SNAscript. friend.mat <- as.matrix(read.table("elfriend.dat",header=false,sep=" "))

Transcription

1 SNAscript ##### Loading the Adjacency Matrices and Nodal Attributes ##data can be loaded from: ## #####Formatting Data into Standard R Format ########################### ### Reading in Networks from.dat Files friend.mat <- as.matrix(read.table("elfriend.dat",header=false,sep=" ")) ### Reading in Nodal Attributes from.dat File node.attr <- read.table("elattr.dat",header=false) ### Naming Columns colnames(node.attr) <- c("seniority","status","gender","office","years","age","practice","school") ### Converting Attributes to Factors node.attr$status <- factor(node.attr$status,levels=c(1,2),labels=c("partner","associate")) node.attr$gender <- factor(node.attr$gender,levels=c(1,2),labels=c("male","female")) node.attr$office <- factor(node.attr$office,levels=c(1,2,3), labels=c("boston","hartford","providence")) node.attr$practice <- factor(node.attr$practice,levels=c(1,2), labels=c("litigation","corporate")) node.attr$school <- factor(node.attr$school,levels=c(1,2,3), labels=c("harvard","yale","other")) ############### ### Helper functions ### Computes matrix of absolute differences cov.abs.diff <- function(node.cov){ nn <- length(node.cov) edge.cov <- matrix(nrow=nn,ncol=nn) for(ii in 1:nn){ for(jj in 1:nn){ edge.cov[ii,jj] <- abs(node.cov[ii] - node.cov[jj]) return(edge.cov) ### Computes matrix with 1 for equality and 0 otherwise cov.same <- function(node.cov){ nn <- length(node.cov) edge.cov <- matrix(nrow=nn,ncol=nn) for(ii in 1:nn){ for(jj in 1:nn){ edge.cov[ii,jj] <- node.cov[ii] == node.cov[jj] return(edge.cov) 1

2 ############# ############# ##Network summary and plotting using "igraph" ################################################################ library(igraph) ### Converting to igraph Object friend.graph <- graph_from_adjacency_matrix(friend.mat) friend.graph$name <- "Lazega Lawyers Friendship Network" vertex_attr(friend.graph) <- node.attr ### Inspecting igraph Object friend.graph ### Vertexes of friend.graph V(friend.graph) ### Edges of friend.graph E(friend.graph) ### Nodal Attributes vertex_attr(friend.graph) ################################## ##### Plotting with igraph ##### ################################## ### Basic Plot Function plot(friend.graph) ### Interactive Plot Functions tkplot(friend.graph) ### 3D Plot Function library(rgl) rglplot(friend.graph) ### Fixing Network Layout kk.layout <- layout_with_kk(friend.graph) plot(friend.graph,layout=kk.layout) ### Coloring Nodes Using Partnership Status pdf("igraph-friend-plot-status.pdf") plot(friend.graph,layout=kk.layout, vertex.color=vertex_attr(friend.graph)$status, vertex.label=na) legend("topright",legend=c("partner","associate"),fill=categorical_pal(2)) ### Coloring Nodes Based on School, Label Based on Status pdf("igraph-friend-plot-school.pdf") plot(friend.graph,layout=kk.layout,vertex.color=vertex_attr(friend.graph)$school, vertex.label=ifelse(vertex_attr(friend.graph)$status=="partner","p","a")) legend("topright",legend=c("harvard","yale","other"),fill=categorical_pal(3)) ### Scaling Age to be Between 10 and 30 2

3 summary(node.attr$age) scaled.age <- 10*(1 + 2*(node.attr$age-min(node.attr$age))/max(node.attr$age - min(node.attr$age))) ### Using Scaled Age as the Size of Nodes pdf("igraph-friend-plot-age-status.pdf") plot(friend.graph,layout=kk.layout,vertex.size=scaled.age,vertex.label=na, vertex.color=vertex_attr(friend.graph)$status,edge.arrow.size=0.5) legend("topright",legend=c("partner","associate"),fill=categorical_pal(2))#,pch=16) ################################# ##### Numerical Summaries ##### ################################# ##### Calculating Degree of Nodes ### In-Degree degree(friend.graph,mode="in") ### Out-Degree degree(friend.graph,mode="out") ### Note Default Degree is In-Degree + Out-Degree for Directed Networks degree(friend.graph) ### Measures of Centrality closeness(friend.graph) betweenness(friend.graph) edge_betweenness(friend.graph) ##transitivity and reciprocity using igraph transitivity(friend.graph) reciprocity(friend.graph) ############### ############### STATNET ############### ## Network summary and plotting using package "network" in statnet library(statnet) ##create an object of class network using the sociomatrix of ## lawyers friendship network friend.net = network(friend.mat) friend.net ##This is a directed network with 71 nodes and no missing edges #assign attributes to the nodes in the network object set.vertex.attribute(friend.net,attrname="gender",value=as.numeric(node.attr$gender == "female")) set.vertex.attribute(friend.net,attrname="harvard",value=as.numeric(node.attr$school == "harvard")) set.vertex.attribute(friend.net,attrname="yale",value=as.numeric(node.attr$school == "yale")) set.vertex.attribute(friend.net,attrname="partner",value=as.numeric(node.attr$status == "partner")) set.vertex.attribute(friend.net,attrname="years",value=as.numeric(node.attr$years)) set.vertex.attribute(friend.net,attrname="age",value=as.numeric(node.attr$age)) #lets look at the network object again to make sure the node attributes are added 3

4 friend.net ########################### ######## PLOTTING using statnet #plot without node labels xy.coord <- plot(friend.net) #plot with node labels plot(friend.net,coord=xy.coord,displaylabels=true) #color nodes by attributes #color nodes by Status StatusColors = rep(0,dim(node.attr)[1]) StatusColors[which(node.attr$status == 1)] = 'red' #Partner StatusColors[which(node.attr$status == 2)] = 'yellow' #Associate pdf("friendsnetworkbystatus.pdf") plot(friend.net,vertex.col=statuscolors,frame=true,vertex.cex=2, coord=xy.coord) legend('topright',legend=c('partner','associate'),col=c('red','yellow'), pch=19,cex=2) #notice very clear clustering by status #Gender GenderColors= ifelse(node.attr$gender=="2","hotpink","dodgerblue") plot(friend.net,vertex.col=gendercolors,frame=true,vertex.cex=2) #pink = females legend("topright",legend=c('female','male'),col=c('hotpink','dodgerblue'), pch=19,cex=2) #notice some clustering by gender #color nodes by Office OfficeColors = rep(0,dim(node.attr)[1]) OfficeColors[which(node.attr$office == 1)] = 'maroon' #Boston OfficeColors[which(node.attr$office == 2)] = 'yellow' #Hartford OfficeColors[which(node.attr$office == 3)] = 'blue' #Providence plot(friend.net,vertex.col=officecolors,frame=true,vertex.cex=2) legend('topright',legend=c('boston','hartford','providence'), col=c('maroon','yellow','blue'),pch=19,cex=2) ##very clear clustering by office #School SchoolColors = rep(0,dim(node.attr)[1]) SchoolColors[which(node.attr$school == 1)] = 'maroon' #Harvard, Yale SchoolColors[which(node.attr$school == 2)] = 'yellow' #UConn SchoolColors[which(node.attr$school == 3)] = 'blue' #others pdf("friendsnetworkbyschool.pdf") plot(friend.net,vertex.col=schoolcolors,frame=true,vertex.cex=2, 4

5 coord=xy.coord) legend('topright',legend=c('harvard/yale','uconn','others'), col=c('maroon','yellow','blue'),pch=19,cex=2) ##### Using Size to Indicate Continuous variables scaled.years <- 1.5*(1 + 2*(node.attr$Years-min(node.attr$Years))/max(node.attr$Years - min(node.attr$ye pdf("friendsnetworkbyofficeyears.pdf") plot(friend.net,vertex.col=officecolors,frame=true,vertex.cex=scaled.years, coord=xy.coord) legend('topright',legend=c('boston','hartford','providence'), col=c('maroon','yellow','blue'),pch=19,cex=2) ##### Using Size to Indicate Continuous variables scaled.years <- 1.5*(1 + 2*(node.attr$years-min(node.attr$years))/max(node.attr$years - min(node.attr$ye pdf("friendsnetworkbygenderyears.pdf") plot(friend.net,vertex.col=gendercolors,frame=true,vertex.cex=scaled.years, coord=xy.coord) legend("topright",legend=c('female','male'),col=c('hotpink','dodgerblue'), pch=19,cex=2) ###### ##Numerical summary statistics using statnet network.size(friend.net) network.edgecount(friend.net) network.density(friend.net) degree(friend.net,cmode='indegree') degree(friend.net,cmode='outdegree') betweenness(friend.net) closeness(friend.net) ### ##to check whether there are any isolates in the network since we got the ##closeness as zero for all the nodes ###isolated nodes make the geodesic distance very large and consequently the closeness tend to be zero node_sub = network.vertex.names(friend.net)[ -which(degree(friend.net)==0)] ##distribution of nodal summary par(mfrow=c(1,3)) hist(degree(friend.net,cmode='outdegree'),breaks=seq(0,25,by=2.5), main='nodal Outdegree',ylim=c(0,26),xlab='Outdegree',cex.main=2,cex.lab=1.75,cex.axis=1.5) hist(degree(friend.net,cmode='indegree'),breaks=seq(0,25,by=2.5), main='nodal Indegree',ylim=c(0,26),xlab='Indegree',cex.main=2,cex.lab=1.75,cex.axis=1.5) hist(betweenness(friend.net),xlab='betweenness', main='nodal Betweenness',cex.main=2,cex.lab=1.75,cex.axis=1.5) 5

6 ################################################################### ########### NETWORK MODELING ##################################################################### ##### ## Network modeling using ERGM ## ##### lazega-ergm.r - Analyzing Data with ERGMs ##### ################################################################xsxs library(ergm) ## note this also loads the 'network' library ##loading 'statnet' package should also load 'ergm' ##### Loading the Adjacency Matrices and Nodal Attributes #load("nodal-covariates.rdata") #load("adjacency-matrices.rdata") #create a network object friend.net <- network(friend.mat) friend.net #assign attributes to the nodes in the network object set.vertex.attribute(friend.net,attrname="gender",value=as.numeric(node.attr$gender == "female")) set.vertex.attribute(friend.net,attrname="harvard",value=as.numeric(node.attr$school == "harvard")) set.vertex.attribute(friend.net,attrname="yale",value=as.numeric(node.attr$school == "yale")) set.vertex.attribute(friend.net,attrname="partner",value=as.numeric(node.attr$status == "partner")) set.vertex.attribute(friend.net,attrname="years",value=as.numeric(node.attr$years)) set.vertex.attribute(friend.net,attrname="age",value=as.numeric(node.attr$age)) ##### Simple ERGM fit.0 <- ergm(friend.net ~ edges) summary(fit.0) par(mfrow=c(2,2)) plot(gof(fit.0)) ##### Simple ERGM fit.1 <- ergm(friend.net ~ triangle) summary(fit.1) par(mfrow=c(2,2)) plot(gof(fit.1)) ##### ERGM with Covariates ##### Note: edges acts as a constant in a regression model fit.2 <- ergm(friend.net ~ edges + nodecov("gender")) summary(fit.2) par(mfrow=c(2,2)) plot(gof(fit.2)) ##### Comparing to Logistic Regression 6

7 nc.2.ec <- function(vec){ nn <- length(vec) mat <- array(rep(vec,each=nn),c(nn,nn)) return(mat + t(mat)) ec.gender <- nc.2.ec(as.numeric(node.attr$gender)-1) diag(friend.mat) <- NA friend.vec <- as.vector(friend.mat[!is.na(friend.mat)]) gender.vec <- as.vector(ec.gender[!is.na(friend.mat)]) fit.log <- glm(friend.vec ~ gender.vec,family="binomial") ##### Complex ERGM with covariates fit.3 <- ergm(friend.net ~ edges + nodecov("gender") + nodecov("harvard") + nodecov("yale") + nodecov("partner") + nodecov("years") + nodecov("age")) summary(fit.3) ##### Using Edge Covariate Information age.diff <- cov.abs.diff(node.attr$age) years.diff <- cov.abs.diff(node.attr$years) fit.4 <- ergm(friend.net ~ edges + nodecov("gender") + nodecov("harvard") + nodecov("yale") + nodecov("partner") + edgecov(age.diff,"age") + edgecov(years.diff,"years")) summary(fit.4) ##### Same School vs. School Absolutes school.same <- cov.same(node.attr$school) gender.same <- cov.same(node.attr$gender) fit.5 <- ergm(friend.net ~ edges + edgecov(gender.same,"same.gender") + nodecov("harvard") + nodecov("ya nodecov("partner") + edgecov(age.diff,"age") + edgecov(years.diff,"years") + edgecov(sch summary(fit.5) ##### Removing Same School (Final Fit) fit.6 <- ergm(friend.net ~ edges + edgecov(gender.same,"same.gender") + nodecov("harvard") + nodecov("ya nodecov("partner") + edgecov(age.diff,"age") + edgecov(years.diff,"years")) summary(fit.6) ############# ############################# ### Latent Space Network Modeling using Latentnet ### Using ERGMM (Exponential Random Graph Mixed Model) function in latentnet ### ####################### library(latentnet) friend.net <- network(friend.mat) friend.net 7

8 ##### LSM fit without covariates system.time(latent.1 <- ergmm(friend.net ~ euclidean(d=2))) summary(latent.1) plot(latent.1) plot(latent.1,what='pmean') mcmc.diagnostics(latent.1) #diagnostic of MCMC ergmm.control(latent.1) #investigating MCMC control parameters ##### Adding edge covariates with latentnet same.status <- cov.same(node.attr$status) system.time(latent.2 <- ergmm(friend.net ~ euclidean(d=2) + edgecov(same.status,"partner"))) #summary, plots and diagnostics summary(latent.2) plot(latent.2) plot(latent.2,what='pmean') mcmc.diagnostics(latent.2) ergmm.control(latent.2) ##LSM with many edge covariates age.diff <- cov.abs.diff(node.attr$age) years.diff <- cov.abs.diff(node.attr$years) school.same <- cov.same(node.attr$school) gender.same <- cov.same(node.attr$gender) latent.3 <- ergmm(friend.net ~ euclidean(d=2) + edgecov(gender.same,"same.gender") + edgecov(same.status,"partner") + edgecov(age.diff,"age") + edgecov(years.diff,"years") + edgecov(school.same,"same.school")) summary(latent.3) plot(latent.3) plot(latent.3,what='pmean') mcmc.diagnostics(latent.3) ergmm.control(latent.3) ## plots of fitted latent positions ############## par(mfrow=c(2,2)) plot(latent.1$mcmc.pmode$z,pch=20,col=node.attr$status, xlab='z_1',ylab='z_2',cex=2,xlim=c(-7.5,7.5),ylim=c(-7.5,7.5), main=paste('fitted Latent Positions','\n', 'using LSM')) plot(latent.2$mcmc.pmode$z,pch=20,col=node.attr$status, xlab='z_1',ylab='z_2',cex=2,xlim=c(-7.5,7.5),ylim=c(-7.5,7.5), main=paste('fitted Latent Positions','\n','using LSM with Covariates')) plot(latent.3$mcmc.pmode$z,pch=20,col=node.attr$status, xlab='z_1',ylab='z_2',cex=2,xlim=c(-7.5,7.5),ylim=c(-7.5,7.5), main=paste('fitted Latent Positions','\n','using LSM with Many Edge Covariates')) 8