we then need to work on a non-parametric regression technique. In this case, we approximate the function by B-splines. B-splines smoothing tends to overfit with increasing knots, then a penalty is added to the quantile objective function. This estimation procedure is called P-splines. As the objective function, we propose to use quantile loss function. The technique will be implemented to the upper respiratory tract infection data in Bandung City which was measured repeatedly from 30 sub district in Bandung City and hence we have a longitudinal data structure.