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

\tableofcontents

News for netdiffuseR package.

#devtools::install_github("USCCANA/netdiffuseR", ref = "47-split-behaviors-rdiffnet")
library(netdiffuseR)

Introduction

• Social networks facilitate the spread of news, gossip, behaviors, and products. Granovetter specified a simple and intuitive mechanism that underpins much of the research on social network diffusion: individuals adopt a behavior if enough others do so.
• More specifically, in an interacting population of individuals where a behavior is spreading, each individual has a particular “threshold” and adopts the behavior if the proportion of others who have already adopted the behavior exceeds the threshold.
• However, adoption booms are commonly followed by periods of bust—riots come to an end, new fashions go out of style, and juicy gossip turns to stale news.
• So the adoption of a fashion is followed by the disadoption of that fashion by a new one.
• This dynamic requires being able to handle more than one 'propagation' at a time.
• Until now, netdiffuseR was not able to simulate more than one diffusion in the same setup.

Allowing multi-behavior diffusion simulations

How rdiffnet works until now

In a (very) simplified way, rdiffnet has 4 steps. Before this current version, the workflow can be diagrammed as:

knitr::include_graphics("~/anibal/netdiffuseR-original/playground/images/diagrams-single-1.png")

How rdiffnet works from now

In the current version, we maintain the basic structure of the workflow, but adding some functions and modifying the existing for allowing multi-behavior diffusion.

knitr::include_graphics("~/anibal/netdiffuseR-original/playground/images/diagrams-multiple-1.png")

As you can see, now in Step 1.0, before identify the seed nodes as initial condition, the inputs seed.p.adopt (default 0.1 for single behavior), seed.nodes (default 'random'), and behavior (default 'random behavior') are passed to an internal function that validates they as accepted inputs and homogenized the objects for the rest of the code.

As before, rdiffnet still accepts several kinds of inputs, for different classes classes and specifications, but the input that characterized the multi-behavior simulation is exclusively seed.p.adopt. If class(seed.p.adopt) is a list, then the simulation will run a total of length(seed.p.adopt) behaviors in the same setup. This table summarize the possible inputs for seed.p.adopt, seed.nodes, threshold.dist, and behavior, showing some examples.

knitr::include_graphics("~/anibal/netdiffuseR-original/playground/images/table_1.png")

All functions in other steps were revised to allow now different object that can handle multi-behavior, while still can execute the already in-build functions for single diffusion within the package (as plot(), plot_diffnet(), and plot_adopters(), among many others).

Additionally, now there is a new function split_behaviors() that returns a list where each element is a separate rdiffnet object, that correspond with each separate behavior. So in this way, you could use the same machinery constructed for single behavior, to plot or analyze now the result of the multi-behavior simulation.

All those features are shown in more detail below.

rdiffnet() examples

For single diffusion:

set.seed(123)

rdiffnet(100, 5)
?rdiffnet

rdiffnet(100, 5, seed.p.adopt = 0.1)

rdiffnet(100, 5, seed.p.adopt = 0.1, behavior = 'tabacco')

rdiffnet(100, 5, seed.p.adopt = 0.1, threshold.dist = 0.3)
rdiffnet(100, 5, seed.p.adopt = 0.1, threshold.dist = function(x) 0.3)
rdiffnet(100, 5, seed.p.adopt = 0.1, threshold.dist = runif(100, .2,.7))

rdiffnet(100, 5, seed.p.adopt = 0.1, seed.nodes = 'central')

seed_nodes <- sample(1:100, 10, replace = FALSE)
rdiffnet(100, 5, seed.nodes = seed_nodes)

but also, we can specify the network:

#| warning: false

set.seed(121)
n          <- 200
t          <- 10
graph      <- rgraph_ws(n, 10, p=.3)  # watts-strogatz model
thr        <- runif(n, .3,.5)

rdiffnet(seed.graph = graph, t = t , seed.p.adopt = 0.1, threshold.dist = thr)

For multi diffusion:

set.seed(124)
rdiffnet(100, 5, seed.p.adopt = list(0.1, 0.08), behavior = 'tabacco')
rdiffnet(100, 5, seed.p.adopt = list(0.1, 0.08), behavior = c('tabacco', 'alcohol'))

diffnet <- rdiffnet(100, 5, seed.p.adopt = list(0.1, 0.08), threshold.dist = 0.3)
diffnet$vertex.static.attrs
rdiffnet(100, 5, seed.p.adopt = list(0.1, 0.08), threshold.dist = runif(100))
diffnet <- rdiffnet(100, 5, seed.p.adopt = list(0.1, 0.08), threshold.dist = function(x) 0.3)
diffnet$vertex.static.attrs
rdiffnet(100, 5, seed.p.adopt = list(0.1, 0.08), threshold.dist = list(0.3, 0.2))
rdiffnet(100, 5, seed.p.adopt = list(0.1, 0.08), threshold.dist = list(runif(100), runif(100)))
rdiffnet(100, 5, seed.p.adopt = list(0.1, 0.08), threshold.dist = list(function(x) 0.3, function(x) 0.2))

set.seed(123)
rdiffnet(100, 5, seed.p.adopt = list(0.1, 0.08), seed.nodes = c('random', 'central'))

set.seed(123)
seed_nodes <- sample(1:100, 10, replace = FALSE)
rdiffnet(100, 5, seed.p.adopt = list(0, 0), seed.nodes = list(seed_nodes, seed_nodes))

Alternatively, we can specify the network:

#| warning: false

set.seed(121)
n          <- 200
t          <- 10
graph      <- rgraph_ws(n, t, p=.3)  # watts-strogatz model
thr        <- runif(n, .3,.5)

diffnet <- rdiffnet(seed.graph = graph, t = t , seed.p.adopt = list(0.1, 0.15),
                    threshold.dist = thr)
diffnet

split_behaviors() and disadoption

If you want to use other function to analyze the results from the simulation focusing in a single behavior, you could use `split_behaviors()`:

#| warning: false

  set.seed(12131)
  n            <- 50
  t            <- 5
  graph        <- rgraph_ws(n, 4, p=.3)
  seed.nodes   <- c(1,5,7,10)
  thr          <- runif(n, .2,.4)

  # Generating identical networks
  net_single <- rdiffnet(seed.graph = graph, t = t, seed.nodes = seed.nodes, 
                         seed.p.adopt = 0.1, rewire = FALSE, threshold.dist = thr)

  net_multiple <- rdiffnet(seed.graph = graph, t = t, seed.nodes = seed.nodes, 
                           seed.p.adopt = list(0.1, 0.1), rewire = FALSE,
                           threshold.dist = thr)

  net_single_from_multiple <- split_behaviors(net_multiple)
  net_single_from_multiple_1 <- net_single_from_multiple[[1]]

  expect_equal(net_single_from_multiple_1$toa, net_single$toa)
  expect_equal(net_single_from_multiple_1$adopt, net_single$adopt)
  expect_equal(net_single_from_multiple_1$cumadopt, net_single$cumadopt)

Plotting each behavior

plot_diffnet(net_single)
plot_diffnet(net_single_from_multiple_1)

Disadoption

Until now the behaviors are independent, but we can add some disadoption function to make them dependent each other. This is achieved by introducing the function you want as an input tho rdiffnet: rdiffnet <- function(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)

set.seed(1231)
n <- 500

d_adopt <- function(expo, cumadopt, time) {

  # Id double adopters
  ids <- which(apply(cumadopt[, time, , drop=FALSE], 1, sum) > 1)

  if (length(ids) == 0)
    return(list(integer(), integer()))

  # Otherwise, make them pick one (literally, you can only adopt
  # a single behavior, in this case, we prefer the second)
  return(list(ids, integer()))

}

ans_d_adopt <- rdiffnet(n = n, t = 10, disadopt = d_adopt,
                        seed.p.adopt = list(0.1, 0.1))

tmat <- toa_mat(ans_d_adopt)
should_be_ones_or_zeros <- tmat[[1]]$cumadopt[, 10] + tmat[[2]]$cumadopt[, 10]

expect_true(all(should_be_ones_or_zeros %in% c(0,1)))

set.seed(1231)

n <- 100; t <- 5;
graph <- rgraph_ws(n, t, p=.3)

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

exposure() examples

• Exposure for multiple behaviors:

#| warning: false

set.seed(12131)
g    <- rgraph_ws(20, 4, p=.3)  # watts-strogatz model
set0 <- c(1,5,7,10)
thr  <- runif(20, .4,.7)

diffnet <- rdiffnet(seed.graph = g, seed.nodes = set0, t = 4, rewire = FALSE,
                 threshold.dist = thr)

cumadopt_2 <- diffnet$cumadopt
cumadopt_2 <- array(c(cumadopt_2,cumadopt_2[rev(1:nrow(cumadopt_2)),]), dim=c(dim(cumadopt_2), 2))

print(exposure(diffnet, cumadopt = cumadopt_2))

rdiffnet_validate_arg()

Maybe not necessary, as this is an internal function.

Threshold

Thresholds

• One of the cannonical concepts is the network threshold. Network thresholds (Valente, 1995; 1996), $\tau$, are defined as the required proportion or number of neighbors that leads you to adopt a particular behavior (innovation), $a=1$. In (very) general terms\pause

$$ a_i = \left{\begin{array}{ll} 1 &\mbox{if } \tau_i\leq E_i \ 0 & \mbox{Otherwise} \end{array}\right. \qquad E_i \equiv \frac{\sum_{j\neq i}\mathbf{X}{ij}a_j}{\sum{j\neq i}\mathbf{X}_{ij}} $$

Where $E_i$ is i's exposure to the innovation and $\mathbf{X}$ is the adjacency matrix (the network).

new_diffnet()

Same, is an internal function.

split_behaviors()

Examples.

• Importantly, while very useful, diffnet objects is not the only way to use netdiffuseR. Most of the functions can also be used with matrices and arrays.

library(netdiffuseR)
knitr::opts_chunk$set(comment = '#')

Raw network data

• We call raw network data to datasets that have a somewhat raw form, for example, edgelists,

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.

• For this tutorial, we classify graph data as follows:
  • Raw R network data: Datasets with edgelist, attributes, survey data, etc.
  • Already R data: already read into R using igraph, statnet, etc.
  • Graph files: DL, UCINET, pajek, etc.
• The includes several options to read such data.

USCCANA/diffusiontest documentation built on Dec. 10, 2024, 9:54 p.m.