Likelihood inference for small area estimation using data cloning

Abstract

Policy decisions regarding allocation of resources to subgroups in a population, called small areas, are based on reliable predictors of their underlying parameters. However, in sample surveys, the information to estimate reliable predictors is often insufficient at the level of the small areas. Hence, parameters of the subgroups are often predicted based on the coarser scale data. In view of this, there is a growing demand for reliable small area predictors by borrowing information from other areas. These models are commonly based on either linear mixed models (LMMs) or generalized linear mixed models (GLMMs). The frequentist analysis of LMM, a special case of GLMM, is computationally difficult. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of LMM and GLMM computationally convenient. Recently developed data cloning method provides a frequentist approach to complex mixed models which is also computationally convenient. Data cloning which yields to maximum likelihood estimation is used to conduct frequentist analysis of small area estimation for Normal and non-Normal responses. It is shown that for the Normal and non-Normal responses, data cloning leads to predictions and prediction intervals of small area parameters that have reasonably good coverage.