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

5.6 Analysis of Variance Models

The -test model of Section 5.3 is designed for the scenario where there are only two groups with means to compare. If there are more than two groups and we only have qualitative independent variables, then the model is called analysis of variance (ANOVA). Extending the -test to an arbitrary (and perhaps large) number of groups leads us to introduce additional capabilities of WinBUGS such as new ways for reading data, new WinBUGS graphical options, and new ways to program parameter comparisons in WinBUGS.

5.6.1 In Practice: One-Way ANOVA

To motivate the use of ANOVA in practice, we examine flows of consumer credit in the United States during the period 2007–2011 as tabulated by the Federal Reserve (Board of Governors of the Federal Reserve System, 2012). The flow of consumer credit is the year-on-year change in credit extended to individuals such that positive values indicate the existence of more credit extended in a given year as compared to the previous year. We examine flows among major nongovernmental holders of consumer credit. Values are in billions of U.S. dollars. The time period covers the period of the 2007–2008 financial crisis and its aftermath. There were five categories of major nongovernmental holders of consumer credit. Annual data ...