Analysis of Diffusion and Contagion Processes on Networks.

netdiffuseR: Analysis of Diffusion and Contagion Processes on Networks

This package contains functions useful for analyzing network data for diffusion of innovations applications.

The package was developed as part of the paper Thomas W. Valente, Stephanie R. Dyal, Kar-Hai Chu, Heather Wipfli, Kayo Fujimoto, Diffusion of innovations theory applied to global tobacco control treaty ratification, Social Science & Medicine, Volume 145, November 2015, Pages 89-97, ISSN 0277-9536 (available here)

From the description:

Empirical statistical analysis, visualization and simulation of diffusion and contagion processes on networks. The package implements algorithms for calculating network diffusion statistics such as transmission rate, hazard rates, exposure models, network threshold levels, infectiousness (contagion), and susceptibility. The package is inspired by work published in Valente, et al., (2015); Valente (1995), Myers (2000), Iyengar and others (2011), Burt (1987); among others.

Acknowledgements: netdiffuseR was created with the support of grant R01 CA157577 from the National Cancer Institute/National Institutes of Health.

citation(package="netdiffuseR")

To cite netdiffuseR in publications use the following paper:

  Valente TW, Vega Yon GG. Diffusion/Contagion Processes on Social
  Networks. Health Education & Behavior. 2020;47(2):235-248.
  doi:10.1177/1090198120901497

And the actual R package:

  Vega Yon G, Valente T (2022). _netdiffuseR: Analysis of Diffusion and
  Contagion Processes on Networks_. doi:10.5281/zenodo.1039317
  <https://doi.org/10.5281/zenodo.1039317>, R package version 1.22.4,
  <https://github.com/USCCANA/netdiffuseR>.

To see these entries in BibTeX format, use 'print(<citation>,
bibtex=TRUE)', 'toBibtex(.)', or set
'options(citation.bibtex.max=999)'.

News

Changelog can be view here.

• [2016-06-02] A video of the netdiffuseR workshop at SUNBELT 2016 is now online on youtube, and the workshop materials can be found here
• [2016-04-11] netdiffuseR will be on useR! 2016 on as a presentation and on IC2S2 2016 in the posters session.
• [2016-03-16] Next CRAN release scheduled for April 11th 2016 (after the workshop).
• [2016-02-18] netdiffuseR vers 1.16.2 is now on CRAN!

Installation

CRAN version

To get the CRAN (stable) version of the package, simple type

install.packages("netdiffuseR")

Bleeding edge version

If you want the latest (unstable) version of netdiffuseR, using the devtools package, you can install netdiffuseR dev version as follows

devtools::install_github('USCCANA/netdiffuseR', build_vignettes = TRUE)

You can skip building vignettes by setting build_vignettes = FALSE (so it is not required).

For the case of OSX users, there seems to be a problem when installing packages depending on Rcpp. This issue, developed here, can be solved by open the terminal and typing the following

curl -O http://r.research.att.com/libs/gfortran-4.8.2-darwin13.tar.bz2
sudo tar fvxz gfortran-4.8.2-darwin13.tar.bz2 -C /

before installing the package through devtools.

Binary versions

For the case of windows and mac users, they can find binary versions of the package here, netdiffuseR_1…zip, and netdiffuseR_1…tgz respectively. They can install this directly as follows (using the 1.16.3.29 version):

1. Install dependencies from CRAN r > install.packages(c("igraph", "Matrix", "SparseM", "RcppArmadillo", "sna"), dependencies=TRUE)

2. Download the binary version and install it as follows:

   > install.packages("netdiffuseR_1.16.3.29.zip", repos=NULL)
   

   For windows users, and for Mac users:

   > install.packages("netdiffuseR_1.16.3.29.tgz", repos=NULL)
   

Tutorials

Since starting netdiffuseR, we have done a couple of workshops at Sunbelt and NASN. Here are the repositories:

• Sunbelt 2018: https://usccana.github.io/netdiffuser-sunbelt2018/ (source code)
• NASN 2017: https://usccana.github.io/netdiffuser-nasn2017/ (source code)
• Sunbelt 2016: https://github.com/USCCANA/netdiffuser-sunbelt2016

Presentations

• ic2s2 2016 Evanston, IL: https://github.com/USCCANA/netdiffuser-ic2s22016 (poster)
• useR! 2016 Stanford, CA: https://github.com/USCCANA/netdiffuser-user2016 (slides)
• useR! 2016: https://github.com/USCCANA/netdiffuser-user2016

Examples

This example has been taken from the package’s vignettes:

library(netdiffuseR)

## 
## Attaching package: 'netdiffuseR'

## The following object is masked from 'package:base':
## 
##     %*%

Infectiousness and Susceptibility

# Generating a random graph
set.seed(1234)
n <- 100
nper <- 20
graph <- rgraph_er(n, nper, .5)
toa <- sample(c(1:(1+nper-1), NA), n, TRUE)
head(toa)

## [1] 16  3 14  3 13  5

# Creating a diffnet object
diffnet <- as_diffnet(graph, toa)
diffnet

## Dynamic network of class -diffnet-
##  Name               : Diffusion Network
##  Behavior           : Unspecified
##  # of nodes         : 100 (1, 2, 3, 4, 5, 6, 7, 8, ...)
##  # of time periods  : 20 (1 - 20)
##  Type               : directed
##  Final prevalence   : 0.95
##  Static attributes  : -
##  Dynamic attributes : -

summary(diffnet)

## Diffusion network summary statistics
## Name     : Diffusion Network
## Behavior : Unspecified
## -----------------------------------------------------------------------------
##  Period   Adopters   Cum Adopt. (%)   Hazard Rate   Density   Moran's I (sd)  
## -------- ---------- ---------------- ------------- --------- ---------------- 
##        1          8         8 (0.08)             -      0.50 -0.01 (0.00)     
##        2          3        11 (0.11)          0.03      0.50 -0.01 (0.00)     
##        3          6        17 (0.17)          0.07      0.51 -0.01 (0.00)     
##        4          3        20 (0.20)          0.04      0.49 -0.01 (0.00)     
##        5          9        29 (0.29)          0.11      0.50 -0.01 (0.00)     
##        6          5        34 (0.34)          0.07      0.50 -0.01 (0.00)     
##        7          2        36 (0.36)          0.03      0.51 -0.01 (0.00)     
##        8          3        39 (0.39)          0.05      0.50 -0.01 (0.00)     
##        9          5        44 (0.44)          0.08      0.50 -0.01 (0.00)     
##       10          1        45 (0.45)          0.02      0.49 -0.01 (0.00)     
##       11          3        48 (0.48)          0.05      0.50 -0.01 (0.00)     
##       12          6        54 (0.54)          0.12      0.50 -0.01 (0.00)     
##       13          8        62 (0.62)          0.17      0.50 -0.01 (0.00)     
##       14          9        71 (0.71)          0.24      0.50 -0.01 (0.00)     
##       15          5        76 (0.76)          0.17      0.50 -0.00 (0.00) **  
##       16          7        83 (0.83)          0.29      0.50 -0.01 (0.00)     
##       17          5        88 (0.88)          0.29      0.49 -0.00 (0.00) *** 
##       18          4        92 (0.92)          0.33      0.50 -0.01 (0.00)     
##       19          1        93 (0.93)          0.12      0.50 -0.01 (0.00)     
##       20          2        95 (0.95)          0.29      0.50 -0.01 (0.00)     
## -----------------------------------------------------------------------------
##  Left censoring  : 0.08 (8)
##  Right centoring : 0.05 (5)
##  # of nodes      : 100
## 
##  Moran's I was computed on contemporaneous autocorrelation using 1/geodesic
##  values. Significane levels  *** <= .01, ** <= .05, * <= .1.

# Visualizing distribution of suscep/infect
out <- plot_infectsuscep(diffnet, bins = 20,K=5, logscale = FALSE, h=.01)

out <- plot_infectsuscep(diffnet, bins = 20,K=5, logscale = TRUE,
                         exclude.zeros = TRUE, h=1)

## Warning in plot_infectsuscep.list(graph$graph, graph$toa, t0, normalize, : When
## applying logscale some observations are missing.

Threshold

# Generating a random graph
set.seed(123)
diffnet <- rdiffnet(500, 20,
                    seed.nodes = "random",
                    rgraph.args = list(m=3),
                    threshold.dist = function(x) runif(1, .3, .7))

## Warning in (function (graph, p, algorithm = "endpoints", both.ends = FALSE, :
## The option -copy.first- is set to TRUE. In this case, the first graph will be
## treated as a baseline, and thus, networks after T=1 will be replaced with T-1.

diffnet

## Dynamic network of class -diffnet-
##  Name               : A diffusion network
##  Behavior           : Random contagion
##  # of nodes         : 500 (1, 2, 3, 4, 5, 6, 7, 8, ...)
##  # of time periods  : 20 (1 - 20)
##  Type               : directed
##  Final prevalence   : 1.00
##  Static attributes  : real_threshold (1)
##  Dynamic attributes : -

# Threshold with fixed vertex size
plot_threshold(diffnet)

Using more features

data("medInnovationsDiffNet")
set.seed(131)
plot_threshold(
  medInnovationsDiffNet,
  vertex.color     = viridisLite::inferno(4)[medInnovationsDiffNet[["city"]]],
  vertex.sides     = medInnovationsDiffNet[["city"]] + 2,
  sub = "Note: Vertices' sizes and shapes given by degree and city respectively",
  jitter.factor = c(1,1), jitter.amount = c(.25,.025)
)

## Warning in (function (graph, expo, toa, include_censored = FALSE, t0 =
## min(toa, : -vertex.sides- will be coerced to integer.

Adoption rate

plot_adopters(diffnet)

Hazard rate

hazard_rate(diffnet)

Diffusion process

plot_diffnet(medInnovationsDiffNet, slices=c(1,9,8))

diffnet.toa(brfarmersDiffNet)[brfarmersDiffNet$toa >= 1965] <- NA
plot_diffnet2(brfarmersDiffNet, vertex.size = "indegree")

set.seed(1231)

# Random scale-free diffusion network
x <- rdiffnet(1000, 4, seed.graph="scale-free", seed.p.adopt = .025,
                           rewire = FALSE, seed.nodes = "central",
                           rgraph.arg=list(self=FALSE, m=4),
                           threshold.dist = function(id) runif(1,.2,.4))

# Diffusion map (no random toa)
dm0 <- diffusionMap(x, kde2d.args=list(n=150, h=1), layout=igraph::layout_with_fr)

# Random
diffnet.toa(x) <- sample(x$toa, size = nnodes(x))

# Diffusion map (random toa)
dm1 <- diffusionMap(x, layout = dm0$coords, kde2d.args=list(n=150, h=.5))

oldpar <- par(no.readonly = TRUE)
col <- viridisLite::plasma(100)
par(mfrow=c(1,2), oma=c(1,0,0,0), cex=.8)
image(dm0, col=col, main="Non-random Times of Adoption\nAdoption from the core.")
image(dm1, col=col, main="Random Times of Adoption")
par(mfrow=c(1,1))
mtext("Both networks have the same distribution on times of adoption", 1,
      outer = TRUE)

par(oldpar)

Adopters classification

out <- classify(kfamilyDiffNet, include_censored = TRUE)
ftable(out)

##                thr Non-Adopters Very Low Thresh. Low Thresh. High Thresh. Very High Thresh.
## toa                                                                                        
## Non-Adopters               0.00             0.00        0.00         0.00              0.00
## Early Adopters             0.00            14.04        8.40         0.57              0.29
## Early Majority             0.00             5.64       11.65         5.54              2.58
## Late Majority              0.00             1.34        5.06         6.21              2.96
## Laggards                   0.00             1.53        0.00         0.00             34.19

# Plotting 
oldpar <- par(no.readonly = TRUE)
par(xpd=TRUE)
plot(out, color=viridisLite::inferno(5), las = 2, xlab="Time of Adoption",
     ylab="Threshold", main="")

# Adding key
legend("bottom", legend = levels(out$thr), fill=viridisLite::inferno(5), horiz = TRUE,
       cex=.6, bty="n", inset=c(0,-.1))

par(oldpar)

Session info

sessionInfo()

## R version 4.2.1 (2022-06-23)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.5 LTS
## 
## Matrix products: default
## BLAS:   /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] stats     graphics  grDevices datasets  utils     methods   base     
## 
## other attached packages:
## [1] netdiffuseR_1.22.4
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.9            sna_2.6               highr_0.9            
##  [4] compiler_4.2.1        pillar_1.8.1          tools_4.2.1          
##  [7] boot_1.3-28           digest_0.6.29         MatchIt_4.4.0        
## [10] evaluate_0.16         tibble_3.1.8          lifecycle_1.0.2      
## [13] lattice_0.20-45       viridisLite_0.4.0     pkgconfig_2.0.3      
## [16] rlang_1.0.5           Matrix_1.5-0          igraph_1.3.2         
## [19] cli_3.4.0             rstudioapi_0.14       yaml_2.3.5           
## [22] SparseM_1.81          xfun_0.32             fastmap_1.1.0        
## [25] coda_0.19-4           stringr_1.4.1         knitr_1.40           
## [28] vctrs_0.4.1           networkDynamic_0.11.1 grid_4.2.1           
## [31] glue_1.6.2            fansi_1.0.3           bspm_0.3.9           
## [34] rmarkdown_2.16        magrittr_2.0.3        backports_1.4.1      
## [37] htmltools_0.5.3       MASS_7.3-58.1         utf8_1.2.2           
## [40] stringi_1.7.8         network_1.17.2        statnet.common_4.7.0

To-do list

• Import/Export functions for interfacing other package’s clases, in particular: statnet set (specially the packages networkDynamic and ndtv), igraph and Rsiena.
• Populate the tests folder.
• Use spells? (select_egoalter would use this)
• Classify individuals by adoption category using early adopters, adopters, and laggards, and by threshold using very low, low, high and very high threshold (Valente 95’ p. 94).
• Double check all functions using adjacency matrix values.
• Remove dimnames from matrices and vectors. It is more efficient to use the ones stored in meta instead.
• Implement the Bass model
• Include function to import survey data (as shown on the vignettes)
• Exposure based on Mahalanobis distances and also Roger Leenders on weighting exposure (internal note).
• (2016-03-30): use xspline for drawing polygons & edges.
• (2016-04-04): Add more options to exposure, namely, self (so removes diagonal or not!).
• (2016-04-19): animal behaviorists.
• (2016-10-18): Review language throughout the manual (more than innovation).
• (2016-10-18): Evaluate and eventually use a standard graph format (network for instance?).
• (2016-10-18): Standarize graph plot methods (choose either statnet/igraph/own)