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

Chapter 7Model Checking and Model Comparison

In the previous chapter, we estimated models with WinBUGS and performed convergence checks for the Markov chains. Now that we are producing samples from the posterior distributions, it is time to examine the performance of the model with respect to the data itself. We can examine how well a given model fits the data. We can also compare different models with each other in terms of fit. In this chapter, we will examine ways of checking our models using WinBUGS. We will also discuss Bayesian approaches to model comparison.

7.1 Graphical Model Checking

We estimate models in an attempt to understand and explain data. Ideally, our model will be a succinct and parsimonious way of describing the relationships occurring within our data. To find out if our model reasonably approximates the relationships in our data, we can examine whether the predictions of the model are consistent with the actual outcomes. We call these activities model checking because we are checking the model's predictions against the actual outcomes.

7.1.1 In Practice: Graphical Fit Plots

In this section, we use the data appearing in McCutchen (1993). McCutchen (1993) examined the determinants of research and development expenditures in the pharmaceutical industry in the 1980s. Twenty pharmaceutical firms were selected from a pool of 36 firms for the study. McCutchen provides each firm's R&D development expenditures in 1980 divided by its 1980 total sales, and we use ...