Poisson-Lognormal model with measurement error in covariate for small area estimation of count data

Abstract

Small Area Estimation (SAE) is a statistical technique to estimate parameters of subpopulation containing small-size of samples. SAE is an indirect estimation method by utilizing the strength of the neighbor area and data sources outside the area so that the sample becomes more effective and reduces the variance of parameter estimators. This paper deals with non-symmetrical count data in SAE which can be modelled based on Poisson-Lognormal distribution using hierarchical Bayesian (HB) approach and information on covariate contains measurement error. We develop the Poisson-Lognormal model for predicting small area counts with structural measurement error in the area-specific covariate. To get the HB Bayes estimator for Poisson-Lognormal model with measurement error in its covariates, the Metropolis-Hastings (MH) algorithm from the Markov Chain Monte Carlo (MCMC) technique is used. The HB estimator performance is studied through simulation and implementation of real data to predict the illiteracy rate at the sub-district level in Kepulauan Riau Province Indonesia based on The National Socio-Economic Survey (Susenas) data in March 2020.