A Simulation Study of Hierarchical Bayesian Fusion Spatial Small Area Model for Binary Outcome under Spatial Misalignment

Abstract

Simulation (stochastic) methods are based on obtaining random samples θ 5 from the desired distribution p ( θ ) and estimating the expectation of any function h ( θ ) . Simulation methods can be used for high-dimensional dis tributions, and there are general algorithms which work for a wide variety of models. Markov chain Monte Carlo (MCMC) methods have been important in making Bayesian inference practical for generic hierarchical models in small area estimation. Small area estimation is a method for producing reliable estimates for small areas. Model based Bayesian small area estimation methods are becoming popular for their ability to combine information from several sources as well as taking account of spatial prediction of spatial data. In this study, detailed simulation algorithm is given and the performance of a non-trivial extension of hierarchical Bayesian model for binary data under spatial misalignment is assessed. Both areal level and unit level latent processes were considered in modeling. The process models generated from the predictors were used to construct the basis so as to alleviate the problem of collinearity between the true predictor variables and the spatial random process. The performance of the proposed model was assessed using MCMC simulation studies. The performance was evaluated with respect to root mean square error (RMSE), Mean absolute error (MAE) and coverage probability of corres ponding 95% CI of the estimate. The estimates from the proposed model perform better than the direct estimate.