On the Application of Discrete Marginal Graphical Models

Abstract

Graphical models are defined by general and possibly complex conditional independence assumptions and are well suited to model direct and indirect associations and effects that are of central importance in many problems of sociology. Such relevance is apparent in research on social mobility. This article provides a unified view of many of the graphical models discussed in a largely scattered literature. The marginal modeling framework proposed here relies on parameters that capture aspects of associations among the variables that are relevant for the graph and, depending on the substantive problem at hand, may lead to deeper insight than other approaches. In this context, model search, which uses a sequence of nested models, means the restriction of increasing subsets of parameters. As a special case, general path models for categorical data are introduced. These models are applied to the social status attainment process, generating substantive results and gaining new insights into the difference between liberal and conservative welfare systems. To help others use these models, all details of the analyses are posted on the Web site for this article at http://nemethr.web.elte.hu/discrete-graphical-models/. Researchers can thus easily modify the analyses to their own data and models.