Last updated: 2019-03-21

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Knit directory: threeprimeseq/analysis/

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File Version Author Date Message
Rmd be9dbbf Briana Mittleman 2019-03-21 add 4su ratio plots
html e1baddd Briana Mittleman 2019-03-19 Build site.
Rmd 6e940ea Briana Mittleman 2019-03-19 change color by density
html 7fc93c8 Briana Mittleman 2019-03-18 Build site.
Rmd 52ab386 Briana Mittleman 2019-03-18 look at gene 1 SD outside mean decay
html 1283669 Briana Mittleman 2019-03-15 Build site.
Rmd 5d6ac93 Briana Mittleman 2019-03-15 add decay analysis

I want to ask if more nuclear specific transcripts compared to total is associated with RNA decay.

library(tidyverse)
── Attaching packages ──────────────────────────────────────────────────────── tidyverse 1.2.1 ──
✔ ggplot2 3.1.0       ✔ purrr   0.3.1  
✔ tibble  2.0.1       ✔ dplyr   0.8.0.1
✔ tidyr   0.8.3       ✔ stringr 1.4.0  
✔ readr   1.3.1       ✔ forcats 0.4.0  
Warning: package 'tibble' was built under R version 3.5.2
Warning: package 'tidyr' was built under R version 3.5.2
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── Conflicts ─────────────────────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
library(reshape2)

Attaching package: 'reshape2'
The following object is masked from 'package:tidyr':

    smiths
library(MASS)

Attaching package: 'MASS'
The following object is masked from 'package:dplyr':

    select
library(viridis)
Loading required package: viridisLite
decay=read.table(file = "../data/RNAdecay/tr_decay_table_norm.txt", header=T, stringsAsFactors = F) %>% dplyr::select(gene_id,contains("RNAdecay"))

Change gene names:

geneNames=read.table("../data/ensemble_to_genename.txt", sep="\t", col.names = c('gene_id', 'GeneName', 'source' ),stringsAsFactors = F)
decay_geneNames=decay %>% inner_join(geneNames, by="gene_id") %>% dplyr::select(GeneName, contains("RNAdecay"))

decay_geneNames_long=melt(decay_geneNames,id.vars = "GeneName", value.name = "RNA_Decay", variable.name = "Decay_Ind") %>% separate(Decay_Ind, into=c("type", "ind"), sep="_") %>% mutate(Individual=paste("X" , ind, sep="")) %>% dplyr::select(GeneName, Individual, RNA_Decay)

Prepare apa value:

For each gene I need to get nuclear counts/nuclear + counts

I want to use the filtered 5% peak counts.

/project2/gilad/briana/threeprimeseq/data/filtPeakOppstrand_cov_noMP_GeneLocAnno_5perc/filtered_APApeaks_merged_allchrom_refseqGenes.GeneLocAnno_NoMP_sm_quant.Nuclear.fixed.5perc.fc

/project2/gilad/briana/threeprimeseq/data/filtPeakOppstrand_cov_noMP_GeneLocAnno_5perc/filtered_APApeaks_merged_allchrom_refseqGenes.GeneLocAnno_NoMP_sm_quant.Total.fixed.5perc.fc

Make a dictionary from the individuals in the first line. I want them to have NA##### format

makepheno4decayComparison.py

nucCounts="/project2/gilad/briana/threeprimeseq/data/filtPeakOppstrand_cov_noMP_GeneLocAnno_5perc/filtered_APApeaks_merged_allchrom_refseqGenes.GeneLocAnno_NoMP_sm_quant.Nuclear.fixed.5perc.fc"

totCounts="/project2/gilad/briana/threeprimeseq/data/filtPeakOppstrand_cov_noMP_GeneLocAnno_5perc/filtered_APApeaks_merged_allchrom_refseqGenes.GeneLocAnno_NoMP_sm_quant.Total.fixed.5perc.fc"

#top key is individual
OutPutdic={}


#problem keeping ind connected to column

Try in R

Nuclear first:

NucAPA=read.table("../data/filtPeakOppstrand_cov_noMP_GeneLocAnno_5perc/filtered_APApeaks_merged_allchrom_refseqGenes.GeneLocAnno_NoMP_sm_quant.Nuclear.fixed.5perc.fc", stringsAsFactors = F, header = T) %>% dplyr::select(-Chr, -Start, -End, -Strand, -Length) %>% separate(Geneid, into=c("peak", "chrom", "start", "end", "strand", "GeneName"), sep=":") %>% dplyr::select(-chrom, -start, -end, -strand)

NucApaMelt=melt(NucAPA, id.vars =c( "peak", "GeneName"), value.name="count", variable.name="Ind") %>% separate(Ind, into=c('Individual', 'fraction') ,sep="_") %>% dplyr::select(peak, GeneName, Individual, count)


NucAPA_bygene= NucApaMelt %>% group_by(GeneName,Individual) %>% summarise(NuclearSum=sum(count))

Total first:

TotAPA=read.table("../data/filtPeakOppstrand_cov_noMP_GeneLocAnno_5perc/filtered_APApeaks_merged_allchrom_refseqGenes.GeneLocAnno_NoMP_sm_quant.Total.fixed.5perc.fc", stringsAsFactors = F, header = T) %>% dplyr::select(-Chr, -Start, -End, -Strand, -Length) %>% separate(Geneid, into=c("peak", "chrom", "start", "end", "strand", "GeneName"), sep=":") %>% dplyr::select(-chrom, -start, -end, -strand)

TotApaMelt=melt(TotAPA, id.vars =c( "peak", "GeneName"), value.name="count", variable.name="Ind")  %>% separate(Ind, into=c('Individual', 'fraction') ,sep="_") %>% dplyr::select(peak, GeneName, Individual, count)


TotAPA_bygene=TotApaMelt %>% group_by(GeneName,Individual) %>% summarise(TotalSum=sum(count))

Sum these together:

Apa_all=TotAPA_bygene %>% inner_join(NucAPA_bygene, by=c("GeneName", "Individual")) %>% filter(NuclearSum>0 |TotalSum>0 )  %>% mutate(APAvalue=NuclearSum/(NuclearSum+TotalSum)) %>% dplyr::select(GeneName, Individual, APAvalue)

Join ith decay

APAandDecay=decay_geneNames_long %>% inner_join(Apa_all, by=c('GeneName', 'Individual'))


ngenes=APAandDecay %>% dplyr::select(GeneName) %>% unique() %>% nrow()
ngenes
[1] 7888

plot it:

summary(lm(data=APAandDecay, APAvalue~RNA_Decay))

Call:
lm(formula = APAvalue ~ RNA_Decay, data = APAandDecay)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.46459 -0.15044 -0.01135  0.13392  0.58497 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.4373568  0.0003228 1354.83   <2e-16 ***
RNA_Decay   -0.0257699  0.0019255  -13.38   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2017 on 398991 degrees of freedom
Multiple R-squared:  0.0004487, Adjusted R-squared:  0.0004462 
F-statistic: 179.1 on 1 and 398991 DF,  p-value: < 2.2e-16
APAdecalAllindplot=ggplot(APAandDecay, aes(y=APAvalue, x=RNA_Decay)) + geom_point(aes(col=Individual)) +geom_density2d(na.rm = TRUE, size = 1, colour = 'red') + geom_smooth(method="lm") + annotate("text", label="Estimated Slope= -.026", y=1, x=-1) + labs(title="Relationship between RNA decay \nand APA fraction counts", x=" mRNA decay rate/h", y= "Nuclear/(Nuclear + Total)")

APAdecalAllindplot

Version Author Date
1283669 Briana Mittleman 2019-03-15
ggsave(APAdecalAllindplot, file="../output/plots/APAandRNADecay_allInd.png", height = 7, width=15)

1 individual:

APAandDecay_18498= APAandDecay %>% filter(Individual=="X18498")

APAdecay_18498=ggplot(APAandDecay_18498, aes(y=APAvalue, x=RNA_Decay)) + geom_point() +geom_density2d(na.rm = TRUE, size = 1, colour = 'red') + annotate("text", label="Estimated Slope= -.133", y=0, x=-.8) + geom_smooth(method="lm")+ labs(title="Relationship between RNA decay \nand APA fraction counts", x=" mRNA decay rate/h", y= "Nuclear/(Nuclear + Total)")



APAdecay_18498

Version Author Date
1283669 Briana Mittleman 2019-03-15
ggsave(APAdecay_18498, file="../output/plots/APAandRNADecay_18498.png")
Saving 7 x 5 in image
summary(lm(data=APAandDecay_18498, APAvalue~RNA_Decay))

Call:
lm(formula = APAvalue ~ RNA_Decay, data = APAandDecay_18498)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.63123 -0.17159  0.00659  0.17479  0.47142 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.581252   0.002667 217.933  < 2e-16 ***
RNA_Decay   -0.133867   0.016938  -7.903 3.09e-15 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2324 on 7766 degrees of freedom
Multiple R-squared:  0.007979,  Adjusted R-squared:  0.007851 
F-statistic: 62.46 on 1 and 7766 DF,  p-value: 3.094e-15

Look at most variable decay values

Most of the genes have a similar decay rate. To se if there is a trend I need to look at the genes with >1sd outside of the mean.

decay_zscore=decay_geneNames_long  %>% mutate(mean=mean(RNA_Decay), sd=sd(RNA_Decay)) %>%  group_by(GeneName) %>% mutate(geneMean=mean(RNA_Decay)) %>% mutate(Zscore=(geneMean-mean)/sd) %>% dplyr::select(GeneName, Zscore) %>% unique() 



decay_1sd= decay_zscore %>% filter(abs(Zscore)>1) %>% dplyr::select(GeneName)

Filter the apa and decay for these genes.

APAandDecay_1sd= APAandDecay %>% filter(GeneName %in% decay_1sd$GeneName)

APAandDecay_1sd %>% dplyr::select(GeneName) %>% unique() %>% nrow()
[1] 938
summary(lm(data=APAandDecay_1sd, APAvalue~RNA_Decay))

Call:
lm(formula = APAvalue ~ RNA_Decay, data = APAandDecay_1sd)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.47225 -0.13964 -0.01415  0.12495  0.63026 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.396160   0.001103  359.08   <2e-16 ***
RNA_Decay   -0.072001   0.003283  -21.93   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1868 on 47713 degrees of freedom
Multiple R-squared:  0.009982,  Adjusted R-squared:  0.009962 
F-statistic: 481.1 on 1 and 47713 DF,  p-value: < 2.2e-16
get_density <- function(x, y, ...) {
  dens <- MASS::kde2d(x, y, ...)
  ix <- findInterval(x, dens$x)
  iy <- findInterval(y, dens$y)
  ii <- cbind(ix, iy)
  return(dens$z[ii])
}

set.seed(1)
dat <- data.frame(
  x = c(
    rnorm(1e4, mean = 0, sd = 0.1),
    rnorm(1e3, mean = 0, sd = 0.1)
  ),
  y = c(
    rnorm(1e4, mean = 0, sd = 0.1),
    rnorm(1e3, mean = 0.1, sd = 0.2)
  )
)

APAandDecay_1sd$density <- get_density(APAandDecay_1sd$APAvalue, APAandDecay_1sd$RNA_Decay, n = 100)


APAdecalAllindplot_zgreat1=ggplot(APAandDecay_1sd, aes(y=APAvalue, x=RNA_Decay)) + geom_point(aes(color=density))+ geom_smooth(method="lm")+ labs(title="Relationship between RNA decay \nand APA fraction counts", x=" mRNA decay rate/h", y= "Nuclear/(Nuclear + Total)")  + scale_color_viridis()


APAdecalAllindplot_zgreat1

Version Author Date
e1baddd Briana Mittleman 2019-03-19
7fc93c8 Briana Mittleman 2019-03-18
ggsave(APAdecalAllindplot_zgreat1, file="../output/plots/APAandRNADecay1SD_allInd.png", height = 7, width=7)
APAandDecay1SD_18498= APAandDecay_1sd %>% filter(Individual=="X18498")



APAandDecay1SD_18498$density <- get_density(APAandDecay1SD_18498$APAvalue, APAandDecay1SD_18498$RNA_Decay, n = 100)

APAdecay1sqd_18498=ggplot(APAandDecay1SD_18498, aes(y=APAvalue, x=RNA_Decay)) + geom_point(aes(color=density)) +geom_smooth(method="lm")+ labs(title="Relationship between RNA decay \nand APA fraction counts", x=" mRNA decay rate/h", y= "Nuclear/(Nuclear + Total)") + scale_color_viridis()

summary(lm(data=APAandDecay1SD_18498, APAvalue~RNA_Decay))

Call:
lm(formula = APAvalue ~ RNA_Decay, data = APAandDecay1SD_18498)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.55209 -0.15612  0.00324  0.15925  0.53943 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.527434   0.009106  57.923  < 2e-16 ***
RNA_Decay   -0.240981   0.029133  -8.272 4.56e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2203 on 928 degrees of freedom
Multiple R-squared:  0.06867,   Adjusted R-squared:  0.06766 
F-statistic: 68.42 on 1 and 928 DF,  p-value: 4.556e-16
APAdecay1sqd_18498

Version Author Date
e1baddd Briana Mittleman 2019-03-19
7fc93c8 Briana Mittleman 2019-03-18
ggsave(APAdecay1sqd_18498, file="../output/plots/APAandRNADecay1SD_18498.png")
Saving 7 x 5 in image

Update plots, 1 per gene, standardize

I need to full join the mapped read sizes to the APA data.

ApaBothFrac=TotAPA_bygene %>% inner_join(NucAPA_bygene, by=c("GeneName", "Individual"))

ApaBothFrac_melt=melt(ApaBothFrac, id.vars=c("GeneName", "Individual"),value.name="APA_val" ) %>% mutate(fraction=ifelse(variable=="TotalSum", "total", "nuclear"), line=substring(Individual, 2)) %>% dplyr::select(GeneName, fraction, line, APA_val)

I need the mapped read stats:

metadata=read.table("../data/threePrimeSeqMetaData55Ind_noDup_WASPMAP.txt", header = T,stringsAsFactors = F) %>% dplyr::select(line, fraction, Mapped_noMP)

metadata$line= as.character(metadata$line)

Join these:

ApaBothFracStand=ApaBothFrac_melt %>% full_join(metadata, by=c("line", "fraction")) %>% mutate(StandApa=APA_val/Mapped_noMP)

Group by the fraction, gene and get the mean of the standard. I can then divide the nuclear mean by the total mean for each gene

ApaBothFracStand_geneMean=ApaBothFracStand %>% group_by(fraction, GeneName) %>% summarise(meanAPA=mean(StandApa, na.rm=T))

I want to spread this by fraction.

ApaBothFracStand_geneMean_spread= spread(ApaBothFracStand_geneMean,fraction,meanAPA ) %>% mutate(APAVal=nuclear/(total+ nuclear)) 

Join with decay

decay_byGene= decay_geneNames_long %>% group_by(GeneName) %>% summarise(MeanDecay=mean(RNA_Decay))



decay_byGene_1d= decay_byGene %>% mutate(Mean=mean(MeanDecay), SD=sd(MeanDecay), Zscore=(MeanDecay-Mean)/SD) %>% filter(abs(Zscore)>1) %>% dplyr::select(GeneName,MeanDecay)
ApaAndDecaySt= ApaBothFracStand_geneMean_spread %>% inner_join(decay_byGene_1d, by="GeneName")

ApaAndDecaySt$density <- get_density(ApaAndDecaySt$APAVal, ApaAndDecaySt$MeanDecay, n = 100)
apaanddecay1sd=ggplot(ApaAndDecaySt, aes(x=MeanDecay, y=APAVal)) + geom_point(aes(color=density)) + geom_smooth(method="lm") + labs(x="relative Decay", y="Nuclear/(Total+Nuclear)", title="Relationship between Nuclear proportion and RNA decay\n for decay gene 1SD outside mean")+ scale_color_viridis()

apaanddecay1sd

ggsave(apaanddecay1sd, file="../output/plots/ApaRationVDecy1SD.png")
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summary(lm(data=ApaAndDecaySt, APAVal~MeanDecay))

Call:
lm(formula = APAVal ~ MeanDecay, data = ApaAndDecaySt)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.3383 -0.1112 -0.0005  0.1085  0.3710 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.48523    0.00359 135.158  < 2e-16 ***
MeanDecay   -0.10327    0.01489  -6.936 5.62e-12 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.138 on 1788 degrees of freedom
Multiple R-squared:  0.0262,    Adjusted R-squared:  0.02566 
F-statistic: 48.11 on 1 and 1788 DF,  p-value: 5.621e-12

Try all of the value:

ApaAndDecayStall= ApaBothFracStand_geneMean_spread %>% inner_join(decay_byGene, by="GeneName")


ApaAndDecayStall$density <- get_density(ApaAndDecayStall$APAVal, ApaAndDecayStall$MeanDecay, n = 100)

apaanddecayallplot=ggplot(ApaAndDecayStall, aes(x=MeanDecay, y=APAVal)) + geom_point(aes(color=density)) + geom_smooth(method="lm") +labs(x="relative Decay", y="Nuclear/(Total+Nuclear)", title="Relationship between Nuclear proportion and RNA decay")+ scale_color_viridis()

apaanddecayallplot

ggsave(apaanddecayallplot, file="../output/plots/ApaRationVDecyAllGenes.png")
Saving 7 x 5 in image
summary(lm(data=ApaAndDecayStall, APAVal~MeanDecay))

Call:
lm(formula = APAVal ~ MeanDecay, data = ApaAndDecayStall)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.39756 -0.10362  0.01145  0.11371  0.39458 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.520235   0.001582 328.887  < 2e-16 ***
MeanDecay   -0.069035   0.012646  -5.459 4.93e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1379 on 7886 degrees of freedom
Multiple R-squared:  0.003765,  Adjusted R-squared:  0.003639 
F-statistic:  29.8 on 1 and 7886 DF,  p-value: 4.928e-08

Make the same plot with transcription on the X (4su/4su+RNA)

4su data

FourSU=read.table(file = "../data/RNAdecay/tr_decay_table_norm.txt", header=T, stringsAsFactors = F) %>%  dplyr::select(gene_id,contains("4su_30"))


FourSU_geneNames=FourSU %>% inner_join(geneNames, by="gene_id") %>% dplyr::select(GeneName, contains("4su_30"))

FourgeneNames_long=melt(FourSU_geneNames,id.vars = "GeneName", value.name = "FourSU", variable.name = "FourSU_ind") %>% separate(FourSU_ind, into=c("type","time", "1400", "MAf", "Individual"), sep="_") %>% dplyr::select(GeneName, Individual, FourSU) 

FourSU_geneMean=FourgeneNames_long %>% group_by(GeneName) %>%summarise(Mean_4su=mean(FourSU))

Gene expression data:

RNA=read.table(file = "../data/RNAdecay/tr_decay_table_norm.txt", header=T, stringsAsFactors = F) %>%  dplyr::select(gene_id,contains("RNAseq_14000"))


RNA_geneNames=RNA %>% inner_join(geneNames, by="gene_id") %>% dplyr::select(GeneName, contains("RNA"))

RNAgeneNames_long=melt(RNA_geneNames,id.vars = "GeneName", value.name = "RNA", variable.name = "RNA_ind") %>%   separate(RNA_ind, into=c("type", "1400", "MAf", "Individual"), sep="_") %>% dplyr::select(GeneName, Individual, RNA) 

RNA_geneMean=RNAgeneNames_long %>% group_by(GeneName) %>%summarise(Mean_RNA=mean(RNA))

Join these and make the transcription phenotype

Transcription=FourSU_geneMean %>% inner_join(RNA_geneMean, by="GeneName") %>% mutate(Transcription=Mean_4su/(Mean_4su + Mean_RNA)) %>% dplyr::select(GeneName, Transcription)

Join with APA:

APAandTranscrption= Transcription %>% inner_join(ApaBothFracStand_geneMean_spread, by="GeneName")
APAandTranscrption$density <- get_density(APAandTranscrption$APAVal, APAandTranscrption$Transcription, n = 100)

apaand4uplot=ggplot(APAandTranscrption, aes(x=Transcription, y=APAVal))+ geom_point(aes(color=density)) + geom_smooth(method = "lm") + labs(x="4su/4su+RNA", y="Nuclear/Nuclear+Total", title="Relationship between APA fraction and transcription") + scale_color_viridis()


summary(lm(data=APAandTranscrption, APAVal~Transcription))

Call:
lm(formula = APAVal ~ Transcription, data = APAandTranscrption)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.45569 -0.09980  0.00815  0.10627  0.38149 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)   0.354663   0.007229   49.06   <2e-16 ***
Transcription 0.319004   0.013488   23.65   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1335 on 7886 degrees of freedom
Multiple R-squared:  0.06623,   Adjusted R-squared:  0.06612 
F-statistic: 559.4 on 1 and 7886 DF,  p-value: < 2.2e-16
apaand4uplot

ggsave(apaand4uplot, file="../output/plots/NuclearTotalRatiov4suRNARatio.png")
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sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14.1

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] viridis_0.5.1     viridisLite_0.3.0 MASS_7.3-51.1    
 [4] reshape2_1.4.3    forcats_0.4.0     stringr_1.4.0    
 [7] dplyr_0.8.0.1     purrr_0.3.1       readr_1.3.1      
[10] tidyr_0.8.3       tibble_2.0.1      ggplot2_3.1.0    
[13] tidyverse_1.2.1  

loaded via a namespace (and not attached):
 [1] tidyselect_0.2.5 xfun_0.5         haven_2.1.0      lattice_0.20-38 
 [5] colorspace_1.4-0 generics_0.0.2   htmltools_0.3.6  yaml_2.2.0      
 [9] rlang_0.3.1      pillar_1.3.1     glue_1.3.0       withr_2.1.2     
[13] modelr_0.1.4     readxl_1.3.0     plyr_1.8.4       munsell_0.5.0   
[17] gtable_0.2.0     workflowr_1.2.0  cellranger_1.1.0 rvest_0.3.2     
[21] evaluate_0.13    labeling_0.3     knitr_1.21       broom_0.5.1     
[25] Rcpp_1.0.0       scales_1.0.0     backports_1.1.3  jsonlite_1.6    
[29] fs_1.2.6         gridExtra_2.3    hms_0.4.2        digest_0.6.18   
[33] stringi_1.3.1    grid_3.5.1       rprojroot_1.3-2  cli_1.0.1       
[37] tools_3.5.1      magrittr_1.5     lazyeval_0.2.1   crayon_1.3.4    
[41] whisker_0.3-2    pkgconfig_2.0.2  xml2_1.2.0       lubridate_1.7.4 
[45] assertthat_0.2.0 rmarkdown_1.11   httr_1.4.0       rstudioapi_0.9.0
[49] R6_2.4.0         nlme_3.1-137     git2r_0.24.0     compiler_3.5.1