gofN function

Linear model diagnostics for multinetwork linear models

gofN() performs a simulation to obtain Pearson residuals for the multivariate linear model for ERGM parameters, which can then be used for a variety of diagnostics and diagnostic plots developed by \insertCite KrCo22t;textualergm.multi.

gofN(
  object,
  GOF = NULL,
  subset = TRUE,
  control = control.gofN.ergm(),
  save_stats = FALSE,
  ...
)

## S3 method for class 'gofN'
x[i, j, ..., drop = FALSE]

## S3 method for class 'gofN'
augment(x, ...)

## S3 method for class 'gofN'
summary(object, by = NULL, ...)

Arguments

• object: an ergm object.

• GOF: a one-sided ergm formula specifying network statistics whose goodness of fit to test, or NULL; if NULL, uses the original model.

• subset: argument for the N term.

• control: See control.gofN.ergm().

• save_stats: If TRUE, save the simulated network statistics; defaults to FALSE to save memory and disk space.

• ...: additional arguments to functions (simulate.ergm()

  and summary.ergm_model()) for the constructor.

• x: a gofN object.

• i: for the indexing operator, index of statistics to be kept in the subset.

• j: for the indexing operator, index of networks to be kept in the subset.

• drop: whether the indexing operator should drop attributes and return simply a list.

• by: a numeric or character vector, or a formula whose RHS gives an expression in terms of network attributes, used as a grouping variable for summarizing the values.

Returns

An object of class gofN: a named list containing a list for every statistic in the specified GOF formula with the following elements vectors of length equal to the number of subnetworks:

• observed: For completely observed networks, their value of the statistic. For partially observed networks, the expected value of their imputations under the model.

• fitted: Expected value of the statistic under the model.

• var: Variance of the statistic under the model.

• var.obs: Conditional variance under imputation statistic.

• pearson: The Pearson residual computed from the above.

• stats,stats.obs: If save_stats control parameter is TRUE, the simulated statistics.

In addition, the following attr-style attributes are included:

• nw: The observed multinetwork object.

• subset: A logical vector giving the subset of networks that were used.

• control: Control parameters passed.

Methods (by generic)

• [: Extract a subset of statistics for which goodness-of-fit had been computed.

• augment(gofN): a method for constructing a tibble of network attributes augmented with goodness of fit information. Columns include:

  • network attributes: the attributes of each of the networks
  • .stat_name: name of the simulated statistic
  • .stat_id: index of the simulated statistic in the gofN object
  • .network_id: index of the network in the networks for which gofN was run (excluding those not in the subset)
  • .fitted: predicted value for the statistic
  • .observed: either the observed (for completely observed networks) or the predicted conditional on observed (for partially observed networks) value of the statistic
  • .pearson: the standardised Pearson residual
  • .var, .var.obs: estimated unconditional and average conditional variance of the statistic
  • .weight: inverse of the variance of the residual

• summary(gofN): A simple summary function.

Examples

data(samplk)
monks <- Networks(samplk1, samplk2, samplk3,samplk1, samplk2, samplk3,samplk1, samplk2, samplk3)
fit <- ergm(monks~N(~edges+nodematch("group")))
fit.gof <- gofN(fit) # GOF = original model
summary(fit.gof)
plot(fit.gof)
fit.gof <- gofN(fit, GOF=~triangles)
summary(fit.gof)
plot(fit.gof)

samplk1[1,]<-NA
samplk2[,2]<-NA
monks <- Networks(samplk1, samplk2, samplk3,samplk1, samplk2, samplk3,samplk1, samplk2, samplk3)
fit <- ergm(monks~N(~edges+nodematch("group")))
fit.gof <- gofN(fit) # GOF = original model
summary(fit.gof)
plot(fit.gof)
fit.gof <- gofN(fit, GOF=~triangles)
summary(fit.gof)
plot(fit.gof)
plot(fit.gof, against=~log(.fitted)) # Plot against transformed fitted values.

### If 'ggplot2' and 'ggrepel' are installed, illustrate the autoplot() method.
if(require("ggplot2") && requireNamespace("ggrepel")){
  autoplot(fit.gof)
}

# Default is good enough in this case, but sometimes, we might want to set it higher. E.g.,
## Not run:

fit.gof <- gofN(fit, GOF=~edges, control=control.gofN.ergm(nsim=400))
## End(Not run)


### If 'generics' is installed, illustrate the augment() method.
if(require("generics")){
  augment(fit.gof)
}

References

\insertAllCited

See Also

plot.gofN() and autoplot.gofN() for plotting gofN

objects to make residual plots; ergm::gof() for single-network goodness-of-fit simulations in list("ergm")