A Bayesian Logit-Normal Model in Small Area Estimation

Abstract

The Logit-Normal model is one of the GLM Bayes models with random covariates used in binary data. This study aimed to examine and evaluate the characteristics of the Logit-Normal model. The second objective was to apply the Logit-Normal model to estimate the proportion of poverty in the small area of Mukomuko District in Bengkulu Province. We used the Hierarchical Bayes (HB) method to estimate parameters model. The simulation results obtained from the optimum number of iterations and gibbs samples, namely 500 iterations and 100 gibbs samples, respectively. In addition, when seen the value of has the same tendency with the parameter pi and . The value of tends to overestimate at ⩽ 60%. Conversely, tends to underestimate > 60%. Furthermore, in the simulation results the estimated value of variance and MSE tends to be smaller than the variance of proportion. The application of the HB method for Logit-Normal model in the Mukomuko District poverty data produces which has the same tendency as the result of direct estimator (). The majority (21 villages) value of var() are smaller or equal to the var(). This indicates that the estimation using the HB method can improve the estimation of the proportion parameters obtained by using the direct estimation method on poverty data.