General Bayesian quantile regression for counts via generative modeling

Although quantile regression has emerged as a powerful tool for understanding various quantiles of a response variable conditioned on a set of covariates, the development of quantile regression for count responses has received far less attention. This paper proposes a new Bayesian approach to quantile regression for count data, which provides a more flexible and interpretable alternative to the existing approaches. The proposed approach associates the continuous latent variable with the discrete response and nonparametrically estimates the joint distribution of the latent variable and a set of covariates. Then, by regressing the estimated continuous conditional quantile on the covariates, the posterior distributions of the covariate effects on the conditional quantiles are obtained through general Bayesian updating via simple optimization. The simulation study and real data analysis demonstrate that the proposed method overcomes the existing limitations and enhances quantile estimation and interpretation of variable relationships, making it a valuable tool for practitioners handling count data.