ergm-terms {ergm.count} R Documentation

## Terms used in Exponential Family Random Graph Models Specific to Counts

### Description

This page describes the possible terms (and hence network statistics) included in the `ergm.count` package.

See the `ergm-terms` documentation in the `ergm` package for a complete description of what ERGM terms are and how they are used.

### Terms to represent network statistics included in the `ergm.count` pacakge

All terms listed are valued.

`CMP`

Conway-Maxwell-Poisson Distribution: This term adds one statistic to the model, of the form ∑_{i,j}\log(y_{i,j}!). This turns a Poisson- or a geometric-reference ERGM into a Conway-Maxwell-Poisson-reference ERGM, allowing it to represent a broad range of disperson values. In particular, combined with a Poisson-reference ERGM, a negative coefficient on this term induces underdispersion and a positive coefficient induces overdispersion. (This behavior is different from 3.1.1, when the negation of this value was used.)

Note that its current implementation may not perform well if the data are overdispersed relative to geometric.

`CMB(trials, coupled = TRUE)`

Conway-Maxwell-Binomial Distribution: If `couple==TRUE`, this term adds one statistic to the model, of the form ∑_{i,j}\log(y_{i,j}!) + \log(t-y_{i,j}!). This turns a Binomial- or a discrete-uniform-reference ERGM into a Conway-Maxwell-Binomial-reference ERGM, allowing it to represent a broad range of disperson values. In particular, combined with a Binomial-reference ERGM, a negative coefficient on this term induces underdispersion and a positive coefficient induces overdispersion.

If `coupled==FALSE` the two summands above are added as their own statistic (each with its own free parameter).

### References

• Handcock M. S., Hunter D. R., Butts C. T., Goodreau S. G., Krivitsky P. N. and Morris M. (2012). _Fit, Simulate and Diagnose Exponential-Family Models for Networks_. Version 3.1. Project home page at <URL: https://www.statnet.org>, <URL: CRAN.R-project.org/package=ergm>.

• Krivitsky P. N. (2012). Exponential-Family Random Graph Models for Valued Networks. Electronic Journal of Statistics, 2012, 6, 1100-1128. doi: 10.1214/12-EJS696

• Shmueli G., Minka T. P., Kadane J. B., Borle S., and Boatwright P. (2005). A Useful Distribution for Fitting Discrete Data: Revival of the Conway–Maxwell–Poisson Distribution. Journal of the Royal Statistical Society: Series C, 54(1): 127-142.

• Shmueli G., Minka T. P., Kadane J. B., Borle S., and Boatwright P. (2005). A Useful Distribution for Fitting Discrete Data: Revival of the Conway–Maxwell–Poisson Distribution. Journal of the Royal Statistical Society: Series C, 54(1): 127-142.

• Kadane, Joseph B. (2016) Sums of Possibly Associated Bernoulli Variables: The Conway-Maxwell-Binomial Distribution. Bayesian Analysis, 11(2): 403–420. doi: 10.1214/15-BA955

`ergm-terms` (from the `ergm` package), `ergm`, `network`, `%v%`, `%n%`