Exploration of Dependencies among Sections in a Supermarket Using a Tree-Structured Undirected Graphical Model

In research of purchase behavior in a supermarket, it is important to understand dependencies among sections of the supermarket, with each section corresponding to a category of items. An undirected graphical model is a powerful tool for this purpose. A problem with the application of an undirected graphical model is that there are many variables and, thus, a lot of computation is needed. In this article, we first apply a tree-structured undirected graphical model to reduce the computational amount, and second, propose a method to impose a restriction, based on our needs, on the tree structured undirected graphical model. The variables we use are the length of time spent in each section and the number of items bought from each section. We found that some of the sections have influence on the adjacent sections and that some of the other sections have no influence on the adjacent sections, but do have influence on the nonadjacent sections. We also found that the number of items and the length of stationary time in the sections that influence a large number of sections are negatively related to those same variables in the other sections. Based on this result, managerial implications are described. Finally, we summarize this article and discuss some problems in the application of graphical models.