Bayesian Nonparametric Multivariate Spatial Mixture Mixed Effects Models with Application to American Community Survey Special Tabulations

TL;DR

This paper introduces a flexible Bayesian nonparametric multivariate spatial mixture model that automatically determines the number of clusters, improving estimation accuracy for heterogeneous and sparse survey data like the American Community Survey.

Contribution

It proposes a novel hierarchical Bayesian nonparametric model for multivariate spatial data that adapts cluster numbers automatically, addressing limitations of Gaussian assumptions.

Findings

Model outperforms Gaussian-based methods in heterogeneity scenarios

Automatically determines the optimal number of clusters

Demonstrated effectiveness on ACS special tabulations

Abstract

Leveraging multivariate spatial dependence to improve the precision of estimates using American Community Survey data and other sample survey data has been a topic of recent interest among data-users and federal statistical agencies. One strategy is to use a multivariate spatial mixed effects model with a Gaussian observation model and latent Gaussian process model. In practice, this works well for a wide range of tabulations. Nevertheless, in situations that exhibit heterogeneity among geographies and/or sparsity in the data, the Gaussian assumptions may be problematic and lead to underperformance. To remedy these situations, we propose a multivariate hierarchical Bayesian nonparametric mixed effects spatial mixture model to increase model flexibility. The number of clusters is chosen automatically in a data-driven manner. The effectiveness of our approach is demonstrated through a simulation study and motivating application of special tabulations for American Community Survey data.