POWRE: Gibbs Regression for Social Networks

University Of Georgia Research Foundation Inc, Athens GA

Investigators

Abstract

This research investigates a Gibbs regression model, which quantifies overall and individual-level effects simultaneously for a social network while modeling a desired response from an individual within that network. This model may be viewed as an extension of a logistic regression model to include a term for modeling pairwise interactions between responses; it may also be viewed as a Gibbs random field on a complete graph; hence, the model's name. A very promising preliminary application of this model to mental health service data took a practical nonparametric approach to estimating the interactions, and precipitated the development of a Markov chain Monte Carlo goodness-of-fit test. The PI will explore the model further using new data gathered specifically for use with Gibbs regression, modeling responses such as whether clients find adequate housing or receive necessary treatment for illness and/or substance abuse. This model holds great theoretical and applied potential. The wealth of questions which arise from this model address parameter estimation, model selection, and model diagnostics. Answering these questions will involve extending and unifying aspects of both logistic regression and random fields, and will include both the frequentist and Bayesian perspectives. Towards applications, the Gibbs regression will be useful for modeling networks of dependent multinomial responses in any field of scientific research (e.g., the social aspect of spread and severity of disease; the relatedness of languages or cultural artifacts; perhaps even the effects of seemingly unrelated gene clusters on inherited characteristics). The POWRE program is a particularly appropriate avenue for funding this research due to its exploratory nature. Though it is a ripe area of research for a young researcher such as the PI, it requires a little more development before it is worthy of a full NSF research grant proposal. The POWRE award also enhances the career of the PI, which - in spite of a necessarily slow start due to a "two-body problem" - is at its critical pre-tenure stage.