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

Modelling the evolution of a bipartite network-Peer referral in interlocking directorates

Abstract in Undetermined A central part of relational ties between social actors is constituted by shared affiliations and events. The action of joint participation reinforces personal ties between social actors as well as mutually shared values and norms that in turn perpetuate the patterns of social action that define groups. Therefore the study of bipartitenetworks is central to social science. Furthermore, the dynamics of these processes suggests that bipartitenetworks should not be considered static structures but rather be studied over time. In order to model the evolution of bipartitenetworks empirically we introduce a class of models and a Bayesian inference scheme that extends previous stochastic actor-oriented models for unimodal graphs. Contemporary research on interlockingdirectorates provides an area of research in which it seems reasonable to apply the model. Specifically, we address the question of how tie formation, i.e. director recruitment, contributes to the structural properties of the interlockingdirectoratenetwork. For boards of directors on the Stockholm stock exchange we propose that a prolific mechanism in tie formation is that of peerreferral. The results indicate that such a mechanism is present, generating multiple interlocks between boards

Bayesian Analysis of Social Influence

The network influence model is a model for binary outcome variables that accounts for dependencies between outcomes for units that are relationally tied. The basic influence model was previously extended to afford a suite of new dependence assumptions and because of its relation to traditional Markov random field models it is often referred to as the auto logistic actor-attribute model (ALAAM). We extend on current approaches for fitting ALAAMs by presenting a comprehensive Bayesian inference scheme that supports testing of dependencies across subsets of data and the presence of missing data. We illustrate different aspects of the procedures through three empirical examples: masculinity attitudes in an all-male Australian school class, educational progression in Swedish schools, and un-employment among adults in a community sample in Australia

Simultaneous modeling of initial conditions and time heterogeneity in dynamic networks: An application to Foreign Direct Investments

In dynamic networks, the presence of ties are subject both to endogenous network dependencies and spatial dependencies. Current statistical models for change over time are typically defined relative to some initial condition, thus skirting the issue of where the first network came from. Additionally, while these longitudinal network models may explain the dynamics of change in the network over time, they do not explain the change in those dynamics. We propose an extension to the longitudinal exponential random graph model that allows for simultaneous inference of the changes over time and the initial conditions, as well as relaxing assumptions of time-homogeneity. Estimation draws on recent Bayesian approaches for cross-sectional exponential random graph models and Bayesian hierarchical models. This is developed in the context of foreign direct investment relations in the global electricity industry in 1995–2003. International investment relations are known to be affected by factors related to: (i) the initial conditions determined by the geographical locations; (ii) time-dependent fluctuations in the global intensity of investment flows; and (iii) endogenous network dependencies. We rely on the well-known gravity model used in research on international trade to represent how spatial embedding and endogenous network dependencies jointly shape the dynamics of investment relations

"Predicting" after peeking into the future: Correcting a fundamental flaw in the SAOM -- TERGM comparison of Leifeld and Cranmer (2019)

We review the empirical comparison of SAOMs and TERGMs by Leifeld and Cranmer (2019) in Network Science. We note that their model specification uses nodal covariates calculated from observed degrees instead of using structural effects, thus turning endogeneity into circularity. In consequence, their out-of-sample predictions using TERGMs are based on out-of-sample information and thereby predict the future using observations from the future. We conclude that their analysis rest on erroneous model specifications that render the article's conclusions meaningless. Consequently, researchers should disregard recommendations from the criticized paper when making informed modelling choices