netdiffuseR_useR2016.Rnw

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\title[netdiffuseR @ useR! 2016]{%
  Network Diffusion of Innovations in R:\\%
  Introducing \ndR}
\author[GGVY \and TWV]{George G. Vega Yon \and Thomas W. Valente\vspace{-3ex}}
\institute[USC + CANA]{%
  \begin{minipage}[m]{.18\linewidth}
    % \includegraphics[width=.3\linewidth, clip=true, trim=1cm 1cm 1cm 1cm ]{cana_logo.pdf}
    \raggedleft
    \includegraphics[width=.8\linewidth]{Small_Use_Seal_BlackOnWhite.pdf}
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  \begin{minipage}[m]{.18\linewidth}
    \raggedright
    \includegraphics[width=.8\linewidth]{cana_logo.pdf}
  \end{minipage}
  \\
  Department of Preventive Medicine\\University of Southern California%
  }
\date[]{%
  \includegraphics[width=.2\linewidth]{userlogo2016.pdf}\\%
  June 29th, 2016
  }

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% \usepackage{tikz}
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% Some commands ----------------------------------------------------------------
\newcommand{\Rpkg}[1]{{\bf\href{https://cloud.r-project.org/web/packages/#1/index.html}{#1}}}
\newcommand{\ndR}{\Rpkg{netdiffuseR}}
\newcommand{\framesec}{}%\frame{\frametitle{Contents}\tableofcontents[currentsection]}}
\newcommand{\framesubsec}{}%\frame{\frametitle{Contents}\tableofcontents[currentsubsection]}}
\newcommand{\code}[1]{{\tt #1}}

\usepackage{ulem}% For st (stroke)

\begin{document}

<<Setup, echo=FALSE, warning=FALSE, message=FALSE>>=
knitr::opts_chunk$set(echo=FALSE, warning = FALSE, message = FALSE)
@


\frame{\titlepage}

\note[enumerate]{
  \item Hi there, I'm George Vega Yon,
  \item and I'm here today to tell you about our R package ndR.
  \item While we have a lot of things to show you, I'll go a little bit fast so we can fit our time!
}

% Acknowledgements
\frame{\frametitle{Acknowledgements}

\begin{quote}
\ndR{} was created with the support of grant R01 CA157577 from the National Cancer Institute/National Institutes of Health.
\end{quote}

\begin{quote}
\ndR{} has benefited from input provided by participants of the Center for Applied Network Analysis (CANA), and the Computational Social Science Lab (CSSL) at the University of Southern California.
\end{quote}

\begin{quote}
\ndR{}'s original code was developed by {\bf Thomas Valente}, improved by {\bf Stephanie Dyal} and {\bf Timothy Hayes}, and extended by {\bf George Vega Yon}.
\end{quote}
}

\note[enumerate]{
  \item Before starting I'd like to make a few acknowledgements.
  \item To tha National Cancer Insitute and the National Institute of Health for their support
  \item To the Center for Applied Network Analysis and Computational Social Science Lab at USC for their feedback, and
  \item To the other team members behind ndR: Thomas Valente, Stephanie Dyal and Timothy Hayes.
  \item Let's get started
}

\frame{\frametitle{Contents}\tableofcontents}

\note[enumerate]{
  \item I'll start by telling something about Network Diffusion of Innovations and ndR itself
  \item To then show you some example using ndR
}

\section{Motivation}\framesec

\begin{frame}
\frametitle{Motivation}
\framesubtitle{{\it Network} Diffusion of Innovations}

\note[item]{Basically, Network Diffusion of Innovations is the product of merging two
    big fields: Diffusion of Innovations (lead by Prof. Rogers's seminal work)
    and Social Network Analysis.}
\note[item]<2->{Further, network diffusion of innovations is a filed itself lead which
    started with Prof. Valente doctoral thesis, 'Network Models of the Diffusion
    of Innovations', to whom Prof. Rogers was the advisor.}
\note[item]<3->{There you'll see ndR's first steps written in GAUSS!}
\begin{center}
\begin{minipage}[m]{.25\linewidth}
  \center
  \includegraphics[width=.9\linewidth]{rogers_2003.jpg}
\end{minipage}\pause
\begin{minipage}[m]{.03\linewidth}
  \centering \Huge \bf +
\end{minipage}
\begin{minipage}[m]{.3\linewidth}
  <<Nice graph, out.width='.9\\linewidth', fig.width=4, fig.height=4, fig.align='center'>>=
  library(netdiffuseR)
  set.seed(231)
  x <- rdiffnet(100, 10, rewire = FALSE, seed.nodes = "central")
  s <- sqrt(dgr(x)[,4] + 1)
  s <- (s - min(s))/(max(s) - min(s))
  s <- s*(90-20)+20
  oldpar <- par(no.readonly = TRUE)
  par(mai=rep(0,4))
  plot_diffnet2(x, key.width = 0, main=NA, vertex.size = s)
  par(oldpar)
  @
\end{minipage}
\pause
\begin{minipage}[m]{.03\linewidth}
  \centering \Huge \bf =
\end{minipage}
\begin{minipage}[m]{.25\linewidth}
  \centering
  \includegraphics[width=.9\linewidth]{valente_1995.jpg}
\end{minipage}
\end{center}\pause
So what is Network Diffusion of Innovations anyway?
\end{frame}

\begin{frame}
\frametitle{Motivation}
\framesubtitle{Network Diffusion of Innovations}

\begin{itemize}
  \item<+-> Tries to explain how new ideas and practices (innovations) spread within and between
  communities.
  \item<+-> While a lot of factors have been shown to influence diffusion (Spatial,
    Economic, Cultural, Biological, etc.), Social Networks is a prominent one.
  \item<+-> More complex than \textit{contagion} $\implies$ a single tie is no longer enough\note{This discipline works on the fact that }
    for an innovation to spread across a social system.
  \item<+-> We think of this in terms of adoption thresholds and social exposure.
\end{itemize}

\end{frame}

\begin{frame}
\frametitle{Motivation}
\framesubtitle{Network Diffusion of Innovations}

\textbf{The basic idea}

\begin{itemize}
\item Network thresholds (Valente, 1995), $\tau$, 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

\begin{equation}
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}}
\end{equation}

Where $E_i$ is i's exposure to the innovation and $\mathbf{X}$ is the adjacency matrix (the network).\note[item]<2->{So it's all about threshold levels and exposures}\pause

\item  This can be generalized and extended to include covariates and other weighting schemes (that's what \ndR{} is all about).\pause
\end{itemize}

So now, what is \ndR?
\end{frame}

\section{\ndR: network diffusion of innovations in R}\framesec

\begin{frame}
\frametitle{\ndR: network diffusion of innovations in R}
% \framesubtitle{General overview}

\ndR{} is an {\bf R} package that\pause

\begin{itemize}[<+->]
\item Is designed for Visualizing, Analyzing and Simulating network diffusion data (in general).
\item Depends on some pretty popular packages:
\begin{itemize}
  \item \Rpkg{RcppArmadillo}: So it's fast,
  \item \Rpkg{Matrix}: So it's big,
  \item \Rpkg{statnet} and \Rpkg{igraph}: So it's not from scratch
\end{itemize}
\item It's roughly 14,000 lines of code (\code{R/} + \code{src/} + \code{tests/}), ~100 pages of manual, and 4 vignettes,\note[item]<7->{BTW, I can't tell you how exited I was when we reached the 100 p in the manual. A very nerdy thing but I see it as a proxy of all the work we've put in it.}
\item Can handle big graphs, more than 4 billion elements adjacency matrix (PR for RcppArmadillo)\note[item]<8->{This after a PR that we submitted to RcppArmadillo!},
\item Already on CRAN (2 iterations) with ~700 downloads since its first version, Feb 2016,
\item A lot of features to make it easy to read network (dynamic) data, making it a nice companion of other net packages.
\end{itemize}

\end{frame}

\begin{frame}
\frametitle{\ndR: network diffusion of innovations in R}
% \framesubtitle{General overview}

\note{
\begin{itemize}
  \item Among other features, ndR includes 3 classical datasets from network diffusion literature
  \item The diffusion of Tetacycline, Hybrid Corn Seed and Family planning methods
  \item Won't enter in details but here is for later reference.
  \item Now some examples!
  \end{itemize}
}

\ndR{} distributes classical diffusion of innovations datasets:

\footnotesize
\begin{table}
\begin{tabular}{l*{3}{m{.225\linewidth}<\centering}} \toprule
 & 	{\bf Medical Innovation}	 & 	{\bf Brazilian Farmers}	 & 	{\bf Korean Family Planning}	\\ \midrule
\textit{Country}	 & 	USA	 & 	Brazil	 & 	Korea	\\
\textit{N Respondents}	 & 	125 Doctors	 & 	692 Farmers	 & 	1,047 Women	\\
\textit{N Communities}	 & 	4	 & 	11	 & 	25	\\
\textit{Innovation}	 & 	Tetracycline	 & 	Hybrid Corn Seed	 & 	Family Planning	\\
\textit{Time for Diffusion}	 & 	18 Months	 & 	20 Years	 & 	11 Years	\\
\textit{Year Data Collected}	 & 	1955-1956	 & 	1966	 & 	1973	\\
\textit{Ave. Time to 0.50}	 & 	6	 & 	16	 & 	7	\\
\textit{Highest Saturation}	 & 	0.89	 & 	0.98	 & 	0.83	\\
\textit{Lowest Saturation}	 & 	0.81	 & 	0.29	 & 	0.44	\\
\textit{Citation}	 & 	Coleman et al (1966)	 & 	Rogers et al (1970)	 & 	Rogers \& Kincaid (1981) \\ \bottomrule
\end{tabular}
\end{table}\pause
\normalsize

Very nice\dots\pause But it's better to show it with examples!

\end{frame}

\section{\ndR: some examples}
\subsection{The basics}\framesubsec

\begin{frame}[fragile]
% \frametitle{\ndR: some examples}
\frametitle{The basics: Reading data}

\note{
\begin{itemize}
  \item Besides of the usual edgelist and adjacency matrix reading, we have put a lot of time on reading data in ndR.
  \item ndR can read survey data!
  \item Take this dataset as an exmaple: We have a longitudinal dataset with network nominations (e.g. name your 5 closest
  friends), including times of adoption for a particular behavior.
  \end{itemize}
}
\note[item]<2->{We can use the s 2 dn function}

\footnotesize
<<Showing data, echo=TRUE>>=

library(netdiffuseR)
print(head(fakesurveyDyn))

@
\normalsize\pause

We can use the \code{survey\_to\_diffnet} function!

\end{frame}

\begin{frame}[fragile]
% \frametitle{\ndR: some examples}
\frametitle{The basics: Reading data}
\scriptsize
<<Reading it, echo=TRUE, warning=FALSE>>=
mydiffnet <- survey_to_diffnet(
  fakesurveyDyn,
  idvar    = "id",                      # Id of each vertex
  netvars  = c("net1", "net2", "net3"), # Net nominations (e.g. 'name 3 closest friends')
  toavar   = "toa",                     # Time of Adoption
  groupvar = "group",                   # Group (e.g. neighbor, village, etc.)
  timevar  = "time"                     # Timestamp
  )

# Print method
mydiffnet
@

This is a \code{diffnet} object.

\normalsize

\end{frame}

\note[enumerate]{
  \item By telling ndR some basics such as the id, network nominations and time of adoption (the others here are optional)
  \item You can get a diffnet object!
}

\begin{frame}[fragile]
% \frametitle{\ndR: some examples}
\frametitle{The basics: \code{diffnet} objects}

\code{diffnet} are

\footnotesize
\begin{minipage}[t]{.35\linewidth}
  Lists that contains (among other things):
  \begin{itemize}
  \item A list of \code{dgCMatrix} objects (sparse matrices),
  \item A set of \code{data.frame}s with vertex attributes,
  \item An \code{integer} vector with times of adoption
  \end{itemize}

\end{minipage}\pause
\hfill
\begin{minipage}[t]{.55\linewidth}
  Nice objects with a lot of methods

  {\bf Common methods}

  \begin{itemize}
  \item[]
  \begin{description}
  \item[\tt print, summary, plot] The usual deal
  \item[\tt [[, [[<-] Attribute access
  \item[\tt [, [<-] Adjacency matrix access
  \item[\tt \%*\%, \^{}, t, c] Matrix mult and others
  \item[\tt +, -, *, \&, |] Arithmetic
  \end{description}
  \end{itemize}\pause

  {\bf Other special functions}

  \begin{itemize}
  \item[]
  \begin{description}
  \item[\tt exposure (threshold)] Basic net-diff stats
  \item[\tt infection, susceptibility] Some friends from epi
  \item[\tt struct\_equiv] Burt's (1987) structural equivalence
  \item[\tt struct\_test] We'll see this later\dots
  \end{description}
  \end{itemize}

\end{minipage}\note<3->{Most of the special functions have methods for non-diffnet objects (matrix friendly).}\pause
\normalsize

So, what can we do with \code{diffnet} objects?
\end{frame}


\subsection{Visualizing Diffusion}\framesubsec

\begin{frame}
% \frametitle{\ndR: some examples}
\frametitle{Visualizing Diffusion: \code{plot\_diffnet}}

<<diffusion plot1, fig.width=12, fig.height=4.5, out.width='1\\linewidth', fig.align='center', cache=TRUE, fig.cap='Diffusion of Hybrid Corn Seed (Brazilian Farmers) - 11 communities/20 years.'>>=
set.seed(123112)
x <- brfarmersDiffNet

diffnet.toa(x)[x$toa==1965] <- NA
oldpar <- par(no.readonly = TRUE)

# source("20160614_plot_diffnet(new).R", echo = FALSE)
oldpar <- par(no.readonly = TRUE)
par(mai=rep(0,4))
coords <- plot_diffnet(x, slices=c(1,10,21),
              vertex.cex = dgr(x)[,1],
              mfrow.par = c(1,3), key.height = .025, intra.space = c(.1,.1),
              rescale.fun = function(x)
                rescale_vertex_igraph(x, adjust=150, minmax.relative.size = c(.005,.025)))
par(oldpar)
@
\end{frame}

\note[enumerate]{
  \item We plot them.
  \item Here we can see how does the usage of a Hybrid corn seed spreads across
    a social the network through time.
  \item Showing three slides (time points), the plot represents non-adopters as
    white squares, new adopters in red and previous adopters in blue.
}

\begin{frame}
% \frametitle{\ndR: some examples}
\frametitle{Visualizing Diffusion: \code{plot\_diffnet2}}

<<diffusion plot2, fig.width=12, fig.height=6, out.width='.7\\linewidth', fig.align='center', cache=TRUE, fig.cap='Diffusion of Hybrid Corn Seed (Brazilian Farmers) - 11 communities/20 years.'>>=
oldpar <- par(no.readonly = TRUE)
par(mai=rep(0,4))
plot_diffnet2(x, layout = coords, vertex.size = dgr(x)[,2], main="",
              rescale.fun = function(x)
                rescale_vertex_igraph(x, minmax.relative.size = c(.005,.025)))
par(oldpar)
@
\end{frame}

\note[enumerate]{
  \item Same information, different visualization
  \item Here diffusion dynamics are observed on the vertex color.
  \item Blu-ish are early adopters and red are laggards, and as before, white
    ones are non-adopters.
}

\begin{frame}
% \frametitle{\ndR: some examples}
\frametitle{Visualizing Diffusion: \code{plot\_infectsuscept}}

\begin{figure}[h]
\centering
<<infection plot, fig.height=5.5, fig.width=7, out.width=".45\\linewidth", fig.show="hold", cache=TRUE, fig.env=''>>=
set.seed(1231)
x <- rdiffnet(400, t=20, seed.graph = "bernoulli")
plot_infectsuscep(x, bins=40, logscale = FALSE, main="(a)")
plot_infectsuscep(x, h=.5, bins=40, main="(b)")
@
\caption{Joint distribution of Infectiousness and Susceptibility in a random bernoulli diffusion network: (b) shows (a) with log-scale.}
\end{figure}

\end{frame}

\note[enumerate]{
  \item Borrowing concepts from epidemiology,
  \item Here we can see (and compute) infectiousness and susceptibility of each
    vertex in linear and log-scale.
}

\begin{frame}
% \frametitle{\ndR: some examples}
\frametitle{Visualizing Diffusion: \code{plot\_threshold} (a classic)}

<<Network Thresholds, fig.width=9, fig.height=5, out.width='.7\\linewidth', fig.align='center', fig.cap='Adoption thresholds and times of adoption for the Brazilian Farmers: Colors and shapes represent villages. Size is scaled accordingly to each vertex degree.', cache=FALSE>>=
V <- as.integer(as.factor(brfarmersDiffNet[['village']])) + 2
C <- rgb(colorRamp(blues9)(V/max(V)), alpha=200, maxColorValue = 255)
plot_threshold(brfarmersDiffNet, vertex.sides = V,
               vertex.col=C, main="")
@
\note{Here we have a classic plot. Threshold vs time of adoption (very fancy, it has a lot of parameters for the user to play with.)}
\end{frame}

\begin{frame}
% \frametitle{\ndR: some examples}
\frametitle{Visualizing Diffusion: \code{classify\_adopters} (also a classic)}

\begin{figure}
\centering
\begin{minipage}[m]{0.3\linewidth}
\tiny
<<echo=FALSE, out.width='1\\linewidth', results='asis'>>=
library(xtable)
out <- classify(kfamilyDiffNet, include_censored = TRUE, addNA=FALSE)
print(
  xtable::xtable(
    as.table(ftable(out, addNA = FALSE)),
    align=c("p{.3\\linewidth}",rep("p{.06\\linewidth}",4))
    ),
  rotate.colnames = TRUE)
@
\normalsize
\end{minipage}
% \hfill
\begin{minipage}[m]{0.65\linewidth}
<<Classification, echo=FALSE, fig.width=8, fig.height=5, out.width='1\\linewidth'>>=

# Computing color
age <- kfamilyDiffNet[["age"]]
age[age==0] <- mean(age)

# Mean by class
cl  <- as.data.frame(out)
Means <- with(out, matrix(0, 4, 4,
                        dimnames = list(levels(toa), levels(thr))))
for (l in levels(out$toa))
  for (h in levels(out$thr))
    Means[l,h] <- mean(age[cl$toa==l & cl$thr==h], na.rm = TRUE)

# Color palette
Col <- Means
Col[] <- (Means - min(Means, na.rm = TRUE))/
  (max(Means, na.rm = TRUE) - min(Means, na.rm = TRUE))
Col[is.nan(Col)] <- mean(Col, na.rm = TRUE)
Col[] <- rgb(colorRamp(blues9)(Col), maxColorValue = 255)

# Plotting and adding key
levels(out$toa) <-
  sapply(strsplit(levels(out$toa), " "), paste, collapse="\n             ")
plot(out, color=Col, las = 2, xlab="Time of Adoption",
     ylab="Threshold", main="", ftable.args=list(addNA=FALSE))

drawColorKey(Means, nlevels = 50, border="transparent",
             main="Age",
             color.palette = colorRampPalette(blues9)(50),
             key.pos = c(.8,.90,.1,.6)
             )

@
\end{minipage}

\caption{Adopters classification in the Korean Family data: From the mosaic we can see that in general
low threshold levels and early adoption seems to be positively correlated with age.}
\end{figure}

\end{frame}

\note[enumerate]{
  \item And further, another classic, we can classify adopters according to Rogers early-adopters vs laggards and Valente's threshold levels, tabulate them and visualize them easily
  \item Now, some of you may be thinking\dots
}

\frame{
\Large What about \ndR{} being big?? \normalsize
}

\begin{frame}
% \frametitle{\ndR: some examples}
\frametitle{Visualizing Diffusion: \code{plot\_diffnet2} w/ big graph}

<<diffusion plot thousand I, cache=TRUE, echo=FALSE, dev='tiff'>>=
set.seed(231)
n <- 5e4
x <- rdiffnet(n, 5, seed.graph = "scale-free", rewire = FALSE,
              seed.nodes="central", rgraph.args = list(m=2), seed.p.adopt = .0675,
              threshold.dist = runif(n, .7,.9))

# Layout and size
layout <- igraph::layout.fruchterman.reingold(
  igraph::graph_from_adjacency_matrix(x$graph[[nslices(x)]])
)
@

<<diffusion plot thousand II,  fig.width=12, fig.height=6, out.width='.8\\linewidth', fig.align='center', echo=FALSE, cache=TRUE, fig.cap='Random scale-free diffusion network: With 5e4 vertices, diffusion started at the central nodes.', dev='CairoPNG'>>=

in_sd <- function(x, k=3, na.rm=TRUE) {
  m <- mean(x, na.rm = na.rm)
  s <- sd(x, na.rm = na.rm)
  r <- m + s*c(-1,1)*k

  (r[1] <= x) & (x <= r[2])
}

index <- apply(layout, 2, in_sd)
index <- apply(index, 1, all)

vs <- dgr(x[index])[,nslices(x)]

oldpar <- par(no.readonly = TRUE)
par(mai=rep(.5,4))
plot_diffnet2(x[index], vertex.size = vs, main="", layout = layout[index,,drop=FALSE],
              edge.color=adjustcolor("gray", .1),
              color.ramp = colorRamp(c("skyblue","yellow", "red")),
              key.width = .1, key.title = "Time of\nAdoption")
par(oldpar)

@

\end{frame}

\note[enumerate]{
  \item Here it is. This is a simulated diffusion network with 50 K vertices
  \item Is a scale-free network in which the diffusion started on the higher degree
    centrality vertices.
  \item The diffusion pattern is clear... right?
}


\begin{frame}
% \frametitle{\ndR: some examples}
\frametitle{Visualizing Diffusion: \code{plot\_diffnet2 + diffmap} w/ big graph}

<<diffusion plot thousand III, fig.width=12, fig.height=6, out.width='.8\\linewidth', fig.align='center', cache=TRUE, fig.cap='Random scale-free diffusion network: With 5e4 vertices, diffusion started at the central nodes.', dev='CairoPNG'>>=
oldpar <- par(no.readonly = TRUE)
par(mai=rep(.5,4))
plot_diffnet2(x[index], vertex.size = vs, main="",
              layout = layout[index,,drop=FALSE],
              add.map="last", edge.color="transparent",
              color.ramp = colorRamp(c("skyblue","yellow", "red")),
              diffmap.args = list(kde2d.args=list(n=100, h=.10)),
              key.width = .1, key.title = "Time of\nAdoption")
par(oldpar)

@

\end{frame}

\note[enumerate]{
  \item What about now!
  \item The diffnet map function takes any vector of length n (covariate), and
    draws it over the graph's layout in a smooth way.
  \item Notice it is not a smoothScatter-plot (the hotter portion of it is outside
    where there's lower density!)
  \item While a very fancy and neat way of visualizing big data, we have to be
    careful with this kind of issues
}

\begin{frame}
% \frametitle{\ndR: some examples}
\frametitle{Visualizing Diffusion: \code{plot\_diffnet2 + diffmap} w/ big graph}

But\dots be careful with this!

\begin{figure}
\centering
\includegraphics[width=.35\linewidth]{xkcd_1138_heatmap.png}
\caption{The heatmaps pitfall (source \url{xkcd.com/1138})}
\end{figure}

\end{frame}

\note[enumerate]{
  \item nevertheless, users must be careful with the heatmaps' pitfall!
  \item Fancy heatmap-like figures aren't always the best way to go!
  \item Now lets checkout the rdiffnet function.
}

\subsection{Simulating Diffusion Process}\framesubsec

\note{ndR is also a toold for simulating diffusion process}

\begin{frame}[fragile]
% \frametitle{\ndR: some examples}
\frametitle{Simulating Diffusion Process: \code{rdiffnet}}

Simulations are a big thing in \ndR. The \code{rdiffnet} function features:

\footnotesize
<<Simulating a diffnet, echo=TRUE>>=

set.seed(887)
mydn <- rdiffnet(
  n=1e3, t=5, # Number of vertices and time points
  seed.nodes     = "random", # Set of initial adopters
  seed.p.adopt   = .15, # Proportion of initial adopters
  seed.graph     = "small-world", # Baseline graph
  rgraph.args    = list(p=4), # Arguments for the rgraph call
  rewire.args    = list(algorithm="swap", p=5), # Rewiring args after time 1
  threshold.dist = function(x) runif(1, .4, .8), # Distribution of thresholds
  exposure.args  = list(normalized=TRUE) # Args for computing exposures
)
@

\normalsize
\end{frame}

\note[enumerate]{
  \item ndR is also a tool for simulating diffusion process.
  \item In this example we use the rdiffnet function to generate a random diffnet
    object.
  \item While it only suffices with specifying the size of the graph and number of
    time periods, this example illustrates several other parameters that can be
    modified by the user: The set of initial adopters (innovators as Rogers would said),
    the seed graph and some rewiring algorithm, the vertices distribution and
    how to compute exposures.
}

% New methods: Non-parametric tests --------------------------------------------
\subsection{Statistical inference}\framesubsec

\begin{frame}
% \frametitle{\ndR: some examples}
\frametitle{Statistical inference: \code{struct\_test}}

<<echo=FALSE, cache=FALSE>>=
library(netdiffuseR)
@


<<Struct test kf, echo=FALSE, cache=TRUE>>=
kf <- kfamilyDiffNet

out.1 <- struct_test(kf, function(x) mean(threshold(x), na.rm = TRUE), R = 1e3,
            parallel="multicore", ncpus=8,
            rewire.args = list(
              p=n_rewires(kf), algorithm="swap"))
@

<<Struct test bf, echo=FALSE, cache=TRUE>>=
bf <- brfarmersDiffNet

out.2 <- struct_test(bf, function(x) mean(threshold(x), na.rm = TRUE), R = 1e3,
            parallel="multicore", ncpus=8,
            rewire.args = list(
              p=n_rewires(bf), algorithm="swap"))
@

<<Struct test mi, echo=FALSE, cache=TRUE>>=
mi <- medInnovationsDiffNet

out.3 <- struct_test(mi, function(x) mean(threshold(x), na.rm = TRUE), R = 1e3,
            parallel="multicore", ncpus=8,
            rewire.args = list(
              p=n_rewires(mi), algorithm="swap"))
@

\begin{align*}
H_0:&\; \mathcal{G} \perp \mbox{Time of Adoption (random time of adoption)}\\
H_a:&\; \mathcal{G} \not\perp \mbox{Time of Adoption (not random time of adoption)}
\end{align*}

<<echo=FALSE>>=
fetch_important <- function(l, args=c(`p-val`="p.value", `Obs. Avg. threshold $t_0$`="t0", `Sim  Avg. threshold $\\bar t$`="mean_t"),
                            format.args=list(digits=4, big.mark=",", format="f")) {
  out <- lapply(l, "[", args)
  out <- lapply(out, function(x) {
    do.call(base::formatC, c(format.args, list(unlist(x))))
  })
  out <- do.call(cbind, out)
  rownames(out) <- names(args)
  out
}
@


\scriptsize
{
\centering
<<Struct test table, echo=FALSE, results='asis'>>=
# knitr::kable(fetch_important(list(KFP=out.1, BF=out.2, MI=out.3)),
#              format="latex", booktabs=TRUE, escape=FALSE)
library(xtable)
print(xtable(fetch_important(list(`Korean Family`=out.1, `Brazilian Farmers`=out.2, `Medical Innovation`=out.3))),
      table.placement='H', sanitize.text.function=function(x) x,
      booktabs=TRUE, with='.6\\linewidth')
@
}
\normalsize

<<Plotting, echo=FALSE, fig.width=10, fig.height=2.75>>=
oldpar <- par(no.readonly = TRUE)
par(mfcol=c(1,3))
hist(out.1, main="Korean Family Planning")
hist(out.2, main="Brazilian Farmers")
hist(out.3, main="Medical Innovation")
par(oldpar)
save(out.1, out.2, out.3, file="rewired.rda")
@


\end{frame}

\note[enumerate]{
  \item Finally, ndR can do statistical inference for network data
  \item The struct test function implements a new non-parametric test that mixes
    network structure and vertices covariates.
  \item A nice alternative for parametric ERGMs and SIENAs for those of you
    close to the network inference. In this example we are testing if time of
    adoption (TOA) was independent from the network structure or not.
  \item Applied to the three classical datasets, it shows strong evidence towards
    diffusion effects on the diffusion of Hybrid Corn Seeds (supporting previous
    findings).
}

\section{Concluding remarks}\framesec

\begin{frame}
\frametitle{Concluding remarks}

So, to conclude, \ndR

\begin{itemize}
\item<+-> Is an R package focused on network diffusion \alt<1>{of innovations}{\sout{of innovations} (in general)}\pause.
\begin{itemize}
\item Health behavior diffusion (tobacco, drinking, etc.),
\item Memes on social media,
\item Country-level spill over effects (FCTC)
\item ... social contagion (human or not) in general.\only<3->{\footnote{Social learning in animals, see \href{http://rspb.royalsocietypublishing.org/cgi/doi/10.1098/rspb.2008.1824}{Franz and Nunn (2009)}}}
\end{itemize}\pause
\item<+-> Provides out-of-the-box tools for network diffusion analysis (both classic and new),
\item<+-> Complements your favorite SNA R package--\Rpkg{igraph}, \Rpkg{statnet}, \Rpkg{RSiena}, etc. (and further, work is been done to extend it to others \textit{s.a.} \Rpkg{spdep}, \Rpkg{spatialprobit})
\item<+-> Is on active development, so stay tuned for more to come!
\end{itemize}

\end{frame}

\frame{

\begin{center}
\Huge Thank you! \normalsize


\begin{minipage}[m]{.35\linewidth}
  % \includegraphics[width=.3\linewidth, clip=true, trim=1cm 1cm 1cm 1cm ]{cana_logo.pdf}
  \raggedleft
  \includegraphics[width=.8\linewidth]{Small_Use_Seal_BlackOnWhite.pdf}
\end{minipage}
\begin{minipage}[m]{.35\linewidth}
  \raggedright
  \includegraphics[width=.8\linewidth]{cana_logo.pdf}
\end{minipage}


\textbf{More info} \\
\url{https://github.com/USCCANA/netdiffuseR}\\
\url{http://cana.usc.edu}

\textbf{contact} \\
\href{mailto:vegayon@usc.edu}{vegayon@usc.edu}\\
\href{https://twitter.com/gvegayon}{@gvegayon}
\end{center}
}

\begin{frame}
\frametitle{Sesssion Info}

\begin{minipage}[m]{.35\linewidth}
\scalebox{.8}{
<<Session info 1, echo=FALSE, results='asis'>>=
knitr::kable(t(data.frame(t(unclass(devtools::session_info()[[1]])))), col.names = " ", format="latex")
@
}
\end{minipage}
\hfill
\begin{minipage}[m]{.6\linewidth}
\scalebox{.65}{
<<Session info 2, echo=FALSE, results='asis'>>=
knitr::kable(devtools::session_info()[[2]], format = "latex")
@
}
\end{minipage}
\end{frame}

\end{document}