Multivariate Analysis as a Network Problem
Ron Breiger, University of Arizona (Sociology)
There was a time when network analysis was concerned exclusively with who-to-whom (“one-mode”) data. Much of the history of network research however has been written as the result of an expanded vision as to what constitutes a network (consider for example: affiliation networks, multi-mode formulations, and McPherson’s ecology of organization types based on overlaps among typical members within an innovative conceptualization of multivariate space). Regression modeling and its many generalizations aim to study networks among variables; relations among the cases are, for the most part, rendered invisible. However, David Melamed (U. of South Carolina) and I and other members of my research group have recently been formulating a dual to regression modeling that I will present and illustrate in this talk. We seek to use the variables to learn about the cases. Building on existing results, bringing them together in new ways and adding a bit, we show how the regression coefficients produced in conventional analyses may be usefully understood as sums across cases and clusters of cases (a two-mode formulation). Predicted values on the outcome variable in logistic (and other) regression models may be seen to be produced from a particular (one-mode projection) network among the cases. Among the gains of our approach: aggregating regression coefficients over an entire sample 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). We use an analysis of clustering among the cases to help us uncover statistical interactions among variables. We show that standard regression models (and generalizations) can be understood from the perspective of sociological field theory. Rather than “transcending” general linear reality, we seek to get more out of it.
October, 27 2014 | 12:30 - 14:00 | Gross Hall 230E