Skip to main content

Table 1 Network effects included in the Stochastic Actor-oriented Models

From: Global dynamics of international migration systems across South–South, North–North, and North–South flows, 1990–2015

Network effect Equation Visual representation
Outdegree \(\sum\limits_{j} {x_{ij} }\)
Dyadic reciprocity \(\sum\limits_{j} {x_{ij} x_{ji} }\)
Indegree popularity (sqrt) \(\sum\limits_{j} {x_{ij} \sqrt {x_{ + j} } }\)
Outdegree popularity (sqrt) \(\sum\limits_{j} {x_{ij} \sqrt {x_{j + } } }\)
Outdegree activity (sqrt) \(\left( {x_{i + } } \right)^{1.5}\)
Transitive triads \(\sum\limits_{j,h} {x_{ih} x_{ij} x_{jh} }\)
Cyclic triads \(\sum\limits_{j,h} {x_{ij} x_{jh} x_{hi} }\)
Transitive reciprocated triads \(\sum\limits_{j,h} {x_{hi} x_{ih} x_{ij} x_{jh} }\)
GWDSP—mixed-stars \(\sum\limits_{h = 1;h \ne i}^{n} {e^{\alpha } \left\{ {1 - \left( {1 - e^{ - \alpha } } \right)\sum\limits_{j = 1}^{n} {x_{ij} x_{jh} } } \right\}}\)
GWDSP—in-stars \(\sum\limits_{h = 1;h \ne i}^{n} {e^{\alpha } \left\{ {1 - \left( {1 - e^{ - \alpha } } \right)\sum\limits_{j = 1}^{n} {x_{ij} x_{hj} } } \right\}}\)
  1. A dotted line represents the creation of a new tie, based on the existing structure of the network as represented by the solid lines
  2. i represents Ego, j represents an Alter, and h represents an Alter different from j
  3. Xij = 1 if the ordered pair i → j exists (Xij = 0 otherwise)
  4. α represents a tuning parameter that may range from 0 to ∞. As recommend by Snijders et al. (2006), α was fixed at 0.69 to model decreasing marginal returns to indirect connections
  5. Replacing an index (e.g., j) by a + denotes summation over that index