Small Area Estimation via Multivariate Fay-Herriot Models with Latent Spatial Dependence

TL;DR

This paper introduces two multivariate Fay-Herriot models incorporating latent spatial dependence for small area estimation, demonstrating improved accuracy over existing models in both state and county level data.

Contribution

The paper develops and compares two formulations of multivariate Fay-Herriot models with spatial dependence, including a novel GMCAR structure, enhancing small area estimation accuracy.

Findings

GMCAR model yields smaller mean square prediction errors than separable models.

Both models outperform state-of-the-art models in county-level data.

Models improve estimation accuracy over traditional approaches.

Abstract

The Fay-Herriot model is a standard model for direct survey estimators in which the true quantity of interest, the superpopulation mean, is latent and its estimation is improved through the use of auxiliary covariates. In the context of small area estimation, these estimates can be further improved by borrowing strength across spatial region or by considering multiple outcomes simultaneously. We provide here two formulations to perform small area estimation with Fay-Herriot models that include both multivariate outcomes and latent spatial dependence. We consider two model formulations, one in which the outcome-by-space dependence structure is separable and one that accounts for the cross dependence through the use of a generalized multivariate conditional autoregressive (GMCAR) structure. The GMCAR model is shown in a state-level example to produce smaller mean square prediction errors, relative to equivalent census variables, than the separable model and the state-of-the-art multivariate model with unstructured dependence between outcomes and no spatial dependence. In addition, both the GMCAR and the separable models give smaller mean squared prediction error than the state-of-the-art model when conducting small area estimation on county level data from the American Community Survey.