ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks

We describe some of the capabilities of the ergm package and the statistical theory underlying it. This package contains tools for accomplishing three important, and inter-related, tasks involving exponential-family random graph models (ERGMs): estimation, simulation, and goodness of fit. More precisely, ergm has the capability of approximating a maximum likelihood estimator for an ERGM given a network data set; simulating new network data sets from a fitted ERGM using Markov chain Monte Carlo; and assessing how well a fitted ERGM does at capturing characteristics of a particular network data set.

A statnet Tutorial

The statnet suite of R packages contains a wide range of functionality for the statistical analysis of social networks, including the implementation of exponential-family random graph (ERG) models. In this paper we illustrate some of the functionality of statnet through a tutorial analysis of a friendship network of 1,461 adolescents.

statnet: Software Tools for the Representation, Visualization, Analysis and Simulation of Network Data

statnet is a suite of software packages for statistical network analysis. The packages implement recent advances in network modeling based on exponential-family random graph models (ERGM). The components of the package provide a comprehensive framework for ERGM-based network modeling, including tools for model estimation, model evaluation, model-based network simulation, and network visualization. This broad functionality is powered by a central Markov chain Monte Carlo (MCMC) algorithm. The coding is optimized for speed and robustness.

Stochastic blockmodels with growing number of classes

We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least poly-logarithmically in this size. We also establish finite-sample confidence bounds on maximum-likelihood blockmodel parameter estimates from data comprising independent Bernoulli random variates; these results hold uniformly over class assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic blockmodel with covariates to a network data example comprising a collection of Facebook profiles, resulting in block estimates that reveal residual structure.Comment: 12 pages, 3 figures; revised versio

Adjusting for Network Size and Composition Effects in Exponential-Family Random Graph Models

Exponential-family random graph models (ERGMs) provide a principled way to model and simulate features common in human social networks, such as propensities for homophily and friend-of-a-friend triad closure. We show that, without adjustment, ERGMs preserve density as network size increases. Density invariance is often not appropriate for social networks. We suggest a simple modification based on an offset which instead preserves the mean degree and accommodates changes in network composition asymptotically. We demonstrate that this approach allows ERGMs to be applied to the important situation of egocentrically sampled data. We analyze data from the National Health and Social Life Survey (NHSLS).Comment: 37 pages, 2 figures, 5 tables; notation revised and clarified, some sections (particularly 4.3 and 5) made more rigorous, some derivations moved into the appendix, typos fixed, some wording change

Estimating PMTCT's Impact on Heterosexual HIV Transmission: A Mathematical Modeling Analysis

Introduction Prevention of mother-to-child HIV transmission (PMTCT) strategies include combined short-course antiretrovirals during pregnancy (Option A), triple-drug antiretroviral treament (ART) during pregnancy and breastfeeding (Option B), or lifelong ART (Option B+). The WHO also recommends ART for HIV treatment and prevention of sexual transmission of HIV. The impact of PMTCT strategies on prevention of sexual HIV transmission of HIV is not known. We estimated the population-level impact of PMTCT interventions on heterosexual HIV transmission in southwestern Uganda and KwaZulu-Natal, South Africa, two regions with different HIV prevalence and fertility rates. Materials and Methods We constructed and validated dynamic, stochastic, network-based HIV transmission models for each region. PMTCT Options A, B, and B+ were simulated over ten years under three scenarios: 1) current ART and PMTCT coverage, 2) current ART and high PMTCT coverage, and 3) high ART and PMTCT coverage. We compared adult HIV incidence after ten years of each intervention to Option A (and current ART) at current coverage. Results At current coverage, Options B and B+ reduced heterosexual HIV incidence by about 5% and 15%, respectively, in both countries. With current ART and high PMTCT coverage, Option B+ reduced HIV incidence by 35% in Uganda and 19% in South Africa, while Option B had smaller, but meaningful, reductions. The greatest reductions in HIV incidence were achieved with high ART and PMTCT coverage. In this scenario, all PMTCT strategies yielded similar results. Discussion Implementation of Options B/B+ reduces adult HIV incidence, with greater effect (relative to Option A at current levels) in Uganda than South Africa. These results are likely driven by Uganda’s higher fertility rates

Evolving Clustered Random Networks

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as generic models for studying the impacts of degree distributions and clustering on dynamical processes as well as null models for detecting other structural properties in empirical networks

Can Geographical Factors Determine the Choices of Farmers in the Ethiopian Highlands to Trade in Livestock Markets?

Proximity and affiliation to the local market appear to be two of the most relevant factors to explain farmer's choices to select a particular trading point. Physical barriers may limit the options , especially in developing countries. A network of villages linked by traders/farmer-traders sharing livestock markets was built with field data collected in 75 villages from 8 kebelles in the Wassona Werna wereda of the Ethiopian Highlands. Two exponential random graph models were fitted with various geographical and demographic attributes of the nodes (dyadic independent model) and three internal network structures (dyadic dependent model). Several diagnostic methods were applied to assess the goodness of fit of the models. The odds of an edge where the distance to the main market Debre Behran and the difference in altitude between two connected villages are both large increases significantly so that villages far away from the main market and at different altitude are more likely to be linked in the network than randomly. The odds of forming an edge between two villages in Abamote or Gudoberet kebelles are approximately 75% lower than an edge between villages in any other kebelles (p<0.05). The conditional log-odds of two villages forming a tie that is not included in a triangle, a 2-star or a 3-star is extremely low, increasing the odds significantly (p<0.05) each time a node is in a 2-star structure and decreasing it when a node is in a 3-star (p<0.05) or in a triangle formation (p<0.05)), conditional on the rest of the network. Two major constraining factors, namely distance and altitude, are not deterrent for the potential contact of susceptible small ruminant populations in the Highlands of Ethiopia

Correlates of condom use in a sample of MSM in Ecuador

BACKGROUND: In Ecuador, the prevalence of HIV in the general population is approximately 0.3%. However, up to 17% prevalence has been reported among specific groups of homosexual and bisexual men. The objective of this study is to explore correlates of condom use among men who have sex with men (MSM) across eight cities in Ecuador. METHODS: A cross-sectional survey design was used. A questionnaire including variables on sexual behaviour, demographics, and socio-economic characteristics was distributed to a sample of MSM in eight Ecuadorian cities. RESULTS: Information was obtained for 2,594 MSM across the eight cities. The largest subcategory of self-identification was active bisexuals (35%), followed by those who described themselves as "hombrados" (masculine gays, 22%). The mean age was 25 years, and the majority were unmarried (78%), with a median of 10 years of schooling (IQR 7 – 12). Regarding condom use, 55% of those interviewed had unprotected penetrative sex with each of their last three partners, and almost 25% had never used a condom. The most important correlates of condom use were single status, high life-skills rating, and high socio-economic status (RP 5.45, 95% CI 4.26 – 6.37; RP 1.84, 95% CI 1.79 – 1.86, and RP 1.20, 95% CI 1.01 – 1.31, respectively). CONCLUSION: Our data illustrate the urgent need for targeted HIV-prevention programs for MSM populations in Ecuador. MSM have the highest HIV prevalence in the country, and condom use is extremely low. It is imperative that prevention strategies be re-evaluated and re-prioritized to more effectively respond to the Ecuadorian epidemic