Bayesian quantile regression and variable selection for count data with an application to Youth Fitness Survey

Quantile regression model estimates the relationship between covariates and the quantile of a response distribution, rather than the mean. This method has been utilized successfully in several fields such as linear models, random effect models, generalized linear models and semiparametric/nonparametric model etc. However, most of the literature have been developed under the assumption that the responses are continuous and the Bayesian quantile regression for count data needs more exploration. In this paper, we present Bayesian regularized quantile regression model for count data and apply it to the study of Youth Fitness Survey. We also compare the results of quantile regression from the common modeling strategy such as Poisson and negative binomial regression. From the results, we observe that Bayesian quantile regression is more flexible and reasonable in the sense that it provide more information about parameter estimation than ordinary regression.