Modeling Networks With Ordinal Data

• In Event: 46.028 - Quantitative Methods for the Analysis of Social Network Data in Education

Abstract

The vast majority of studies on social networks assume that the edges are defined only as binary: the tie exists or does not. This means that in cases where the apparent weight of the edge is important, either to inform us about the importance to other edges or to outcomes on the network's members, we may lose a critical degree of information. And because the vast majority of models for social network ties assume binary edges, we are often left in a cycle where the nature of these ties with value are perpetually ignored.

To overcome this deficiency, we show how the Conditionally Independent Dyad model for networks can be easily adapted to process ties whose outcomes are ordinal in nature, with the ordinal value determined by a latent Gaussian variable that determines the strength of the tie. The same latent structures that drive other network models, such as the Stochastic Block Model and Latent Space Model, can be immediately adapted to serve this link function. I demonstrate this on several real-data examples where strengths of ties have been provided in survey data.

Author

• Andrew C. Thomas, Carnegie Mellon University