Borrowing strength over space in small area estimation: Comparing parametric, semi-parametric and non-parametric random effects and M-quantile small area models

In recent years there have been significant developments in model-based small area methods that incorporate spatial information in an attempt to improve the efficiency of small area estimates by borrowing strength over space. A popular approach parametrically models spatial correlation in area effects using Simultaneous Autoregressive (SAR) random effects models. An alternative approach incorporates the spatial information via M-quantile Geographically Weighted Regression (GWR), which fits a local model to the M-quantiles of the conditional distribution of the outcome variable given the covariates. A further approach uses spline approximations to fit nonparametric unit level nested error regression and M-quantile regression models that reflect spatial variation in the data and then uses these nonparametric models for small area estimation. In this presentation we contrast the performance of these alternative small area models using data with geographical information. We also examine how these models perform when estimation is for out of sample areas i.e. areas with zero sample, and discuss issues related to estimation of mean squared error of the resulting small area estimators. Our analysis is illustrated using simulations based on data from the U.S. Environmental Protection Agency’s Environmental Monitoring and Assessment Program.