Policy and Complex Systems
finds a structural hole , it uses the following formula to determine the probability that an agent will fill that structural hole :
where :
Calculation of the formula produces a threshold probability for the link to be added , calculated between 0 and 1 . Both organization of the pairing could act to add the link and the model calculates the probability twice , once from each member of the pairing , but ERGM only considers attribute values and pairings based on observed dyads and structural holes . To prevent this double counting , we halved the threshold . A random draw between 0 and 1 determines if the model adds the link . If the random draw value falls below or equal to the threshold , then the link is added . If the random value falls above the threshold , then the link is not added .
Link Decay : Burt ’ s ( 2000 , 2002 ) processes for link decay are calculated
independently , so only one or the other should be applied at a time . We chose to use decay rates of network bridges , without factoring the influence of homophily and heterophily . Use of decay based on homophily and heterophily would create collinearities between accretion and decay while using bridge decay rates would allow the decay algorithm to remain independent of the accretion algorithm and the ERGM . Rates of decay for both bridge and nonbridge links are a function of the link ’ s age such that older links are less likely to decay ( Burt , 2002 ). Rephrased , the older a link is , the more likely it is to persist . When a link is either created through accretion or included in the model ’ s initial conditions , the model records the time . A threshold value is calculated for removal , using the values listed in table 3 . Just as with link accretion , the threshold is halved to prevent double counting and a random draw between 0 and 1 determines whether the model removes the specified link . Draw values equal to or below the threshold result in the link being removed , while draws above the threshold result in the link being retained .
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