Formulas

A model is a list of terms, each contributing one or more network statistics. ergmx takes it in two forms.

A string in R syntax, so models can be pasted from R:

import ergmx
from ergmx import datasets

mesa = datasets.load("faux.mesa.high")
ergmx.summary_stats(mesa, "edges + nodematch('Grade') + gwesp(0.5, fixed=TRUE)")

{'edges': 203.0,
 'nodematch.Grade': 163.0,
 'gwesp.fixed.0.5': 141.92580555386385}

summary_stats is R’s summary(net ~ formula): the statistics of a network. The string follows R’s conventions: TRUE/FALSE (or True/False), c(2, 3) and 2:3 for vectors, and a left-hand side such as "mesa ~ edges + triangle" is ignored. Nothing in it is evaluated: arguments must be literals.

Terms combined with +, which a program can build:

from ergmx import edges, gwesp, nodematch

formula = edges() + nodematch("Grade") + gwesp(0.5, fixed=True)
ergmx.summary_stats(mesa, formula)

{'edges': 203.0,
 'nodematch.Grade': 163.0,
 'gwesp.fixed.0.5': 141.92580555386385}

Both forms can be mixed: edges() + "triangle".

Operators

Two operators wrap other terms, as in ergm. offset(term) fixes a term’s coefficient instead of estimating it (see Fixed coefficients), and F(~terms, ~filter) evaluates terms on the ties that pass a filter, such as the ties within a group:

ergmx.summary_stats(mesa, "F(~edges + triangle, ~nodematch('Grade')) + offset(edges)")

{'F(nodematch("Grade"))~edges': 163.0,
 'F(nodematch("Grade"))~triangle': 52.0,
 'offset(edges)': 203.0}

In Python, F(edges() + triangle(), nodematch("Grade")) and offset(edges()).

Statistic names

Names follow ergm, so tables can be compared with R’s output line by line. Terms with several statistics name each of them:

ergmx.summary_stats(mesa, "kstar(2:3) + nodefactor('Race') + nodematch('Sex', diff=TRUE)")

{'kstar2': 659.0,
 'kstar3': 1010.0,
 'nodefactor.Race.Hisp': 178.0,
 'nodefactor.Race.NatAm': 156.0,
 'nodefactor.Race.Other': 1.0,
 'nodefactor.Race.White': 45.0,
 'nodematch.Sex.F': 82.0,
 'nodematch.Sex.M': 50.0}

Errors

Unknown terms, bad arguments and terms that don’t apply to the network fail before any fitting, with a message that says why:

try:
    ergmx.summary_stats(mesa, "edges + mutual")   # mutual needs a directed network
except ValueError as error:
    print(error)

mutual() is only implemented for directed networks

The term reference lists every term, its statistic and the networks it applies to.