Hierarchical Bayesian bivariate spatial modeling of small area proportions with application to health survey data

In this article, we propose bivariate small area estimation methods for proportions based on the logit-normal mixed models with latent spatial dependence. We incorporate multivariate conditional autoregressive structures for the random effects under the hierarchical Bayesian modeling framework, and extend the methods to accommodate non-sampled regions. Posterior inference is obtained via adaptive Markov chain Monte Carlo algorithms. Extensive simulation studies are carried out to demonstrate the effectiveness of the proposed bivariate spatial models. The results suggest that the proposed methods are more efficient than the univariate and non-spatial methods in estimation and prediction, particularly when bivariate spatial dependence exists. Practical guidelines for model selection based on the simulation results are provided. We further illustrate the application of our methods by estimating the province-level heart disease rates and dyslipidemia rates among the middle-aged and elderly population in China's 31 mainland provinces in 2020.