diff --git a/publication_rmd/simulation_example_fig1/figure1.Rmd b/publication_rmd/simulation_example_fig1/figure1.Rmd new file mode 100644 index 0000000..12800b2 --- /dev/null +++ b/publication_rmd/simulation_example_fig1/figure1.Rmd @@ -0,0 +1,258 @@ +--- +title: "figure_1" +output: + html_document: + code_folding: hide +--- + +This is a simulation example that shows that confounders and batch effects impact reconstruction of gene co-expression networks. Using this example we also show that true underlying network structure can be reconstructed after principal component correction of gene expression data as described in the paper. + +This script generates Figure 1 in the paper -- "Addressing confounding artifacts in reconstruction of gene co-expression networks" + +```{r} +rm(list = ls()) + +## load libraries +#library(pcalg) +library(mvtnorm) +library(clusterGeneration) +library(sva) +#library(spacejam) +library(gridExtra) +library(gtable) +library(glasso) +library(huge) +library(devtools) +install_github('alyssafrazee/RSkittleBrewer') +library(RSkittleBrewer) +tropical = RSkittleBrewer('tropical') +library(ggplot2) +library(reshape2) +library(cowplot) +### Data: 5 features, 10 samples +p=8 +n=10 + +V=diag(1,nrow=p,ncol=p) +V[1,3]=V[3,1]=.35 +V[4,7]=V[7,4]=.3 +V[1,8]=V[8,1]=.3 +V.inv=solve(V) + +colnames(V)=rownames(V)=colnames(V.inv)=rownames(V.inv)=paste(1:8) + +A.generating=V +for(i in 1:p){ + for(j in 1:p){ + if(abs(V[i,j])>0.05){ + A.generating[i,j]=1 + } + if(abs(V[i,j])<=0.05){ + A.generating[i,j]=0 + } + } +} +g.generating=graph.adjacency(A.generating,mode="undirected", diag=FALSE,add.colnames=TRUE) + +set.seed(4747) +data=rmvnorm((1000*n),mean=rep(1,p),sigma=V) +rownames(data)=1:(1000*n) +colnames(data)=1:8 + +cor.data=cor(data) + +## Graph +lambda=seq(1,0.01,length.out=200) +glasso.unconfounded.lambda=huge(data,lambda,method="glasso") +glasso.adjacency.unconfounded.lambda=glasso.unconfounded.lambda$path +glasso.graph.unconfounded.lambda=list() + +for(i in 1:200){ + glasso.graph.unconfounded.lambda[[i]]=graph.adjacency(glasso.adjacency.unconfounded.lambda[[i]],mode="undirected", diag=FALSE) +} + +############ Confounding ############ +data.confounded=data +grp=rnorm(1000*n) +for(i in 2:6){ + data.confounded[,i] = data.confounded[,i] + 50*grp +} + +rownames(data.confounded)=1:(1000*n) +colnames(data.confounded)=1:8 + +cor.data.confounded=cor(data.confounded) +colnames(cor.data.confounded)=rownames(cor.data.confounded)=1:8 + +colnames(data.confounded)=1:8 +rownames(data.confounded)=1:10000 + +glasso.confounded=huge(data.confounded,lambda,method="glasso") + +glasso.adjacency.confounded=glasso.confounded$path +glasso.graph.confounded=list() +for(i in 1:200){ + glasso.graph.confounded[[i]]=graph.adjacency(glasso.adjacency.confounded[[i]],mode="undirected", diag=FALSE) +} + +############ Correct for Confounding (Residuals from PC) ############ +mod=matrix(1,nrow=dim(data.confounded)[1],ncol=1) +colnames(mod)="Intercept" +nsv=num.sv(t(data.confounded),mod) + +ss=svd(data.confounded - colMeans(data.confounded)) +grp.est=ss$u[,1] +data.corrected=data.confounded*0 +for(i in 1:8){ + data.corrected[,i]=lm(data.confounded[,i] ~ grp.est)$residuals +} + +rownames(data.corrected)=1:(1000*n) +colnames(data.corrected)=1:8 + +cor.data.corrected=cor(data.corrected) +colnames(cor.data.corrected)=rownames(cor.data.corrected)=1:8 + + +glasso.corrected.lambda=huge(data.corrected,method="glasso",lambda) +glasso.graph.corrected.lambda=list() +for(i in 1:200){ + glasso.graph.corrected.lambda[[i]]=graph.adjacency(glasso.corrected.lambda$path[[i]],mode="undirected", diag=FALSE) + +} + +## For a given gene, samples are standard normal +z.data=data +for(j in 1:8){ + mean=mean(data[,j]) + sd=sd(data[,j]) + z.data[,j]=(data[,j]-mean)/sd +} + +z.data.confounded=data.confounded +for(j in 1:8){ + mean=mean(data.confounded[,j]) + sd=sd(data.confounded[,j]) + z.data.confounded[,j]=(data.confounded[,j]-mean)/sd +} + +z.data.corrected=data.corrected +for(j in 1:8){ + mean=mean(data.corrected[,j]) + sd=sd(data.corrected[,j]) + z.data.corrected[,j]=(data.corrected[,j]-mean)/sd +} + +``` + +This part generates plots for each figure panel and saves it in a pdf + +```{r, echo=FALSE} +### Plots + +col.expr=colorRampPalette(c("#d8b365", "#f5f5f5", "#5ab4ac")) +col.corr=colorRampPalette(c("#ef8a62", "#f7f7f7", "#67a9cf")) + +at=seq(-1,1,length.out=50) +layout=layout.circle(g.generating) + +## unconfounded data + +plot.z.data = melt(z.data[1:10,]) +plot.z.data$Var1 <- factor(plot.z.data$Var1) +plot.z.data$Var2 <- factor(plot.z.data$Var2) + +plot.cor.data = melt(cor.data) +plot.cor.data$Var1 <- factor(plot.cor.data$Var1) +plot.cor.data$Var2 <- factor(plot.cor.data$Var2) + +### Panel a +panela <- ggplot(plot.z.data, aes(Var1, Var2))+ + geom_tile(aes(fill = value))+ + scale_fill_gradientn(colours = col.expr(50), limits = c(-2.5,2.5))+theme_bw() + xlab("Sample") + ylab("Gene") + +### Panel b +panelb <- ggplot(plot.cor.data, aes(Var1, Var2))+ + geom_tile(aes(fill = value))+ + scale_fill_gradientn(colours = col.corr(50), + limits = c(-1,1))+theme_bw() + xlab("Gene") + ylab("Gene") + +### Panel c +pdf("panelc.pdf", height = 3, width = 3) +plot(glasso.graph.unconfounded.lambda[[150]],layout=layout,vertex.label=1:8,vertex.size=50,edge.color="limegreen",edge.width=4, vertex.color="cornsilk") +dev.off() + + +## confounded +plot.z.data.confounded = melt(z.data.confounded[1:10,]) +plot.z.data.confounded$Var1 <- factor(plot.z.data.confounded$Var1) +plot.z.data.confounded$Var2 <- factor(plot.z.data.confounded$Var2) + +plot.cor.data.confounded = melt(cor.data.confounded) +plot.cor.data.confounded$Var1 <- factor(plot.cor.data.confounded$Var1) +plot.cor.data.confounded$Var2 <- factor(plot.cor.data.confounded$Var2) + +### Panel d +paneld <- ggplot(plot.z.data.confounded, aes(Var1, Var2))+ + geom_tile(aes(fill = value))+ + scale_fill_gradientn(colours = col.expr(50), limits = c(-2.5,2.5))+theme_bw() + xlab("Sample") + ylab("Gene") + + +### Panel e +panele <- ggplot(plot.cor.data.confounded, aes(Var1, Var2))+ + geom_tile(aes(fill = value))+ + scale_fill_gradientn(colours = col.corr(50), + limits = c(-1,1))+theme_bw() + xlab("Gene") + ylab("Gene") + +### Panel f +pdf("panelf.pdf", height = 3, width = 3) +plot(glasso.graph.confounded[[150]],layout=layout,vertex.label=1:8,vertex.size=50,edge.color="limegreen",edge.width=4, vertex.color="cornsilk") +dev.off() + +## corrected +plot.z.data.corrected = melt(z.data.corrected[1:10,]) +plot.z.data.corrected$Var1 <- factor(plot.z.data.corrected$Var1) +plot.z.data.corrected$Var2 <- factor(plot.z.data.corrected$Var2) + +plot.cor.data.corrected = melt(cor.data.corrected) +plot.cor.data.corrected$Var1 <- factor(plot.cor.data.corrected$Var1) +plot.cor.data.corrected$Var2 <- factor(plot.cor.data.corrected$Var2) + +### Panel g +panelg <- ggplot(plot.z.data.corrected, aes(Var1, Var2))+ + geom_tile(aes(fill = value))+ + scale_fill_gradientn(colours = col.expr(50), limits = c(-2.5,2.5))+ theme_bw() + xlab("Sample") + ylab("Gene") + + + +### Panel h +panelh <- ggplot(plot.cor.data.corrected, aes(Var1, Var2))+ + geom_tile(aes(fill = value))+ + scale_fill_gradientn(colours = col.corr(50), + limits = c(-1,1))+theme_bw() + xlab("Gene") + ylab("Gene") + +### Panel i +pdf("paneli.pdf", height = 3, width = 3) +plot(glasso.graph.corrected.lambda[[150]],layout=layout,vertex.label=1:8,vertex.size=50,edge.color="limegreen",edge.width=4, vertex.color="cornsilk") +dev.off() + +fig1 <- plot_grid(panela + theme(legend.position="none"), + panelb + theme(legend.position="none"), + NULL, + paneld + theme(legend.position="none"), + panele + theme(legend.position="none"), + NULL, + panelg + theme(legend.position="none"), + panelh + theme(legend.position="none"), + NULL, + labels=letters[1:9], ncol = 3) + +legenda <- get_legend(panela + theme(legend.direction = "horizontal", legend.position = "top")) +legendb <- get_legend(panelb + theme(legend.direction = "horizontal", legend.position = "top")) +legend <- plot_grid(legenda, legendb, NULL, ncol = 3) +fig1 <- plot_grid( legend, fig1, rel_heights = c(.1, 1), ncol = 1) + +pdf("merged.pdf", height = 6, width = 6) +print(fig1) +dev.off() +``` diff --git a/publication_rmd/simulation_example_fig1/figure1.html b/publication_rmd/simulation_example_fig1/figure1.html new file mode 100644 index 0000000..703b0b1 --- /dev/null +++ b/publication_rmd/simulation_example_fig1/figure1.html @@ -0,0 +1,870 @@ + + + + + + + + + + + + + + + + + + + + + + + + +

This report was automatically generated with the R package knitr +(version 1.17).

+ +
---
+title: "figure_1"
+output:
+  html_document:
+    code_folding: hide
+---
+
+This is a simulation example that shows that confounders and batch effects impact reconstruction of gene co-expression networks. Using this example we also show that true underlying network structure can be reconstructed after principal component correction of gene expression data as described in the paper.
+
+This script generates Figure 1 in the paper -- "Addressing confounding artifacts in reconstruction of gene co-expression networks"
+
+ +
## Error: <text>:8:6: unexpected symbol
+## 7: 
+## 8: This is
+##         ^
+
+ +
rm(list = ls())
+
+## load libraries
+#library(pcalg)
+library(mvtnorm)
+library(clusterGeneration)
+
+ +
## Loading required package: MASS
+
+ +
library(sva)
+
+ +
## Loading required package: mgcv
+
+ +
## Loading required package: nlme
+
+ +
## This is mgcv 1.8-22. For overview type 'help("mgcv-package")'.
+
+ +
## Loading required package: genefilter
+
+ +
## Warning: replacing previous import 'stats::sd' by 'BiocGenerics::sd' when
+## loading 'S4Vectors'
+
+ +
## Warning: replacing previous import 'stats::var' by 'BiocGenerics::var' when
+## loading 'S4Vectors'
+
+ +
## Warning: replacing previous import 'stats::sd' by 'BiocGenerics::sd' when
+## loading 'IRanges'
+
+ +
## Warning: replacing previous import 'stats::var' by 'BiocGenerics::var' when
+## loading 'IRanges'
+
+ +
## 
+## Attaching package: 'genefilter'
+
+ +
## The following object is masked from 'package:MASS':
+## 
+##     area
+
+ +
#library(spacejam)
+library(gridExtra)
+library(gtable)
+library(glasso)
+library(huge)
+
+ +
## Loading required package: Matrix
+
+ +
## Loading required package: lattice
+
+ +
## Loading required package: igraph
+
+ +
## Loading required package: methods
+
+ +
## 
+## Attaching package: 'igraph'
+
+ +
## The following objects are masked from 'package:stats':
+## 
+##     decompose, spectrum
+
+ +
## The following object is masked from 'package:base':
+## 
+##     union
+
+ +
library(devtools)
+install_github('alyssafrazee/RSkittleBrewer')
+
+ +
## Skipping install of 'RSkittleBrewer' from a github remote, the SHA1 (00881122) has not changed since last install.
+##   Use `force = TRUE` to force installation
+
+ +
library(RSkittleBrewer)
+tropical = RSkittleBrewer('tropical')
+library(ggplot2)
+library(reshape2)
+library(cowplot)
+
+ +
## 
+## Attaching package: 'cowplot'
+
+ +
## The following object is masked from 'package:ggplot2':
+## 
+##     ggsave
+
+ +
### Data: 5 features, 10 samples
+p=8
+n=10
+
+V=diag(1,nrow=p,ncol=p)
+V[1,3]=V[3,1]=.35
+V[4,7]=V[7,4]=.3
+V[1,8]=V[8,1]=.3
+V.inv=solve(V)
+
+colnames(V)=rownames(V)=colnames(V.inv)=rownames(V.inv)=paste(1:8)
+
+A.generating=V
+for(i in 1:p){
+  for(j in 1:p){
+    if(abs(V[i,j])>0.05){
+      A.generating[i,j]=1
+    }
+    if(abs(V[i,j])<=0.05){
+      A.generating[i,j]=0
+    }
+  }
+}
+g.generating=graph.adjacency(A.generating,mode="undirected", diag=FALSE,add.colnames=TRUE)
+
+set.seed(4747)
+data=rmvnorm((1000*n),mean=rep(1,p),sigma=V)
+rownames(data)=1:(1000*n)
+colnames(data)=1:8
+
+cor.data=cor(data)
+
+## Graph 
+lambda=seq(1,0.01,length.out=200)
+glasso.unconfounded.lambda=huge(data,lambda,method="glasso")
+
+ +
## Conducting the graphical lasso (glasso) with lossless screening....in progress:0% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:0% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:1% 
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+Conducting the graphical lasso (glasso) with lossless screening....in progress:34% 
+Conducting the graphical lasso (glasso)....done.                                          
+
+ +
glasso.adjacency.unconfounded.lambda=glasso.unconfounded.lambda$path
+glasso.graph.unconfounded.lambda=list()
+
+for(i in 1:200){
+  glasso.graph.unconfounded.lambda[[i]]=graph.adjacency(glasso.adjacency.unconfounded.lambda[[i]],mode="undirected", diag=FALSE)
+}
+
+############ Confounding ############
+data.confounded=data
+grp=rnorm(1000*n)
+for(i in 2:6){
+  data.confounded[,i] = data.confounded[,i] + 50*grp
+}
+
+rownames(data.confounded)=1:(1000*n)
+colnames(data.confounded)=1:8
+
+cor.data.confounded=cor(data.confounded)
+colnames(cor.data.confounded)=rownames(cor.data.confounded)=1:8
+
+colnames(data.confounded)=1:8
+rownames(data.confounded)=1:10000 
+
+glasso.confounded=huge(data.confounded,lambda,method="glasso")
+
+ +
## Conducting the graphical lasso (glasso) with lossless screening....in progress:0% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:0% 
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+Conducting the graphical lasso (glasso) with lossless screening....in progress:21% 
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+Conducting the graphical lasso (glasso) with lossless screening....in progress:24% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:25% 
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+Conducting the graphical lasso (glasso) with lossless screening....in progress:26% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:27% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:27% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:28% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:28% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:29% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:29% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:30% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:30% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:31% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:31% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:31% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:32% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:32% 
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+Conducting the graphical lasso (glasso) with lossless screening....in progress:34% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:34% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:35% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:35% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:36% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:36% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:37% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:37% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:38% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:38% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:39% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:39% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:40% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:40% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:41% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:41% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:42% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:42% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:43% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:43% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:43% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:44% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:44% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:45% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:46% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:46% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:47% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:47% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:48% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:48% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:49% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:49% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:50% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:50% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:51% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:51% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:52% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:52% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:53% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:53% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:54% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:54% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:55% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:55% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:56% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:56% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:57% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:57% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:58% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:58% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:59% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:59% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:60% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:60% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:61% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:61% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:62% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:62% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:63% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:63% 
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+Conducting the graphical lasso (glasso) with lossless screening....in progress:64% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:65% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:65% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:65% 
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+Conducting the graphical lasso (glasso) with lossless screening....in progress:68% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:69% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:69% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:70% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:70% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:71% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:71% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:72% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:72% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:73% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:73% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:74% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:74% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:75% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:75% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:76% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:76% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:77% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:77% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:78% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:78% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:79% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:79% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:80% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:80% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:81% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:81% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:82% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:82% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:83% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:83% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:84% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:84% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:85% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:85% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:86% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:86% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:87% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:87% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:88% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:88% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:89% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:89% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:90% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:90% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:91% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:91% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:92% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:92% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:93% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:93% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:94% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:94% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:95% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:95% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:96% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:96% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:97% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:97% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:98% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:98% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:99% 
+Conducting the graphical lasso (glasso)....done.                                          
+
+ +
glasso.adjacency.confounded=glasso.confounded$path
+glasso.graph.confounded=list()
+for(i in 1:200){
+  glasso.graph.confounded[[i]]=graph.adjacency(glasso.adjacency.confounded[[i]],mode="undirected", diag=FALSE)
+}
+
+############ Correct for Confounding (Residuals from PC) ############
+mod=matrix(1,nrow=dim(data.confounded)[1],ncol=1)
+colnames(mod)="Intercept"
+nsv=num.sv(t(data.confounded),mod)
+
+ss=svd(data.confounded - colMeans(data.confounded))
+grp.est=ss$u[,1]
+data.corrected=data.confounded*0
+for(i in 1:8){
+  data.corrected[,i]=lm(data.confounded[,i] ~ grp.est)$residuals
+}
+
+rownames(data.corrected)=1:(1000*n)
+colnames(data.corrected)=1:8
+
+cor.data.corrected=cor(data.corrected)
+colnames(cor.data.corrected)=rownames(cor.data.corrected)=1:8
+
+
+glasso.corrected.lambda=huge(data.corrected,method="glasso",lambda)
+
+ +
## Conducting the graphical lasso (glasso) with lossless screening....in progress:0% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:0% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:1% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:1% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:2% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:2% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:3% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:3% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:4% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:4% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:5% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:5% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:6% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:6% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:6% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:7% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:7% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:8% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:8% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:9% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:9% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:10% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:10% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:11% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:12% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:12% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:13% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:13% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:14% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:14% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:15% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:15% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:16% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:16% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:17% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:17% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:18% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:18% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:18% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:19% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:19% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:20% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:20% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:21% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:21% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:22% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:23% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:23% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:24% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:24% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:25% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:25% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:26% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:26% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:27% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:27% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:28% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:28% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:29% 
+Conducting the graphical lasso (glasso) with lossless screening....in progress:29% 
+Conducting the graphical lasso (glasso)....done.                                          
+
+ +
glasso.graph.corrected.lambda=list()
+for(i in 1:200){
+  glasso.graph.corrected.lambda[[i]]=graph.adjacency(glasso.corrected.lambda$path[[i]],mode="undirected", diag=FALSE)
+
+}
+
+## For a given gene, samples are standard normal
+z.data=data
+for(j in 1:8){
+  mean=mean(data[,j])
+  sd=sd(data[,j])
+  z.data[,j]=(data[,j]-mean)/sd
+}
+
+z.data.confounded=data.confounded
+for(j in 1:8){
+  mean=mean(data.confounded[,j])
+  sd=sd(data.confounded[,j])
+  z.data.confounded[,j]=(data.confounded[,j]-mean)/sd
+}
+
+z.data.corrected=data.corrected
+for(j in 1:8){
+  mean=mean(data.corrected[,j])
+  sd=sd(data.corrected[,j])
+  z.data.corrected[,j]=(data.corrected[,j]-mean)/sd
+}
+
+ +

This part generates plots for each figure panel and saves it in a pdf

+ +
## png 
+##   2
+
+ +
## png 
+##   2
+
+ +
## png 
+##   2
+
+ +
## png 
+##   2
+
+ +

+The R session information (including the OS info, R version and all
+packages used):
+
+
+```r
+sessionInfo()
+
+ +
## R version 3.3.1 (2016-06-21)
+## Platform: x86_64-pc-linux-gnu (64-bit)
+## Running under: CentOS release 6.7 (Final)
+## 
+## 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] methods   stats     graphics  grDevices utils     datasets  base     
+## 
+## other attached packages:
+##  [1] cowplot_0.8.0           reshape2_1.4.2         
+##  [3] ggplot2_2.2.1           RSkittleBrewer_1.1     
+##  [5] devtools_1.13.3         huge_1.2.7             
+##  [7] igraph_1.1.2            lattice_0.20-35        
+##  [9] Matrix_1.2-11           glasso_1.8             
+## [11] gtable_0.2.0            gridExtra_2.3          
+## [13] sva_3.22.0              genefilter_1.56.0      
+## [15] mgcv_1.8-22             nlme_3.1-131           
+## [17] clusterGeneration_1.3.4 MASS_7.3-47            
+## [19] mvtnorm_1.0-6           knitr_1.17             
+## 
+## loaded via a namespace (and not attached):
+##  [1] splines_3.3.1        colorspace_1.3-2     stats4_3.3.1        
+##  [4] blob_1.1.0           survival_2.41-3      XML_3.98-1.9        
+##  [7] rlang_0.1.2          withr_2.0.0          DBI_0.7             
+## [10] BiocGenerics_0.21.3  bit64_0.9-7          plyr_1.8.4          
+## [13] stringr_1.2.0        munsell_0.4.3        memoise_1.1.0       
+## [16] evaluate_0.10.1      labeling_0.3         Biobase_2.34.0      
+## [19] IRanges_2.8.2        parallel_3.3.1       curl_2.8.1          
+## [22] AnnotationDbi_1.36.2 Rcpp_0.12.13         xtable_1.8-2        
+## [25] scales_0.5.0         S4Vectors_0.12.2     annotate_1.52.1     
+## [28] bit_1.1-12           digest_0.6.12        stringi_1.1.5       
+## [31] grid_3.3.1           tools_3.3.1          bitops_1.0-6        
+## [34] magrittr_1.5         RCurl_1.95-4.8       lazyeval_0.2.0      
+## [37] tibble_1.3.4         RSQLite_2.0          pkgconfig_2.0.1     
+## [40] httr_1.3.1           R6_2.2.2             git2r_0.19.0
+
+ +
Sys.time()
+
+ +
## [1] "2017-10-13 13:58:52 EDT"
+
+ + + + diff --git a/publication_rmd/simulation_example_fig1/figure1.md b/publication_rmd/simulation_example_fig1/figure1.md new file mode 100644 index 0000000..abbfc93 --- /dev/null +++ b/publication_rmd/simulation_example_fig1/figure1.md @@ -0,0 +1,383 @@ + + + + +This report was automatically generated with the R package **knitr** +(version 1.17). + + +```r +--- +title: "figure_1" +output: + html_document: + code_folding: hide +--- + +This is a simulation example that shows that confounders and batch effects impact reconstruction of gene co-expression networks. Using this example we also show that true underlying network structure can be reconstructed after principal component correction of gene expression data as described in the paper. + +This script generates Figure 1 in the paper -- "Addressing confounding artifacts in reconstruction of gene co-expression networks" +``` + +``` +## Error: :8:6: unexpected symbol +## 7: +## 8: This is +## ^ +``` + +```r +rm(list = ls()) + +## load libraries +#library(pcalg) +library(mvtnorm) +library(clusterGeneration) +``` + +``` +## Loading required package: MASS +``` + +```r +library(sva) +``` + +``` +## Loading required package: mgcv +``` + +``` +## Loading required package: nlme +``` + +``` +## This is mgcv 1.8-22. For overview type 'help("mgcv-package")'. +``` + +``` +## Loading required package: genefilter +``` + +``` +## Warning: replacing previous import 'stats::sd' by 'BiocGenerics::sd' when +## loading 'S4Vectors' +``` + +``` +## Warning: replacing previous import 'stats::var' by 'BiocGenerics::var' when +## loading 'S4Vectors' +``` + +``` +## Warning: replacing previous import 'stats::sd' by 'BiocGenerics::sd' when +## loading 'IRanges' +``` + +``` +## Warning: replacing previous import 'stats::var' by 'BiocGenerics::var' when +## loading 'IRanges' +``` + +``` +## +## Attaching package: 'genefilter' +``` + +``` +## The following object is masked from 'package:MASS': +## +## area +``` + +```r +#library(spacejam) +library(gridExtra) +library(gtable) +library(glasso) +library(huge) +``` + +``` +## Loading required package: Matrix +``` + +``` +## Loading required package: lattice +``` + +``` +## Loading required package: igraph +``` + +``` +## Loading required package: methods +``` + +``` +## +## Attaching package: 'igraph' +``` + +``` +## The following objects are masked from 'package:stats': +## +## decompose, spectrum +``` + +``` +## The following object is masked from 'package:base': +## +## union +``` + +```r +library(devtools) +install_github('alyssafrazee/RSkittleBrewer') +``` + +``` +## Skipping install of 'RSkittleBrewer' from a github remote, the SHA1 (00881122) has not changed since last install. +## Use `force = TRUE` to force installation +``` + +```r +library(RSkittleBrewer) +tropical = RSkittleBrewer('tropical') +library(ggplot2) +library(reshape2) +library(cowplot) +``` + +``` +## +## Attaching package: 'cowplot' +``` + +``` +## The following object is masked from 'package:ggplot2': +## +## ggsave +``` + +```r +### Data: 5 features, 10 samples +p=8 +n=10 + +V=diag(1,nrow=p,ncol=p) +V[1,3]=V[3,1]=.35 +V[4,7]=V[7,4]=.3 +V[1,8]=V[8,1]=.3 +V.inv=solve(V) + +colnames(V)=rownames(V)=colnames(V.inv)=rownames(V.inv)=paste(1:8) + +A.generating=V +for(i in 1:p){ + for(j in 1:p){ + if(abs(V[i,j])>0.05){ + A.generating[i,j]=1 + } + if(abs(V[i,j])<=0.05){ + A.generating[i,j]=0 + } + } +} +g.generating=graph.adjacency(A.generating,mode="undirected", diag=FALSE,add.colnames=TRUE) + +set.seed(4747) +data=rmvnorm((1000*n),mean=rep(1,p),sigma=V) +rownames(data)=1:(1000*n) +colnames(data)=1:8 + +cor.data=cor(data) + +## Graph +lambda=seq(1,0.01,length.out=200) +glasso.unconfounded.lambda=huge(data,lambda,method="glasso") +``` + +``` +## Conducting the graphical lasso (glasso) with lossless screening....in progress:0% Conducting the graphical lasso (glasso) with lossless screening....in progress:0% Conducting the graphical lasso (glasso) with lossless screening....in progress:1% Conducting the graphical lasso (glasso) with lossless screening....in progress:1% Conducting the graphical lasso (glasso) with lossless screening....in progress:2% Conducting the graphical lasso (glasso) with lossless screening....in progress:2% Conducting the graphical lasso 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+rownames(data.confounded)=1:10000 + +glasso.confounded=huge(data.confounded,lambda,method="glasso") +``` + +``` +## Conducting the graphical lasso (glasso) with lossless screening....in progress:0% Conducting the graphical lasso (glasso) with lossless screening....in progress:0% Conducting the graphical lasso (glasso) with lossless screening....in progress:1% Conducting the graphical lasso (glasso) with lossless screening....in progress:1% Conducting the graphical lasso (glasso) with lossless screening....in progress:2% Conducting the graphical lasso (glasso) with lossless screening....in progress:2% Conducting the graphical lasso (glasso) with lossless screening....in progress:3% Conducting the graphical lasso (glasso) with lossless screening....in progress:3% Conducting the graphical lasso (glasso) with lossless screening....in progress:4% Conducting the graphical lasso (glasso) with lossless screening....in progress:4% Conducting the graphical lasso (glasso) with lossless 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(Residuals from PC) ############ +mod=matrix(1,nrow=dim(data.confounded)[1],ncol=1) +colnames(mod)="Intercept" +nsv=num.sv(t(data.confounded),mod) + +ss=svd(data.confounded - colMeans(data.confounded)) +grp.est=ss$u[,1] +data.corrected=data.confounded*0 +for(i in 1:8){ + data.corrected[,i]=lm(data.confounded[,i] ~ grp.est)$residuals +} + +rownames(data.corrected)=1:(1000*n) +colnames(data.corrected)=1:8 + +cor.data.corrected=cor(data.corrected) +colnames(cor.data.corrected)=rownames(cor.data.corrected)=1:8 + + +glasso.corrected.lambda=huge(data.corrected,method="glasso",lambda) +``` + +``` +## Conducting the graphical lasso (glasso) with lossless screening....in progress:0% Conducting the graphical lasso (glasso) with lossless screening....in progress:0% Conducting the graphical lasso (glasso) with lossless screening....in progress:1% Conducting the graphical lasso (glasso) with lossless screening....in progress:1% Conducting the graphical lasso (glasso) with lossless screening....in 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Conducting the graphical lasso (glasso) with lossless screening....in progress:20% Conducting the graphical lasso (glasso) with lossless screening....in progress:20% Conducting the graphical lasso (glasso) with lossless screening....in progress:21% Conducting the graphical lasso (glasso) with lossless screening....in progress:21% Conducting the graphical lasso (glasso) with lossless screening....in progress:22% Conducting the graphical lasso (glasso) with lossless screening....in progress:23% Conducting the graphical lasso (glasso) with lossless screening....in progress:23% Conducting the graphical lasso (glasso) with lossless screening....in progress:24% Conducting the graphical lasso (glasso) with lossless screening....in progress:24% Conducting the graphical lasso (glasso) with lossless screening....in progress:25% Conducting the graphical lasso (glasso) with lossless screening....in progress:25% Conducting the graphical lasso (glasso) with lossless screening....in progress:26% Conducting the graphical lasso (glasso) with lossless screening....in progress:26% Conducting the graphical lasso (glasso) with lossless screening....in progress:27% Conducting the graphical lasso (glasso) with lossless screening....in progress:27% Conducting the graphical lasso (glasso) with lossless screening....in progress:28% Conducting the graphical lasso (glasso) with lossless screening....in progress:28% Conducting the graphical lasso (glasso) with lossless screening....in progress:29% Conducting the graphical lasso (glasso) with lossless screening....in progress:29% Conducting the graphical lasso (glasso)....done. +``` + +```r +glasso.graph.corrected.lambda=list() +for(i in 1:200){ + glasso.graph.corrected.lambda[[i]]=graph.adjacency(glasso.corrected.lambda$path[[i]],mode="undirected", diag=FALSE) + +} + +## For a given gene, samples are standard normal +z.data=data +for(j in 1:8){ + mean=mean(data[,j]) + sd=sd(data[,j]) + z.data[,j]=(data[,j]-mean)/sd +} + +z.data.confounded=data.confounded +for(j in 1:8){ + mean=mean(data.confounded[,j]) + sd=sd(data.confounded[,j]) + z.data.confounded[,j]=(data.confounded[,j]-mean)/sd +} + +z.data.corrected=data.corrected +for(j in 1:8){ + mean=mean(data.corrected[,j]) + sd=sd(data.corrected[,j]) + z.data.corrected[,j]=(data.corrected[,j]-mean)/sd +} +``` + +This part generates plots for each figure panel and saves it in a pdf + + +``` +## png +## 2 +``` + +``` +## png +## 2 +``` + +``` +## png +## 2 +``` + +``` +## png +## 2 +``` +``` + +The R session information (including the OS info, R version and all +packages used): + + +```r +sessionInfo() +``` + +``` +## R version 3.3.1 (2016-06-21) +## Platform: x86_64-pc-linux-gnu (64-bit) +## Running under: CentOS release 6.7 (Final) +## +## 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] methods stats graphics grDevices utils datasets base +## +## other attached packages: +## [1] cowplot_0.8.0 reshape2_1.4.2 +## [3] ggplot2_2.2.1 RSkittleBrewer_1.1 +## [5] devtools_1.13.3 huge_1.2.7 +## [7] igraph_1.1.2 lattice_0.20-35 +## [9] Matrix_1.2-11 glasso_1.8 +## [11] gtable_0.2.0 gridExtra_2.3 +## [13] sva_3.22.0 genefilter_1.56.0 +## [15] mgcv_1.8-22 nlme_3.1-131 +## [17] clusterGeneration_1.3.4 MASS_7.3-47 +## [19] mvtnorm_1.0-6 knitr_1.17 +## +## loaded via a namespace (and not attached): +## [1] splines_3.3.1 colorspace_1.3-2 stats4_3.3.1 +## [4] blob_1.1.0 survival_2.41-3 XML_3.98-1.9 +## [7] rlang_0.1.2 withr_2.0.0 DBI_0.7 +## [10] BiocGenerics_0.21.3 bit64_0.9-7 plyr_1.8.4 +## [13] stringr_1.2.0 munsell_0.4.3 memoise_1.1.0 +## [16] evaluate_0.10.1 labeling_0.3 Biobase_2.34.0 +## [19] IRanges_2.8.2 parallel_3.3.1 curl_2.8.1 +## [22] AnnotationDbi_1.36.2 Rcpp_0.12.13 xtable_1.8-2 +## [25] scales_0.5.0 S4Vectors_0.12.2 annotate_1.52.1 +## [28] bit_1.1-12 digest_0.6.12 stringi_1.1.5 +## [31] grid_3.3.1 tools_3.3.1 bitops_1.0-6 +## [34] magrittr_1.5 RCurl_1.95-4.8 lazyeval_0.2.0 +## [37] tibble_1.3.4 RSQLite_2.0 pkgconfig_2.0.1 +## [40] httr_1.3.1 R6_2.2.2 git2r_0.19.0 +``` + +```r +Sys.time() +``` + +``` +## [1] "2017-10-13 13:58:52 EDT" +``` + diff --git a/publication_rmd/simulation_example_fig1/merged.pdf b/publication_rmd/simulation_example_fig1/merged.pdf new file mode 100644 index 0000000..8374cb3 Binary files /dev/null and b/publication_rmd/simulation_example_fig1/merged.pdf differ diff --git a/publication_rmd/simulation_example_fig1/panelc.pdf b/publication_rmd/simulation_example_fig1/panelc.pdf new file mode 100644 index 0000000..e8a82c3 Binary files /dev/null and b/publication_rmd/simulation_example_fig1/panelc.pdf differ diff --git a/publication_rmd/simulation_example_fig1/panelf.pdf 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