A0708
Title: A spike-and-slab prior for dimension selection in generalized linear network eigenmodels
Authors: Joshua Loyal - Florida State University (United States) [presenting]
Yuguo Chen - University of Illinois at Urbana-Champaign (United States)
Abstract: Latent space models (LSMs) are frequently used to model network data by embedding a network's nodes into a low-dimensional latent space; however, choosing the dimension of this space remains a challenge. To this end, the aim is to begin by formalizing a class of LSMs called generalized linear network eigenmodels (GLNEMs) that can model various edge types (binary, ordinal, non-negative continuous) found in scientific applications. This model class subsumes the traditional eigenmodel by embedding it in a generalized linear model with an exponential dispersion family random component and fixes identifiability issues that hindered interpretability. Next, a Bayesian approach is proposed to dimension selection for GLNEMs based on an ordered spike-and-slab prior that provides improved dimension estimation and satisfies several appealing theoretical properties. It is shown that the model's posterior is consistent and concentrates on low-dimensional models near the truth. The approach's consistent dimension selection is demonstrated on simulated networks. Lastly, GLNEMs are used to study the effect of covariates on the formation of networks from biology, ecology, and economics and the existence of residual latent structure.
