Approximate hierarchical Bayes small area estimation using NEF-QVF and poststratification

TL;DR

This paper introduces an approximate hierarchical Bayes method using NEF-QVF for small area estimation, combining multiple data sources without requiring a full population model, and allowing for practical model selection.

Contribution

It presents a novel Bayesian approach that avoids modeling all units and links multiple data sources for improved small area estimates.

Findings

Method applied to real survey data demonstrating effectiveness

Provides practical model selection procedures

Improves estimates without full population modeling

Abstract

We propose an approximate hierarchical Bayes approach that uses the Natural Exponential Family with Quadratic Variance Function in combining information from multiple sources to improve traditional survey estimates of finite population means for small areas. Unlike other Bayesian approaches in finite population sampling, we do not assume a model for all units of the finite population and do not require linking sampled units to the finite population frame. We assume a model only for the finite population units in which the outcome variable is observed; because, for these units, the assumed model can be checked using existing statistical tools. We do not posit an elaborate model on the true means for unobserved units. Instead, we assume that population means of cells with the same combination of factor levels are identical across small areas, and that the population mean for a cell is identical to the mean of the observed units in that cell. We apply our proposed methodology to a real-life survey, linking information from multiple disparate data sources. We also provide practical ways of model selection that can be applied to a wider class of models under similar setting but for a diverse range of scientific problems.