Model-based quantile regression for count panel data

Abstract

Panel data are observed in many research areas such as econometrics, social sciences and medicine. It involves repeated observations of the same subjects over a short or long period of time, where the multiple subjects are independent but the repeated measurements over time within one subject are non-independent. The objective of the Final Year Project (FYP) is to propose a model-based quantile regression method to estimate count panel data. By linking Generalized Linear Mixed Model (GLMM) based on Poisson distribution and the Quantile Regression (QR) model, we can map the parameters of the response variable to the regression quantiles and then estimate the regression quantiles through the likelihood function with Asymmetric Laplace Distribution (ALD). On top of that, an extension of the discrete responses is explored by adding continuous generalization to the response variable.