Varying Coefficient Model for Dengue Fevers using P-Splines Quantile Regression

Abstract

Bandung, one of the biggest cities in Indonesia, has a serious problem with dengue fever. Dengue virus is mostly transmitted by Aedes mosquitoes. The distribution of dengue rate varies over times. One may be interested to investigate the dengue rate level every month (e.g., low, medium low, medium high and high). In order to investigate the dengue rate distribution, we propose a quantile regression technique with several quantile levels. We obtain not only some conditional quantile values for dengue rate, but also the information of time. Hence, we need to build a flexible modeling technique involving not only some covariates but also the information of time. Therefore, we propose a (time) varying-coefficient model (VCM) where the coefficients vary over time. In VCM, we consider the coefficients as an unknown function of time variable. Those coefficients can be approximated by a B-splines function. The quantile objective function itself is penalized by a difference operator on the coefficients of the basis B-splines, which we call P-splines quantile objective function. The tuning parameter of the penalty term is chosen in a data driven way, in this case, we propose to use Schwarz Information Criteria. We consider two models for the variability in the VCM: homoscedastic and simple heteroscedastic models. Year 2017 is shown to have a consistent low level of dengue rate over the months.