TITLE:
A Simulation Study of Hierarchical Bayesian Fusion Spatial Small Area Model for Binary Outcome under Spatial Misalignment
AUTHORS:
Kindie Fentahun Muchie, Anthony Kibira Wanjoya, Samuel Musili Mwalili
KEYWORDS:
Simulation, Small Area Estimation, Hierarchical Bayesian, Spatial Misalign-ment, Fusion Process
JOURNAL NAME:
Open Journal of Statistics,
Vol.11 No.6,
December
10,
2021
ABSTRACT: Simulation (stochastic) methods are based on obtaining random samplesθ5from the desired distribution p(θ)and estimating the
expectation of any function h(θ). Simulation methods can be used for high-dimensional distributions,
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 corresponding 95% CI of the estimate. The estimates from
the proposed model perform better than the direct estimate.