Growing Collaborations
expected accretion and decay , respectively . Expected values are drawn from the fixed initial conditions control ; the count of links only in the observed network for the control output provide the expected accretion while the count of links only in the forecast network provide the expected decay . Our model tracks the count of links added and deleted in each algorithm repetition , takes averages across all the repetitions in each model run and reports that average ( see Figure 2 ). For the existing subnetworks , used in phase 1 , the expected decay is not measured for either the control runs or model algorithm runs since decay is not permitted in phase 1 . The ratio values in table 5 allow for determining the rate of either over- or underforecasting both accretion and decay . Our results show that our model over-forecasts decay at a consistent rate , while the ratio is less consistent for accretion .
Discussion
An Agent Based Method for Forecasting Network Growth
Network theory recognizes homophily , heterophily , transitivity , and preferential attachment as bases for agents ’ link selection ( Wasserman and Faust , 1994 ). Though it cannot be assumed that these are the only factors driving network formation , networks do form from individual agents , whether organizations or persons , applying these four decision criteria . The results in tables 3 and 4 show that ERGM can provide not only a careful assessment of how a network developed from these four criteria but that that assessment can be repurposed to forecast future change . In forecasting the 2014 subnetworks from the 2012 subnetworks , we achieved error rates comparable to those of the fixed initial conditions control and better than achieved by the Erdos-Renyi control . The stochastic elements of our algorithm will require multiple runs for any real forecast , but the stochastic elements will also allow for both serendipitous change and the calculation of confidence intervals for how different a forecasted network will be from an existing network .
The ratios calculated in table 5 can provide a weighting parameter to the model that offers a means of calibration for an ABM that applies our forecasting algorithm . After applying our algorithm for accretion and either of Burt ’ s ( 2000 , 2002 ) algorithms for decay , any threshold value could be weighted by this ratio to improve the fit of the general algorithm to the specific network . This process would require at least two periods of network data to execute . Sufficiently rich network data can be difficult to obtain ; dynamic network analyses of the growth of scientific collaboration networks have been successful due in part to the ready availability of dynamic network data from databases of published works that , as of the time of Barabasi et al .’ s ( 2002 ) publication , contained almost 71,000 scientific articles from around 210,000 different authors ( Barabasi et al ., 2002 ). Dynamic network analyses have been unable to address mechanisms of change due at least in part to the lack of readily available data about the scientists whose research is cataloged in the databases . We sought a method that would support forecasting using a single period of data . We found a single period of data to be sufficient to prove only that our algorithm could make plausible forecasts but that more data are needed to make accurate forecasts .
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