Melbourne School of Psychological Sciences - Research Publications

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    New specifications for exponential random graph models
    Snijders, TAB ; Pattison, PE ; Robins, GL ; Handcock, MS ; Stolzenberg, RM (WILEY-BLACKWELL, 2006)
    The most promising class of statistical models for expressing structural properties of social networks observed at one moment in time is the class of exponential random graph models (ERGMs), also known as p* models. The strong point of these models is that they can represent a variety of structural tendencies, such as transitivity, that define complicated dependence patterns not easily modeled by more basic probability models. Recently, Markov chain Monte Carlo (MCMC) algorithms have been developed that produce approximate maximum likelihood estimators. Applying these models in their traditional specification to observed network data often has led to problems, however, which can be traced back to the fact that important parts of the parameter space correspond to nearly degenerate distributions, which may lead to convergence problems of estimation algorithms, and a poor fit to empirical data. This paper proposes new specifications of exponential random graph models. These specifications represent structural properties such as transitivity and heterogeneity of degrees by more complicated graph statistics than the traditional star and triangle counts. Three kinds of statistics are proposed: geometrically weighted degree distributions, alternating k-triangles, and alternating independent two-paths. Examples are presented both of modeling graphs and digraphs, in which the new specifications lead to much better results than the earlier existing specifications of the ERGM. It is concluded that the new specifications increase the range and applicability of the ERGM as a tool for the statistical analysis of social networks.
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    Changing places: the impact of rural restructuring on mental health in Australia
    Fraser, C ; Jackson, H ; Judd, F ; Komiti, A ; Robins, G ; Murray, G ; Humphreys, J ; Pattison, P ; Hodgins, G (ELSEVIER SCI LTD, 2005-06)
    Significant demographic, social and economic change has come to characterise much of rural Australia, with some authors arguing there are now two sharply differentiated zones, one of growth and one of decline. This restructuring process, which has been similar to other western nations, has had a profound impact upon rural places-socially, economically and physically. Findings from research investigating the relationship between health, place and income inequality suggest that rural 'desertification', which is characterised by decline of the agricultural sector, net population loss and the deterioration of demographic structures, may negatively influence mental health outcomes in these areas. By contrast, the growth in rural areas, which is associated with expanding employment opportunities and the movement of capital and people, may confer positive benefits to mental health. The aim of this study was to investigate differences in mental health and well-being between rural communities experiencing growth and decline as measured by net population change. Utilising a survey methodology, questionnaires were distributed to 20,000 people randomly sampled from the electoral role in rural Australia. We selected four sub-regions from the sample area that were characteristic of areas experiencing population growth and decline in Australia and analysed the results of respondents from these four regions (n = 1334). The analysis provided support for our hypothesis that living in a declining area is associated with poorer mental health status; however, the factors that underpin growth and decline may also be important in influencing mental health. Discussed are the mechanisms by which demographic and social change influence mental health. The findings of this study highlight the diversity of health outcomes in rural areas and suggest that aspects of place in declining rural areas may present risk factors for mental health.
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    Recent developments in exponential random graph (p*) models for social networks
    Robins, G ; Snijders, T ; Wang, P ; Handcock, M ; Pattison, P (ELSEVIER, 2007-05)
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    An introduction to exponential random graph (p*) models for social networks
    Robins, G ; Pattison, P ; Kalish, Y ; Lusher, D (ELSEVIER, 2007-05)
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    Small and other worlds: Global network structures from local processes
    Robins, G ; Pattison, P ; Woolcock, J (UNIV CHICAGO PRESS, 2005-01)
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    Manufacturing relations: An empirical study of the organization of production across multiple networks
    Lomi, A ; Pattison, P (INFORMS, 2006)
    Organizational communities present two generic features that are recurrently documented in empirical studies, but only imperfectly accounted for in current models of interorganizational relations. The first is the tendency of participant organizations to construct observed macrostructure locally, through relational activities that involve only a small subset of possible network ties. The second is the tendency for different types of ties to overlap, concatenate, and induce a variety of local structures - or relational motifs - across network domains. A critical task in the analysis of organizational communities is to specify appropriate local dependence structures across multiple networks, starting from detailed observation of dyadic interaction among participants. In this paper we illustrate one way in which this analytical task might be accomplished in the context of a study of interorganizational networks. We use data that we have collected on different types of relationships among 106 organizations, located in Southern Italy, involved in the production of means of transportation to test hypotheses about patterns of local network ties and paths across multiple networks. Our empirical analysis is guided by the general claim that the formation of network ties is subject to endogenous and exogenous processes. We specify statistical models for random graphs that allow us to examine this claim, and to formulate and test specific hypotheses about the form that such network-based processes might take. The results that we report provide clear empirical support for the relational motifs implied by our hypotheses. We also find strong empirical support for the proposition that interorganizational dependencies extend across multiple networks.