Model Tie Formation with Exponential Random Graph Models
Build an ERGM that compares the observed network with plausible alternatives while representing density, reciprocity, closure, and actor attributes explicitly.
Method sources
By the end of this tutorial
- 1Express a network hypothesis as a set of interpretable ERGM terms.
- 2Separate endogenous network structure from actor or dyadic covariates.
- 3Use convergence, simulation, and goodness-of-fit checks before interpreting parameters.
SNA
Network specification
Analysis scenario
A school wants to understand whether a mentoring network reflects simple opportunity, reciprocal choice, triadic closure, or similarity in teaching experience. The observed network is treated as one realization among many networks that could have formed on the same set of educators.
Nodes
Educators participating in one bounded mentoring program.
Ties
A directed tie records that educator A regularly seeks instructional advice from educator B.
Network type
One-mode, directed, binary network with educator attributes and a dyadic same-department indicator.
Step-by-step tutorial
Define the reference process
Begin with an edges term so every additional effect is interpreted relative to the baseline prevalence of ties. State the node set, which dyads were possible, and whether missing nominations mean no tie or missing data.
Checkpoint
You can explain what a network generated by the baseline model would look like and which ties were eligible to occur.
Add theory-driven terms
Represent reciprocity with a mutual term, local closure with an appropriate shared-partner term, and actor or dyadic hypotheses with covariates. Add terms because they answer a research question, not because they improve significance.
Checkpoint
Every term has a written hypothesis, a direction you expect, and a clear distinction between structure and attributes.
Fit and diagnose the model
Inspect MCMC diagnostics, parameter stability, warnings, and signs of degeneracy. Simulate networks from the fitted model and compare statistics that were fitted as well as meaningful statistics that were not included directly.
Checkpoint
Simulated networks are plausible for the study setting and do not collapse into nearly empty or complete graphs.
Interpret conditional associations
Translate coefficients into conditional changes in the log odds of a tie while holding the rest of the network fixed. Report uncertainty, specification choices, goodness of fit, and sensitivity to alternative terms.
Checkpoint
Your conclusion describes modeled association in a bounded network and does not claim that an ERGM alone identified a causal mechanism.
Interpret with care
A positive reciprocity parameter means mutual ties occur more often than expected under the rest of the fitted model. A positive closure term means two actors with shared partners have greater conditional propensity to connect, given the included structure and covariates. The meaning is always conditional on the full specification.
Parameter signs are not enough. A useful ERGM must converge, generate credible networks, and reproduce important features not forced directly by the model. Competing specifications may support different interpretations, so the final account should document the model-building path and rejected alternatives.