Generalized linear mixed quantile regression with panel data

A new generalized linear mixed quantile model for panel data is proposed. This proposed approach applies GEE with smoothed estimating functions, which leads to asymptotically equivalent estimation of the regression coefficients. Random effects are predicted by using the best linear unbiased predictors (BLUP) based on the Tweedie exponential dispersion distributions which cover a wide range of distributions, including those widely used ones, such as the normal distribution, Poisson distribution and gamma distribution. A Taylor expansion of the quantile estimating function is used to linearize the random effects in the quantile process. The parameter estimation is based on the Newton-Raphson iteration method. Our proposed quantile mixed model gives consistent estimates that have asymptotic normal distributions. Simulation studies are carried out to investigate the small sample performance of the proposed approach. As an illustration, the proposed method is applied to analyze the epilepsy data.