netdiffuseR (version 1.16.2)

struct_test: Structure dependence test

Description

Test whether or not a network estimates can be considered structurally dependent, i.e. a function of the network structure. By rewiring the graph and calculating a particular statistic $t$, the test compares the observed mean of $t$ against the empirical distribution of it obtained from rewiring the network.

Usage

struct_test(graph, statistic, R, rewire.args = list(p = 1, undirected =
  getOption("diffnet.undirected"), both.ends = TRUE), ...)
## S3 method for class 'diffnet_struct_test':
print(x, ...)
## S3 method for class 'diffnet_struct_test':
hist(x,
  main = "Distribution of Statistic on\\nrewired network",
  xlab = expression(Values ~ of ~ t), breaks = 20, annotated = TRUE,
  b0 = expression(atop(plain("") %up% plain("")), t[0]),
  b = expression(atop(plain("") %up% plain("")), t[]), ...)

Arguments

graph

A diffnet graph.

statistic

A function that returns either a scalar or a vector.

R

Integer scalar. Number of repetitions.

rewire.args

List. Arguments to be passed to rewire_graph

...

Further arguments passed to the method (see details).

x

A diffnet_boot 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.

Value

• A list of class diffnet_bot containing the following:
• graph
  The graph passed to struct_test.
• statistic
  The function statistic passed to struct_test.
• boot
  A boot class object as return from the call to boot.
• The output from the hist method is the same as hist.default.

Details

struct_test is a wrapper for the function boot from the boot package. Instead of resampling data--vertices or edges--in each iteration the function rewires the original graph using rewire_graph and applies the function defined by the user in statistic.

In struct_test ... are passed to boot, otherwise are passed to the corresponding method (hist for instance).

From the print method, p-value for the null of the statistic been equal between graph and its rewired versions is computed as follows

$$p(\tau)=2\times\min\left(\mbox{Pr}(t\leq\tau), \mbox{Pr}(t\geq\tau)\right)$$

Where $\mbox{Pr}{\cdot}$ is approximated using the Empirical Distribution Function retrieved from the simulations.

The test is actually on development by Vega Yon and Valente. A copy of the working paper can be distributed upon request to [e-mail]

References

Vega Yon, George G. and Valente, Thomas W. (On development).

Davidson, R., & MacKinnon, J. G. (2004). Econometric Theory and Methods. New York: Oxford University Press.

Examples

# Creating a random graph
set.seed(881)
diffnet <- rdiffnet(100, 10)

# Testing structure-dependency of threshold
res <- struct_test(diffnet, function(g) mean(threshold(g), na.rm=TRUE), R=100)
res
hist(res)

# Adding a legend
legend("topright", bty="n",
 legend=c(
   expression(t[0]:~Baseline),
   expression(t:~Rewired~average)
 )
 )

# Running in parallel fashion
res <- struct_test(diffnet, function(g) mean(threshold(g), na.rm=TRUE), R=100,
ncpus=4, parallel="multicore")
res
hist(res)