bootnet: Network Bootstrapping

In netdiffuseR: Analysis of Diffusion and Contagion Processes on Networks

Network Bootstrapping

Description

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

Usage

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

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

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

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

## S3 method for class '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,
  ...
)

## S3 method for class 'diffnet_bootnet'
plot(x, y, ...)

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).
y	Ignored.

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.

The 'plot.diffnet_bootnet' method is a wrapper for the 'hist' method.

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.

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

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

ans <- bootnet(g, function(w, ...) length(w@x), R=100)
ans

# Generating

netdiffuseR documentation built on Aug. 30, 2023, 5:07 p.m.