Hierarchical Modeling

In this chapter, we illustrate the use of R to summarize an exchangeable hierarchical model. We begin by giving a brief introduction to hierarchical modeling. Then we consider the simultaneous estimation of the true mortality rates from heart transplants for a large number of hospitals. Some of the individual estimated mortality rates are based on limited data and it may be desirable to combine the individual rates in some way to obtain more accurate estimates. We describe a two-stage model, a mixture of gamma distributions, to represent prior beliefs that the true mortality rates are exchangeable. We describe the use of R to simulate from the posterior distribution. We first use contour graphs and simulation to learn about the posterior distribution of the hyperparameters.