Bayesian spatial modeling of poverty risk in Kelantan

Abstract

Poverty data vary in rural areas, in certain states or regions, and some urban areas. These areal data tends to have spatial autocorrelation. A Bayesian hierarchical model is commonly used to estimates the risks using a combination of available covariate data and a set of spatial random effects. These random effects are commonly modelled by conditional autoregressive (CAR) prior distributions, a type of Markov random field model. Spatial autocorrelation between the random effects, φ in CAR models is induced by a n n neighbourhood matrix, W. However, many studies assumed that the W is fixed when fitting the model. Therefore, this study evaluates the performance of the Poisson-log linear Leroux Conditional Autoregressive (CAR) model with m-nearest neighbourhood weight matrices using a simulation study. This study creates simulated poverty data for 66 districts of Kelantan with different scenarios that related with random effects and covariate. A Poisson log-linear Leroux CAR model with m = 1, 5 and 10 nearest neighbours are applied to the simulated poverty data. The performance of the models is evaluated using bias, Root Mean Square of Error (RMSE) and Deviance Information Criterion (DIC). The results show that the choice of m = 1, 5 and 10 neighbourhood matrices and scenarios do not affect the bias for either the regression parameter β or the risk Rk and RMSE for the risk Rk . Nevertheless, there is the dissimilarity of the performance of the models in the RMSE of regression parameter β. The results suggest that the Poisson log-linear Leroux CAR model with the m = 5 nearest neighbours performed overall best for simulated poverty data. It consistently gives good results across different strength of spatial autocorrelation of random effects φ and covariate. The model also gives the lowest DIC in all the scenarios, indicating a better fitting model than other models. The findings of this study give guidance in choosing the suitable m-nearest neighbourhood matrices to estimate the poverty risk in Kelantan.