Policy and Complex Systems
network , typically modeled as an Erdos- Renyi random graph of similar size and density ( Erdos & Renyi , 1959 ), to define small world networks . In this control for testing our model ’ s performance , new ties are assigned randomly throughout the network with a fixed probability , equal to the network ’ s density . This control is referred to as the Erdos-Renyi control , since it approximates the method used to calculate an Erdos-Renyi random network . Use of these two controls , the Erdos-Renyi control and the fixed initial conditions control , allows performance to be measured not just by error rates but also by whether or not our model out-performs the controls .
Design Concepts
Emergence : Homophily , heterophily , transitivity , and preferential attachment can be viewed as the measureable outcomes of the underlying decisions that agents make , regardless of whether or not the agents are thinking in terms of networking with similar , dissimilar , multiple acquaintances , or particularly well-connected partners ( Goodreau et al ., 2009 ). All four can be expected to have had an influence on the network ’ s observed structure . ERGM can be applied to measure the influence that each concept had on network formation ( Goodreau et al ., 2009 ). Our approach to preferential attachment differs from Barabasi et al .’ s ( 2002 ) in that , Barabasi et al . ( 2002 ) seek to recreate a specific , observed degree distribution , while we measure the influence that the degree distribution has on agents ’ decision making . With the correct set of attributes , agents ’ decisions regarding the selection of interaction partners throughout the network , measured using an ERGM , can reproduce the observed network and forecast the development of new links in that network .
Stochasticity : The model uses a stochastic method to determine which specific links are to be added and deleted . The algorithms , described under Submodels , determine the probability that any given link will be added or deleted . A random draw then determines whether that link is added or deleted . We repeat the model ’ s algorithm for updating network links 100 times in each model run , with each repetition ’ s results recorded and averaged to produce the model ’ s output . This repetition prevents random outlier cases where the model randomly determines to add a particularly large or small number of links from dominating the model ’ s results . Such dominance would falsely indicate particularly good or particularly poor performance . We then take the average each distance measurement across these process repetitions . The graphs in Figure 2 record the performance of the Hamming and Jaccard distances over a model run .
Details Initialization
The model is initiated using empirical data from a survey of the members of the Vermont Farm to Plate Network . Our research team , in partnership with the Vermont Sustainable Jobs Fund , conducted two network surveys of the organizations that participate in the Farm to Plate Network . These surveys were conducted in 2012 and 2014 and the structure of the survey did not change significantly between the two editions . Links are collected using an alter roster approach where respondents are asked to identify interaction partners from a comprehensive list of potential partners ( Marsden , 2005 ; Pustejovsky & Spillane , 2009 ). The list of network agents does vary between the two editions .
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