Some Relationships Are Never Meant To Be

The Problem with Dyadic Data: It’s All Connected

Including Structure in Our Analyses

We need to account for the way ties are formed and structured.

• Defense alliances (Transitivity/Triangles): If A and B have a defense alliance, and B and C have one, then A and C are more likely to have a defense alliance.

• International trade (Reciprocity/Mutual Ties): If A exports a raw commodity to B, B is unlikely to export that same raw commodity back to A.

• Conflict: War between two states might increase the probability of a third state intervening.

The Solution: Exponential Random Graph Models

Allow us to model how the presence of specific network structures influences the probability of any given tie forming.

• The models treat the formation of ties as a function of both actor attributes (nodal covariates) and network structure (endogenous features)

• They model the entire network structure rather than just individual ties

The Basic Logic of ERGMs

ERGMs work by defining a probability distribution over the set of all possible networks on a given set of nodes.

But Wait! Directed Node Constraints

In many political processes, not all actors can send or receive ties. Using the full sample space of possible networks is incorrect when certain ties are impossible.

• International Trade: Not all states produce certain goods for export, restricting their role to importers only for those goods

• Judicial Systems: Higher courts cannot appeal to lower courts

• Foreign Aid: Developing countries that receive foreign aid often lack the capacity to provide aid themselves

The Novel Contribution: The New Sample Space

Model the network using a constrained sample space.

• Nodes that are restricted to send-only or receive-only ties are excluded from the possibility of forming the prohibited tie types

The Novel Contribution: The New Sample Space

Proving Improvements: Constrained ERGMs

• The restricted sample space leads to improved model fit and often yields stronger or more precise estimates of the structural effects (e.g., Reciprocity or Transitivity)

• The results are now based on a sample space that is theoretically congruent with the actual political process being studied

Proving Improvements

Goodness of Fit - Unconstrained

Goodness of Fit - Constrained

Conclusion

Use ERGMs in Political Science!

• ERGMs are a powerful framework to analyze interdependent networked political phenomena

• They provide unbiased and consistent estimates of tie formation by simultaneously modeling structural and nodal effects

• Here are two introductory posts that include the R code to get you started:

  • Part 1: Introduction to ERGMs

  • Part 2: Advanced ERGM Techniques

Conclusion

Use the Constrained Modification!

• When nodes are restricted to only send or receive ties (e.g., trade, aid, courts), the constrained sample space is necessary

• This novel modification yields a more precise and theoretically sound model of the political process, improving our explanatory and predictive power