gof: Conduct Goodness-of-Fit Diagnostics on a Exponential Family Random Graph Model

Description

gof calculates $p$-values for geodesic distance, degree, and reachability summaries to diagnose the goodness-of-fit of exponential family random graph models. See ergm for more information on these models.

Usage

"gof"(object,...)
"gof"(object,  ...,  coef=NULL, GOF=NULL, constraints=~., control=control.gof.formula(),
		      unconditional=TRUE, verbose=FALSE)
"gof"(object,  ..., coef=NULL,  GOF=NULL, constraints=NULL, control=control.gof.ergm(), verbose=FALSE)

Arguments

object

an R object. Either a formula or an ergm object. See documentation for ergm.

...

Additional arguments, to be passed to lower-level functions in the future.

coef

When given either a formula or an object of class ergm, coef are the parameters from which the sample is drawn. By default set to a vector of 0.

GOF

formula; an R formula object, of the form ~ specifying the statistics to use to diagnosis the goodness-of-fit of the model. They do not need to be in the model formula specified in formula, and typically are not. Currently supported terms are the degree distribution (“degree” for undirected graphs, or “idegree” and/or “odegree” for directed graphs), geodesic distances (“distance”), shared partner distributions (“espartners” and “dspartners”), the triad census (“triadcensus”), and the terms of the original model (“model”). The default formula for undirected networks is ~ degree + espartners + distance, and the default formula for directed networks is ~ idegree + odegree + espartners + distance.

constraints

A one-sided formula specifying one or more constraints on the support of the distribution of the networks being modeled. See the help for similarly-named argument in ergm for more information. For gof.formula, defaults to unconstrained. For gof.ergm, defaults to the constraints with which object was fitted.

control

A list to control parameters, constructed using control.gof.formula or control.gof.ergm (which have different defaults).

unconditional

logical; if TRUE, the simulation is unconditional on the observed dyads. if not TRUE, the simulation is conditional on the observed dyads. This is primarily used internally when the network has missing data and a conditional GoF is produced.

verbose

Provide verbose information on the progress of the simulation.

Value

, gof.ergm, and gof.formula return an object of class gofobject. This is a list of the tables of statistics and $p$-values. This is typically plotted using plot.gofobject.

Details

A sample of graphs is randomly drawn from the specified model. The first argument is typically the output of a call to ergm and the model used for that call is the one fit.

A plot of the summary measures is plotted. More information can be found by looking at the documentation of ergm. For GOF = ~model, the model's observed sufficient statistics are plotted as quantiles of the simulated sample. In a good fit, the observed statistics should be near the sample median (0.5). For gof.ergm and gof.formula, default behavior depends on the directedness of the network involved; if undirected then degree, espartners, and distance are used as default properties to examine. If the network in question is directed, “degree” in the above is replaced by idegree and odegree.

Examples

Run this code


data(florentine)
gest <- ergm(flomarriage ~ edges + kstar(2))
gest
summary(gest)

# test the gof.ergm function
gofflo <- gof(gest)
gofflo
summary(gofflo)

# Plot all three on the same page
# with nice margins
par(mfrow=c(1,3))
par(oma=c(0.5,2,1,0.5))
plot(gofflo)

# And now the log-odds
plot(gofflo, plotlogodds=TRUE)

# Use the formula version of gof
gofflo2 <-gof(flomarriage ~ edges + kstar(2), coef=c(-1.6339, 0.0049))
plot(gofflo2)