Bayesian Methods for Management and Business: Pragmatic Solutions for Real Problems

Chapter 8Hierarchical Models

The models we have considered so far in this book have made an important assumption: that each observation arises in a consistent, independent manner with respect to all other observations after accounting for its predicted value. The data may not always have this property. Consider salaries at a firm. A worker's salary from year to year does not usually jump up and down in an independent manner. Instead, if you know the salary at a given time, you may have a fairly good idea where it has been in the previous six months and where it would be six months in the future. It would probably be easier to guess where this worker's salary would be in six months than it would be to guess the salary of some other randomly selected worker.

In this chapter, we will examine models for data that have a structure where certain data points are believed to be more similar than others. This data is often called panel data, repeated measures data, or longitudinal data. Models for this kind of data also have various names that have arisen in different disciplines. These names include hierarchical models, multilevel models, random-effects models, variance-components models, and mixed models. No matter what the name is, hierarchical models have much to offer to those wishing to understand business problems and are a natural extension of conventional linear models. Many business datasets arise as panels, and so it is important to have models for this type of data.

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