Dynamic Social Network Modeling and Analysis Workshop Summary and Papers (2003) / Chapter Skim
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Local Rules and Global Properties: Modeling the Emergence of Network Structure
Local Rules and Global Properties: Modeling the Emergence of Network Structure
Pages 174-186
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From page 174... ...
social network theory explicitly focused on the link between local dynamics and ~,lobal structures. One root can be traced back to social anthropology and exchange theory.
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The descriptive approach drew inspiration from mathematical graph theory, using tools from linear algebra to manipulate the adjacency matnx, and focusing on issues of clustering and connectivity. These tools have become the heart of the field, providing a rich framework for thinking about networks and a wide range of summary measures to represent both the network position occupied by specific nodes, and the overall network structure.
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The simplest spatial models represent observations as points on a lattice, and assume that only the nearest neighbors have an influence on the status of a site. For example, imagine an agricultural plot, divided into a grid along two orthogonal axes (see Figure I
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Because the nature of the "spatial" dependence is the primary focus of interest in network analysis, the parameters that define this dependence are not nuisance parameters, but the parameters of most interest. This also changes the kinds of models that are appropriate DYNAMIC SOCIAL NETWORK MODELING ED ISIS 177
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From page 178... ...
is still referred to as a dyad~c independence model. But products of non-reciprocal links are a fairly straightforward generalization, and models with these terms are referred to as dyadic dependence models.
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Here, as there, these are essentially nuisance parameters. Homogeneity constraints are often imposed for parsimony, but they can also be used to represent exogenous covanates.
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Models are the bridge between theory and data. And while there is a certain attraction to simple abstract forms, like Markov graphs, small world graphs, or scale free networks, the simplification we seek will be embedded in each substantive context.
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tIlO overall network secure won a small number of partnership formation mIes that operate at the local individual level. If this is true, it will radically simplify data collection needs, and give network analysis a central place in the tools of sexually transmitted infection (STI)
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From page 182... ...
-- rat =, ~ =~ .~ .~_ Linking network data to network simulation requires a statistical bndge: a modeling framework that enables the key structural parameters to be estimated from network data, so that these can be used to directly drive a simulation. ERGMs have the potential to do this.
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From page 183... ...
In addition to providing, more accurate estimates, this approach is particularly interesting for our purposes because the MCMC method effectively simulates the network in order to maximize the likelihood. We can, however, just as easily use the MCMC algorithm to simulate the network given the parameter estimates, and this provides the ideal solution to the problem of lining network data to the network simulation.
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From page 184... ...
This makes it possible to test whether the local organizing features represented in the model reproduce the larger structural features of the network. We can therefore develop formal tests for the hypothesis that mixing and concurrency capture the epidemiologically relevant vacation in network structure.
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''Cogit models and logistic regressions for social networks: I An introduction to Markov graphs and p*
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186 DYNAMIC SOCIAL NE:TWOltKA1ODEf~G~D TRYSTS
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