Unit level model for small area estimation with count data under square root transformation

Abstract

In recent years, the demand for small area statistics has greatly increased worldwide. Small area models are formulated with random area-specific effects assumed to account for the between-area variation that is not explained by auxiliary variables. The unit level models relate the unit values of a study variable to unit-specific covariates. The main aim of this paper is to consider small area estimation under unit level models based on count data. In particular, instead of modelling the variables assuming the Poisson distribution, which is a usual choice, we consider the square root transformation of the original data. One practical advantage is that the proposed transformation achieves approximate homoscedasticity of the error variances, reducing one layer of estimation problem. Inference for the model is carried out under the hierarchical Bayes approach. The square root transformation is evaluated under a simulation study and two design-based studies with real datasets.