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

This article focuses on developing Bayesian hierarchical (HB) bivariate small area estimation (SAE) methods for proportions using logit-normal mixed models that incorporate latent spatial dependence via multivariate conditional autoregressive (MCAR) and generalized MCAR (GMCAR) structures. The proposed models borrow strength from both within-area outcome correlation and between-area spatial correlation, enabling improved estimation and prediction, including for non-sampled small areas. Extensive simulation studies based on China's 31 mainland provinces demonstrate that bivariate spatial models outperform univariate and non-spatial methods, particularly when bivariate spatial dependence exists, and practical model selection guidelines using criteria such as coefficient of variation (CV), deviance information criterion (DIC), and mean squared prediction error (MSPE) are provided. The methods are applied to estimate province-level heart disease and dyslipidemia rates among the middle-aged and elderly population in China using 2020 China Health and Retirement Longitudinal Study (CHARLS) data, revealing spatial patterns and improved estimation stability compared to direct survey estimates.