## The Annals of Applied Statistics

- Ann. Appl. Stat.
- Volume 11, Number 1 (2017), 427-455.

### Inference for social network models from egocentrically sampled data, with application to understanding persistent racial disparities in HIV prevalence in the US

Pavel N. Krivitsky and Martina Morris

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#### Abstract

Egocentric network sampling observes the network of interest from the point of view of a set of sampled actors, who provide information about themselves and anonymized information on their network neighbors. In survey research, this is often the most practical, and sometimes the only, way to observe certain classes of networks, with the sexual networks that underlie HIV transmission being the archetypal case. Although methods exist for recovering some descriptive network features, there is no rigorous and practical statistical foundation for estimation and inference for network models from such data. We identify a subclass of exponential-family random graph models (ERGMs) amenable to being estimated from egocentrically sampled network data, and apply pseudo-maximum-likelihood estimation to do so and to rigorously quantify the uncertainty of the estimates. For ERGMs parametrized to be invariant to network size, we describe a computationally tractable approach to this problem. We use this methodology to help understand persistent racial disparities in HIV prevalence in the US. We also discuss some extensions, including how our framework may be applied to triadic effects when data about ties among the respondent’s neighbors are also collected.

#### Article information

**Source**

Ann. Appl. Stat., Volume 11, Number 1 (2017), 427-455.

**Dates**

Received: March 2015

Revised: December 2016

First available in Project Euclid: 8 April 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aoas/1491616887

**Digital Object Identifier**

doi:10.1214/16-AOAS1010

**Mathematical Reviews number (MathSciNet)**

MR3634330

**Zentralblatt MATH identifier**

1366.62225

**Keywords**

Social network ERGM random graph egocentrically sampled data pseudo maximum likelihood pseudolikelihood

#### Citation

Krivitsky, Pavel N.; Morris, Martina. Inference for social network models from egocentrically sampled data, with application to understanding persistent racial disparities in HIV prevalence in the US. Ann. Appl. Stat. 11 (2017), no. 1, 427--455. doi:10.1214/16-AOAS1010. https://projecteuclid.org/euclid.aoas/1491616887

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#### Supplemental materials

- Appendices A–C. Additional derivations and results referenced in Sections 5, 6, 7, and 8.Digital Object Identifier: doi:10.1214/16-AOAS1010SUPPSupplemental files are immediately available to subscribers. Non-subscribers gain access to supplemental files with the purchase of the article.

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