Maximum likelihood estimation for social network dynamics

A model for network panel data is discussed, based on the assumption that the observed data are discrete observations of a continuous-time Markov process on the space of all directed graphs on a given node set, in which changes in tie variables are independent conditional on the current graph. The model for tie changes is parametric and designed for applications to social network analysis, where the network dynamics can be interpreted as being generated by choices made by the social actors represented by the nodes of the graph. An algorithm for calculating the Maximum Likelihood estimator is presented, based on data augmentation and stochastic approximation. An application to an evolving friendship network is given and a small simulation study is presented which suggests that for small data sets the Maximum Likelihood estimator is more efficient than the earlier proposed Method of Moments estimator.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS313 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A comparison of various approaches to the exponential random graph model:A reanalysis of 102 student networks in school classes

This paper describes an empirical comparison of four specifications of the exponential family of random graph models (ERGM), distinguished by model specification (dyadic independence, Markov, partial conditional dependence) and, for the Markov model, by estimation method (Maximum Pseudolikelihood, Maximum Likelihood). This was done by reanalyzing 102 student networks in 57 junior high school classes. At the level of all classes combined, earlier substantive conclusions were supported by all specifications. However, the different specifications led to different conclusions for individual classes. PL produced unreliable estimates (when ML is regarded as the standard) and had more convergence problems than ML. Furthermore, the estimates of covariate effects were affected considerably by controlling for network structure, although the precise specification of the structural part (Markov or partial conditional dependence) mattered less. (C) 2007 Elsevier BX All rights reserved

Explained Variation in dynamic network models

A measure for explained variation is proposed for stochastic actor-driven models for data on social networks. The measure is based on the entropy of the distribution of the choices made by the actors during the network evolution process. This measure can be helpful in the specification and interpretation of statistical models for longitudinal network data.On propose une mesure de la part de variation expliquée par un modèle stochastique de la dynamique des réseaux sociaux complets. Cette mesure est fondée sur l'entropie de la distribution des choix faits par les acteurs au cours du processus d'évolution du réseau. Elle a pour but d'aider à effectuer une meilleure interprétation et à sélectionner une spécification appropriée dans l'application des modèles statistiques s'appliquant aux données longitudinales concernant des relations

The Dynamics of Interethnic Friendships and Negative Ties in Secondary School:The Role of Peer-Perceived Ethnicity

This study examines ethnic integration in secondary school. Social identity theory suggests that perception of relevant individual attributes plays a crucial role in defining ingroups and outgroups, contributing to befriending, and disliking others. Therefore, we analyze the role of peer-perceived ethnicity in social ties. Networks of friendship, dislike, and perceived ethnicity were modeled together using dynamic stochastic actor-oriented models, separating the effect of perceived ethnicity on social ties from that of social ties on perceived ethnicity. Data came from a Hungarian sample of 12 school classes with one minority group: the Roma. Treating friendship and dislike as mutually exclusive and comparing them to neutral relations, we found evidence for the role of perceived ethnicity in dislike-majority students disliked those they perceived as minority peers. However, we saw no direct effect of ethnicity on the friendship network. Implications of the joint modeling of mutually exclusive relationship aspects are discussed

Forms of Dependence: Comparing SAOMs and ERGMs From Basic Principles

Two approaches for the statistical analysis of social network generation are widely used; the tie-oriented exponential random graph model (ERGM) and the stochastic actor-oriented model (SAOM) or Siena model. While the choice for either model by empirical researchers often seems arbitrary, there are important differences between these models that current literature tends to miss. First, the ERGM is defined on the graph level, while the SAOM is defined on the transition level. This allows the SAOM to model asymmetric or one-sided tie transition dependence. Second, network statistics in the ERGM are defined globally but are nested in actors in the SAOM. Consequently, dependence assumptions in the SAOM are generally stronger than in the ERGM. Resulting from both, meso- and macro-level properties of networks that can be represented by either model differ substantively and analyzing the same network employing ERGMs and SAOMs can lead to distinct results. Guidelines for theoretically founded model choice are suggested

Modeling Partitions of Individuals

Despite the central role of self-assembled groups in animal and human societies, statistical tools to explain their composition are limited. We introduce a statistical framework for cross-sectional observations of groups with exclusive membership to illuminate the social and organizational mechanisms that bring people together. Drawing from stochastic models for networks and partitions, the proposed framework introduces an exponential family of distributions for partitions. We derive its main mathematical properties and suggest strategies to specify and estimate such models. A case study on hackathon events applies the developed framework to the study of mechanisms underlying the formation of self-assembled project teams

Contemporaneous Statistics for Estimation in Stochastic Actor-Oriented Co-evolution Models

Stochastic actor-oriented models (SAOMs) can be used to analyse dynamic network data, collected by observing a network and a behaviour in a panel design. The parameters of SAOMs are usually estimated by the method of moments (MoM) implemented by a stochastic approximation algorithm, where statistics defining the moment conditions correspond in a natural way to the parameters. Here, we propose to apply the generalized method of moments (GMoM), using more statistics than parameters. We concentrate on statistics depending jointly on the network and the behaviour, because of the importance of their interdependence, and propose to add contemporaneous statistics to the usual cross-lagged statistics. We describe the stochastic algorithm developed to approximate the GMoM solution. A small simulation study supports the greater statistical efficiency of the GMoM estimator compared to the MoM