rdiffnet: Random diffnet network

In srdyal/diffusiontest: Analysis of Diffusion and Contagion Processes on Networks

Random diffnet network

Description

Simulates a diffusion network by creating a random dynamic network and adoption threshold levels. You can perform a simulation for a single behavior (using seed.p.adopt of class numeric in rdiffnet), conduct multiple simulations for a single behavior (with rdiffnet_multiple), or run a simulation with multiple behaviors simultaneously (using seed.p.adopt of class list in rdiffnet)

Usage

rdiffnet_multiple(R, statistic, ..., ncpus = 1L, cl = NULL)

rdiffnet(
  n,
  t,
  seed.nodes = "random",
  seed.p.adopt = 0.05,
  seed.graph = "scale-free",
  rgraph.args = list(),
  rewire = TRUE,
  rewire.args = list(),
  threshold.dist = runif(n),
  exposure.args = list(),
  name = "A diffusion network",
  behavior = "Random contagion",
  stop.no.diff = TRUE,
  disadopt = NULL
)

Arguments

R	Integer scalar. Number of simulations to be done.
statistic	A Function to be applied to each simulated diffusion network.
...	Further arguments to be passed to rdiffnet.
ncpus	Integer scalar. Number of processors to be used (see details).
cl	An object of class c("SOCKcluster", "cluster") (see details).
n	Integer scalar. Number of vertices.
t	Integer scalar. Time length.
seed.nodes	Either a character scalar, a vector or a list (multiple behaviors only). Type of seed nodes (see details).
seed.p.adopt	Numeric scalar or a list (multiple behaviors only). Proportion of early adopters.
seed.graph	Baseline graph used for the simulation (see details).
rgraph.args	List. Arguments to be passed to rgraph.
rewire	Logical scalar. When TRUE, network slices are generated by rewiring (see rewire_graph).
rewire.args	List. Arguments to be passed to rewire_graph.
threshold.dist	For a single behavior diffusion, either a function to be applied via sapply, a numeric scalar, or a vector/matrix with n elements. For Q behavior diffusion, it can also be an n \times Q matrix or a list of Q single behavior inputs. Sets the adoption threshold for each node.
exposure.args	List. Arguments to be passed to exposure.
name	Character scalar. Passed to as_diffnet.
behavior	Character scalar or a list or character scalar (multiple behaviors only). Passed to as_diffnet.
stop.no.diff	Logical scalar. When TRUE, the function will return with error if there was no diffusion. Otherwise it throws a warning.
disadopt	Function of disadoption, with current exposition, cumulative adoption, and time as possible inputs.

Details

Instead of randomizing whether an individual adopts the innovation or not, this toy model randomizes threshold levels, seed adopters and network structure, so an individual adopts the innovation in time T iff his exposure is above or equal to his threshold. The simulation is done in the following steps:

1. Using seed.graph, a baseline graph is created.

2. Given the baseline graph, the set of initial adopters is defined using seed.nodes.

3. Afterwards, if rewire=TRUE, t-1 slices of the network are created by iteratively rewiring the baseline graph.

4. The threshold.dist function is applied to each node in the graph.

5. Simulation starts at t=2 assigning adopters in each time period accordingly to each vertex's threshold and exposure.

When seed.nodes is a character scalar it can be "marginal", "central" or "random", so each of these values sets the initial adopters using the vertices with lowest degree, with highest degree or completely randomly.

For a single behavior diffusion, the number of early adopters is set as seed.p.adopt * n. To run multiple behavior diffusion, seed.p.adopt must be a list (see examples below). Please note that when marginal nodes are set as seed it may be the case that no diffusion process is attained as the chosen set of first adopters can be isolated. Any other case will be considered as an index (via [<- methods), hence the user can manually set the set of initial adopters, for example if the user sets seed.nodes=c(1, 4, 7) then nodes 1, 4 and 7 will be selected as initial adopters.

The argument seed.graph can be either a function that generates a graph (Any class of accepted graph format (see netdiffuseR-graphs)), a graph itself or a character scalar in which the user sets the algorithm used to generate the first network (network in t=1), this can be either "scale-free" (Barabasi-Albert model using the rgraph_ba function, the default), "bernoulli" (Erdos-Renyi model using the rgraph_er function), or "small-world" (Watts-Strogatz model using the rgraph_ws function). The list rgraph.args passes arguments to the chosen algorithm.

When rewire=TRUE, the networks that follow t=1 will be generated using the rewire_graph function as G(t) = R(G(t-1)), where R is the rewiring algorithm.

If a function, the argument threshold.dist sets the threshold for each vertex in the graph. It is applied using sapply as follows

sapply(1:n, threshold.dist)

By default sets the threshold to be random for each node in the graph.

If seed.graph is provided, no random graph is generated and the simulation is applied using that graph instead.

rewire.args has the following default options:

p	.1
undirected	getOption("diffnet.undirected", FALSE)
self	getOption("diffnet.self", FALSE)

exposure.args has the following default options:

outgoing	TRUE
valued	getOption("diffnet.valued", FALSE)
normalized	TRUE

The function rdiffnet_multiple is a wrapper of rdiffnet wich allows simulating multiple diffusion networks with the same parameters and apply the same function to all of them. This function is designed to allow the user to perform larger simulation studies in which the distribution of a particular statistic is observed.

When cl is provided, then simulations are done via parSapply. If ncpus is greater than 1, then the function creates a cluster via makeCluster which is stopped (removed) once the process is complete.

Value

A random diffnet class object.

rdiffnet_multiple returns either a vector or an array depending on what statistic is (see sapply and parSapply).

Author(s)

George G. Vega Yon & Aníbal Olivera M.

See Also

Other simulation functions: permute_graph(), rewire_graph(), rgraph_ba(), rgraph_er(), rgraph_ws(), ring_lattice()

Examples

# (Single behavior): --------------------------------------------------------

# A simple example
set.seed(123)
diffnet_1 <- rdiffnet(100,10)
diffnet_1
summary(diffnet_1)

# Adopt if at least two neighbors have adopted ------
n <- 100; t <- 5;
graph <- rgraph_ws(n, t, p=.3)

diffnet_2 <- rdiffnet(seed.graph = graph, t = t, threshold.dist=function(x) 2,
    exposure.args=list(valued=FALSE, normalized=FALSE))

# Re thinking the Adoption of Tetracycline ----------
newMI <- rdiffnet(seed.graph = medInnovationsDiffNet$graph,
 threshold.dist = threshold(medInnovationsDiffNet), rewire=FALSE)

# (Multiple behavior): ------------------------------------------------------

# A simple example
set.seed(123)
diffnet_3 <- rdiffnet(100, 10, seed.p.adopt = list(0.1, 0.15))
diffnet_3
summary(diffnet_3)

# Fully specified multi-behavior example ------------

threshold_matrix <- matrix(runif(n * 2), nrow = n, ncol = 2)
seed_nodes <- sample(1:100, 10, replace = FALSE)
diffnet_4 <- rdiffnet(100, 10, seed.p.adopt = list(0, 0),
                      seed.nodes = list(seed_nodes, seed_nodes),
                      threshold.dist = threshold_matrix,
                      behavior = c("tobacco", "alcohol"))
diffnet_4

# Adopt if at least one neighbor has adopted the first behavior,
# and at least two neighbors have adopted the second behavior. ---

diffnet_5 <- rdiffnet(seed.graph = graph, t = t, seed.p.adopt = list(0.1, 0.1),
                      threshold.dist = list(function(x) 2, function(x) 2),
                      exposure.args=list(valued=FALSE, normalized=FALSE))
diffnet_5

# With a disadoption function -----------------------

set.seed(1231)

random_dis <- function(expo, cumadopt, time) {
  num_of_behaviors <- dim(cumadopt)[3]

  list_disadopt <- list()

  for (q in 1:num_of_behaviors) {
    adopters <- which(cumadopt[, time, q, drop=FALSE] == 1)
    if (length(adopters) == 0) {
      # only disadopt those behaviors with adopters
      list_disadopt[[q]] <- integer()
    } else {
      # selecting 10% of adopters to disadopt
      list_disadopt[[q]] <- sample(adopters, ceiling(0.10 * length(adopters)))
    }
  }
  return(list_disadopt)
}

diffnet_6 <- rdiffnet(seed.graph = graph, t = 10, disadopt = random_dis, seed.p.adopt = list(0.1, 0.1))

# (Multiple simulations of single behavior): --------------------------------
# Simulation study comparing the diffusion with diff sets of seed nodes

# Random seed nodes
set.seed(1)
ans0 <- rdiffnet_multiple(R=50, statistic=function(x) sum(!is.na(x$toa)),
    n = 100, t = 4, seed.nodes = "random", stop.no.diff=FALSE)

# Central seed nodes
set.seed(1)
ans1 <- rdiffnet_multiple(R=50, statistic=function(x) sum(!is.na(x$toa)),
    n = 100, t = 4, seed.nodes = "central", stop.no.diff=FALSE)

boxplot(cbind(Random = ans0, Central = ans1), main="Number of adopters")

srdyal/diffusiontest documentation built on Dec. 9, 2024, 1:14 a.m.