Estimation and bootstrapping under spatiotemporal models with unobserved heterogeneity

Proposed herein is a novel spatiotemporal model to characterize the unobserved heterogeneity across individuals using quantile-function-based correlated random effects and heteroscedastic innovations in a general framework. This model can be used to explore the influence of space -specific factors on latent effects at different quantile levels by controlling for spatiotemporal effects. A two-stage estimation procedure is introduced in which (i) the method of moments is used to estimate spatiotemporal effects then (ii) quantile regression is used for individual effects. A hybrid double bootstrapping procedure is then proposed to approximate the asymptotic distributions of coefficient estimators. The validity of the estimation and bootstrapping is established theoretically and then confirmed by simulation studies, and the usefulness of the proposed model is demonstrated with a real example involving city air quality.