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

Chapter 9Generalized Linear Models

Most of the models that have been discussed so far in this book have assumed that the data has a normal distribution. However, there is much variety in business data and a normal distribution is not always the most appropriate one for a particular analysis. In this chapter, we explore models for non-normal data. We will see that we can greatly expand our analytical toolbox with some basic changes to our WinBUGS code.

9.1 Fundamentals of Generalized Linear Models

The normal distribution plays a central role in statistics because of its attractive properties and its applicability. Historically, normal linear models were the first to receive extensive development, and these models (including ANOVA, simple/multiple regression, and ANCOVA) remain important cornerstones of statistical modeling. The true distribution of a given dataset is almost always unknown; however, the normal distribution often makes for a good approximation. Still, many kinds of data do not have a normal distribution even approximately. In Section 2.1, we discussed how coin flips could be modeled with the binomial likelihood function, while in Section 3.7 we discussed modeling count data with the Poisson distribution. A coin flip taking on the vales of heads or tails clearly does not have a normal distribution, and nonnegative integer-valued counts are not well approximated by a normal distribution unless the sample size and the magnitude of the data are both large.

While our ...