Network Bootstrapping

Implements the bootstrapping method described in Snijders and Borgatti (1999). This function is essentially a wrapper of boot.

resample_graph(graph, self = NULL, useR = FALSE, ...)

bootnet(graph, statistic, R, resample.args = list(self = FALSE), ...)

# S3 method for diffnet_bootnet
c(..., recursive = FALSE)

# S3 method for diffnet_bootnet
print(x, ...)

# S3 method for diffnet_bootnet
hist(
  x,
  main = "Empirical Distribution of Statistic",
  xlab = expression(Values ~ of ~ t),
  breaks = 20,
  annotated = TRUE,
  b0 = expression(atop(plain("") %up% plain("")), t[0]),
  b = expression(atop(plain("") %up% plain("")), t[]),
  ask = TRUE,
  ...
)

Arguments

graph	Any class of accepted graph format (see netdiffuseR-graphs).
self	Logical scalar. When TRUE autolinks (loops, self edges) are allowed (see details).
useR	Logical scalar. When TRUE, autolinks are filled using an R based rutine. Otherwise it uses the Rcpp implementation (default). This is intended for testing only.
...	Further arguments passed to the method (see details).
statistic	A function that returns a vector with the statistic(s) of interest. The first argument must be the graph, and the second argument a vector of indices (see details)
R	Number of reps
resample.args	List. Arguments to be passed to resample_graph
recursive	Ignored
x	A diffnet_bootnet class object.
main	Character scalar. Title of the histogram.
xlab	Character scalar. x-axis label.
breaks	Passed to hist.
annotated	Logical scalar. When TRUE marks the observed data average and the simulated data average.
b0	Character scalar. When annotated=TRUE, label for the value of b0.
b	Character scalar. When annotated=TRUE, label for the value of b.
ask	Logical scalar. When TRUE, asks the user to type <Enter> to see each plot (as many as statistics where computed).

Value

A list of class diffnet_bootnet containing the following:

graph

The graph passed to bootnet.

p.value

The resulting p-value of the test (see details).

t0

The observed value of the statistic.

mean_t

The average value of the statistic applied to the simulated networks.

var_t

A vector of length length(t0). Bootstrap variances.

R

Number of simulations.

statistic

The function statistic passed to bootnet.

boot

A boot class object as return from the call to boot.

resample.args

The list resample.args passed to bootnet.

Details

Just like the boot function of the boot package, the statistic that is passed must have as arguments the original data (the graph in this case), and a vector of indicides. In each repetition, the graph that is passed is a resampled version generated as described in Snijders and Borgatti (1999).

When self = FALSE, for pairs of individuals that haven been drawn more than once the algorithm, in particular, resample_graph, takes care of filling these pseudo autolinks that are not in the diagonal of the network. By default it is assumed that these pseudo-autolinks depend on whether the original graph had any, hence, if the diagonal has any non-zero value the algorithm assumes that self = TRUE, skiping the 'filling algorithm'. It is important to notice that, in order to preserve the density of the original network, when assigning an edge value to a pair of the form \((i,i)\) (pseudo-autolinks), such is done with probabilty proportional to the density of the network, in other words, before choosing from the existing list of edge values, the algorithm decides whether to set a zero value first.

The vector of indices that is passed to statistic, an integer vector with range 1 to \(n\), corresponds to the drawn sample of nodes, so the user can, for example, use it to get a subset of a data.frame that will be used with the graph.

References

Snijders, T. A. B., & Borgatti, S. P. (1999). Non-Parametric Standard Errors and Tests for Network Statistics. Connections, 22(2), 1–10. Retrieved from https://www.stats.ox.ac.uk/~snijders/Snijders_Borgatti.pdf

See also

Other Functions for inference: moran(), struct_test()

Examples

#
set.seed(13)
g <- rgraph_ba(t=99)

ans <- bootnet(g, function(w, ...) length(w@x), R=100)
ans
#> 
#> Network Bootstrap (Snijders and Borgatti, 1999)
#> # Num. of draws   : 100
#> # nodes           : 100
#> # of time periods : 1
#> --------------------------------------------------------------------------------
#>   original        bias  std. error       p.val
#>   100.0000     -2.9400     28.9576      0.0000