An Applied Comparison of Area-Level Linear Mixed Models in Small Area Estimation

Abstract

This article reviews four area-level linear mixed models that borrow strength by exploiting the possible correlation among the neighboring areas or/and past time periods. Its main goal is to study if there are efficiency gains when a spatial dependence or/and a temporal autocorrelation among random-area effects are included into the models. The Fay–Herriot estimator is used as benchmark. A design-based simulation study based on real data collected from a longitudinal survey conducted by a statistical office is presented. Our results show that models that explore both spatial and chronological association considerably improve the efficiency of small area estimates.

Keywords:

• Empirical best linear unbiased prediction
• Linear mixed model
• Small area estimation
• Spatial correlation
• Temporal autocorrelation

Mathematics Subject Classification:

• 62D05
• 62G09
• 62J05
• 62P20

Acknowledgments

The authors acknowledge the Portuguese statistical office for the availability of the data used in the research. The views expressed here are solely those of the authors. The authors also thank the Fundação para a Ciência e a Tecnologia (Portugal) for financial support.