ABSTRACT
Estimating a large set of parameters reliably is often the goal of many small area analyses. This chapter and the next (Chapter 8) presents a family of Bayesian hierarchical models defined at the unit level where outcome values are reported at the individual (household) level. Bayesian hierarchical models encompass all the area-specific parameters within a common prior distribution. This hierarchical structure on the parameters gives rise to a distinctive feature known as information borrowing – the ability to borrow (or share) information across areas when estimating the area-specific parameters. This feature allows estimation of a large set of parameters in a way that addresses the issues arising from heterogeneity and data sparsity. We start by introducing the Newcastle household-level income data, the illustrative example that will run through both this chapter and the next, and describe four strategies for modelling the area-specific parameters. Two non-hierarchical models are first constructed and applied to the income data in order to illustrate their shortcomings (Strategies 1 and 2). Then a Bayesian hierarchical model with the so-called “exchangeable” structure on the area-specific parameters – a modelling structure that allows information to be shared globally within the study region – is presented (Strategy 3).
