Melbourne School of Psychological Sciences - Research Publications
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ItemDiversity and Community Can Coexist(WILEY, 2016-03)We examine the (in)compatibility of diversity and sense of community by means of agent-based models based on the well-known Schelling model of residential segregation and Axelrod model of cultural dissemination. We find that diversity and highly clustered social networks, on the assumptions of social tie formation based on spatial proximity and homophily, are incompatible when agent features are immutable, and this holds even for multiple independent features. We include both mutable and immutable features into a model that integrates Schelling and Axelrod models, and we find that even for multiple independent features, diversity and highly clustered social networks can be incompatible on the assumptions of social tie formation based on spatial proximity and homophily. However, this incompatibility breaks down when cultural diversity can be sufficiently large, at which point diversity and clustering need not be negatively correlated. This implies that segregation based on immutable characteristics such as race can possibly be overcome by sufficient similarity on mutable characteristics based on culture, which are subject to a process of social influence, provided a sufficiently large "scope of cultural possibilities" exists.
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ItemFast Maximum Likelihood Estimation via Equilibrium Expectation for Large Network Data(NATURE PORTFOLIO, 2018-07-31)A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach becomes increasingly problematic as network size increases. In the context of current research on efficient estimation of models for large network data sets, we propose a fast algorithm for maximum likelihood estimation (MLE) that affords a significant increase in the size of networks amenable to direct empirical analysis. The algorithm we propose in this paper relies on properties of Markov chains at equilibrium, and for this reason it is called equilibrium expectation (EE). We demonstrate the performance of the EE algorithm in the context of exponential random graph models (ERGMs) a family of statistical models commonly used in empirical research based on network data observed at a single period in time. Thus far, the lack of efficient computational strategies has limited the empirical scope of ERGMs to relatively small networks with a few thousand nodes. The approach we propose allows a dramatic increase in the size of networks that may be analyzed using ERGMs. This is illustrated in an analysis of several biological networks and one social network with 104,103 nodes.
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ItemExponential random graph model parameter estimation for very large directed networks(PUBLIC LIBRARY SCIENCE, 2020-01-24)Exponential random graph models (ERGMs) are widely used for modeling social networks observed at one point in time. However the computational difficulty of ERGM parameter estimation has limited the practical application of this class of models to relatively small networks, up to a few thousand nodes at most, with usually only a few hundred nodes or fewer. In the case of undirected networks, snowball sampling can be used to find ERGM parameter estimates of larger networks via network samples, and recently published improvements in ERGM network distribution sampling and ERGM estimation algorithms have allowed ERGM parameter estimates of undirected networks with over one hundred thousand nodes to be made. However the implementations of these algorithms to date have been limited in their scalability, and also restricted to undirected networks. Here we describe an implementation of the recently published Equilibrium Expectation (EE) algorithm for ERGM parameter estimation of large directed networks. We test it on some simulated networks, and demonstrate its application to an online social network with over 1.6 million nodes.
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ItemUltrametric distribution of culture vectors in an extended Axelrod model of cultural dissemination(NATURE PORTFOLIO, 2014-05-02)The Axelrod model of cultural diffusion is an apparently simple model that is capable of complex behaviour. A recent work used a real-world dataset of opinions as initial conditions, demonstrating the effects of the ultrametric distribution of empirical opinion vectors in promoting cultural diversity in the model. Here we quantify the degree of ultrametricity of the initial culture vectors and investigate the effect of varying degrees of ultrametricity on the absorbing state of both a simple and extended model. Unlike the simple model, ultrametricity alone is not sufficient to sustain long-term diversity in the extended Axelrod model; rather, the initial conditions must also have sufficiently large variance in intervector distances. Further, we find that a scheme for evolving synthetic opinion vectors from cultural "prototypes" shows the same behaviour as real opinion data in maintaining cultural diversity in the extended model; whereas neutral evolution of cultural vectors does not.