4.8 Hierarchical linear regression

In Chapter 3, we learned the rudiments of hierarchical models, a very powerful concept that allows us to model complex data structures. Hierarchical models allow us to deal with inferences at the group level and estimations above the group level. As we have already seen, this is done by including hyperpriors. We also showed that groups can share information by using a common hyperprior and this provides shrinkage, which can help us to regularize the estimates.

We can apply these very same concepts to linear regression to obtain hierarchical linear regression models. In this section, we are going to walk through two examples to elucidate the application of these concepts in practical scenarios. The first one uses a synthetic dataset, and the second one uses the pigs dataset.

For the first example, I have created eight related groups, including one group with just one data point. We can see what the data looks like from Figure 4.15. If you want to learn...