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.

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

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

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

Network structure and rapid HIV transmission among people who inject drugs: A simulation-based analysis

As HIV incidence among people who inject drugs grows in the context of an escalating drug overdose epidemic in North America, investigating how network structure may affect vulnerability to rapid HIV transmission is necessary for preventing outbreaks. We compared the characteristics of the observed contact tracing network from the 2015 outbreak in rural Indiana with 1000 networks generated by an agent-based network model with approximately the same number of individuals (n = 420) and ties between them (n = 913). We introduced an initial HIV infection into the simulated networks and compared the subsequent epidemic behavior (e.g., cumulative HIV infections over 5 years). The model was able to produce networks with largely comparable characteristics and total numbers of incident HIV infections. Although the model was unable to produce networks with comparable cohesiveness (where the observed network had a transitivity value 35.7 standard deviations from the mean of the simulated networks), the structural variability of the simulated networks allowed for investigation into their potential facilitation of HIV transmission. These findings emphasize the need for continued development of injection network simulation studies in tandem with empirical data collection to further investigate how network characteristics played a role in this and future outbreaks

Effects of External Vibration Stimulation on Shoulder Internal Rotation and Hamstring Strength

Introduction Percussion therapy has gained popularity in recent years for its effectiveness in both rehabilitation and sports performance. Percussion therapy is an instrument-assisted treatment targeting soft tissue structures using torque, amplitude, and frequency for delivery. 1 Objective Evaluate the effects of localized percussion application treatment to the gluteal and sacral region on shoulder internal rotation (IR) range of motion (ROM) and isometric hamstring strength using the concept of regional interdependence 2,4,5 Participants 54 healthy adults from Concordia University - St. Paul and local exercise facilities 21 females 33 males Average age: 23.9 Methods Pre-therapeutic intervention measurements Supine shoulder IR ROM with manual goniometry Prone hamstring strength using MicroFET™ 3 Therapeutic intervention: application of percussion via Hypervolt PlusⓇ to 5 landmarks on the gluteal region for 40 seconds total Post-therapeutic intervention measurements Prone hamstring strength using MicroFET™ Supine shoulder IR ROM with manual goniometry3 Results Statistical significance (p \u3c 0.05) demonstrated for increased shoulder IR (mean difference 4.78°) and for increased hamstring strength (mean difference 2.8#) Conclusion Improvements in both measurements were found post application of percussion, theorized to be a result of neural facilitation and regional interdependence Clinical Relevance Application to a non-local site impacting a distal irritated joint. Facilitation of strength and ROM for athletes, such as a pitcher with impingement or a runner with hamstring deficits. 5 Future Research Assessment of the duration of the percussive effects following application. Assessment of the effectiveness on a population with injuries

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