How to Turn Linear Modeling into a study of Networks and Fields

LOCATION: 509 Knox Hall

Conventional regression modeling and its generalizations often apply to a matrix of cases-by-variables, analogous to the two-mode arrays often studied in network science, and pertain exclusively to relations among variables. In this talk however I show that such modeling has a dual, and that it may be turned “inside out,” in that the usual regression coefficients and predicted values may in fact be usefully defined and computed from a network among the cases. Research on network modeling, and insights from sociological field theory, may be applied to this network, and doing so leads to new insight about the organizational and relational underpinnings of regression models and their applications. I review recent work of my research group on these topics, and discuss several different examples involving welfare states and other forms of social organization. We seek to use the variables to learn about the cases. Among the gains of our approach: aggregating regression coefficients over an entire sample (as is usually done) may mask systematic variability that our approach helps to sort out (some sets of cases may be associated with strong positive effects while others exhibit strong negative effects). Standard regression models (and generalizations) can be understood from the perspective of sociological field theory. I argue that, rather than seeking to transcend “general linear reality,” relationally-oriented students of social organization should seek to get more out of it.

Ronald Breiger is Professor of Sociology at the University of Arizona. He is Regents’ Professor at that institution, effective July 2016. His interests include social networks, adversarial networks, stratification, mathematical models, theory, and measurement issues in cultural and institutional analysis. He currently serves as Editor for Social and Political Science for the Cambridge University Press journal Network Science.