Multilevel hierarchical Bayesian vs. state-space approach in time series small area estimation; the Dutch Travel Survey

This study compares state space models (estimated with the Kalman filter with a frequentist approach to hyperparameter estimation) with multilevel time series models (based on the hierarchical Bayesian framework). The application chosen is the Dutch Travel Survey featuring small sample sizes and discontinuities caused by the survey redesigns. Both modelling approaches deliver similar point and variance estimates. Slight differences in model-based variance estimates appear mostly in small-scaled domains and are due to neglecting uncertainty around the hyperparameter estimates in the state space models, and to a lesser extent to skewness in the posterior distributions of the parameters of interest. The results suggest that the reduction in design-based standard errors with the hierarchical Bayesian approach is over 50% at the provincial level, and over 30% at the national level.