## The Annals of Applied Statistics

### Latent space models for multiview network data

#### Abstract

Social relationships consist of interactions along multiple dimensions. In social networks, this means that individuals form multiple types of relationships with the same person (e.g., an individual will not trust all of his/her acquaintances). Statistical models for these data require understanding two related types of dependence structure: (i) structure within each relationship type, or network view, and (ii) the association between views. In this paper, we propose a statistical framework that parsimoniously represents dependence between relationship types while also maintaining enough flexibility to allow individuals to serve different roles in different relationship types. Our approach builds on work on latent space models for networks [see, e.g., J. Amer. Statist. Assoc. 97 (2002) 1090–1098]. These models represent the propensity for two individuals to form edges as conditionally independent given the distance between the individuals in an unobserved social space. Our work departs from previous work in this area by representing dependence structure between network views through a multivariate Bernoulli likelihood, providing a representation of between-view association. This approach infers correlations between views not explained by the latent space model. Using our method, we explore 6 multiview network structures across 75 villages in rural southern Karnataka, India [Banerjee et al. (2013)].

#### Article information

Source
Ann. Appl. Stat., Volume 11, Number 3 (2017), 1217-1244.

Dates
Revised: April 2016
First available in Project Euclid: 5 October 2017

https://projecteuclid.org/euclid.aoas/1507168828

Digital Object Identifier
doi:10.1214/16-AOAS955

Mathematical Reviews number (MathSciNet)
MR3709558

Zentralblatt MATH identifier
1380.62269

#### Citation

Salter-Townshend, Michael; McCormick, Tyler H. Latent space models for multiview network data. Ann. Appl. Stat. 11 (2017), no. 3, 1217--1244. doi:10.1214/16-AOAS955. https://projecteuclid.org/euclid.aoas/1507168828

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#### Supplemental materials

• Supplement to “Latent space models for multiview network data”. Additional results and replication codes are provided in the supplementary materials.