Last updated: 2020-04-27

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Knit directory: Comparative_APA/analysis/

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Unstaged changes:
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Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.


These are the previous versions of the R Markdown and HTML files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view them.

File Version Author Date Message
Rmd b653f27 brimittleman 2020-04-27 add simpson
html 448aa08 brimittleman 2020-04-24 Build site.
Rmd 93d00f3 brimittleman 2020-04-24 add info content

library(tidyverse)
── Attaching packages ───────────────────────────────────────────────────────────── tidyverse 1.2.1 ──
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── Conflicts ──────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
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library(ggpubr)
Loading required package: magrittr

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library(workflowr)
This is workflowr version 1.6.0
Run ?workflowr for help getting started

Packages/functions for this:

vegan: diversity, can calculate shannon or simpson

I will probably do this in python because I can go gene by gene easier:

scipy stats example

This is good because I will be able to change the base and see how it effects the measurements

https://kite.com/python/docs/scipy.stats.entropy

default base is e

from scipy.stats import entropy
import numpy as np
from math import log, e
entropy([1/2, 1/2], base=2)
  
#shannon 
Shannon2 = -np.sum(pA*np.log2(pA))

I most likely want to use a uniform prior. for this. I could get more complicated in the future by weighting differences by utr and intron. this would help find “more surpising” results.

simpson- squares the probability

from ecopy import diversity 

diversity(x, medod="simpson")


#x- side x species matrix, sites are rows, columns are species - ie column counts, row == pas
library(vegan)
Loading required package: permute
Loading required package: lattice
This is vegan 2.5-3
data(BCI)
dim(BCI)
[1]  50 225
H <- diversity(BCI)
length(H)
[1] 50
diversity(c(.5,.5,.5))
[1] 1.098612
diversity(c(.25,.75,.25))
[1] 0.9502705
#more peak= lower 


diversity(c(.5,.5,.5), "simpson")
[1] 0.6666667
diversity(c(.25,.75,.25),"simpson")
[1] 0.56
#more peak= lower


diversity(c(.5,.5,.5), "inv")
[1] 3
diversity(c(.25,.75,.25),"inv")
[1] 2.272727

Seem like it is most simple to use the mean usages for this.

First test:

use entropy in python with different bases. -base 2 is the classic shannon and it uses the - when probabilities are given (ie uniform prior)

the python code will work with my meta file for now and take species as an input.

\(H=-\sum^{s}_{i=1}p_{i}log_{2}p_{i}\)

\(H=-\sum^{s}_{i=1}p_{i}lnp_{i}\)

mkdir ../data/InfoContent

python InfoContentShannon.py Human
python InfoContentShannon.py Chimp

Results:

HumanResInfo= read.table("../data/InfoContent/Human_InfoContent.txt", header = T,stringsAsFactors = F) %>% rename(Human_Base2=base2, Human_basee= basee)
ChimpResInfo= read.table("../data/InfoContent/Chimp_InfoContent.txt", header = T,stringsAsFactors = F) %>% rename(Chimp_Base2=base2, Chimp_basee= basee)

BothResInfo= HumanResInfo %>% inner_join(ChimpResInfo, by=c("gene", "numPAS")) %>% filter(numPAS > 1)

First plot the distributions:

BothResInfo_2= BothResInfo %>% select(gene, contains("Base2")) %>% gather("species", "base2", -gene)

ggplot(BothResInfo_2, aes(x=base2, fill=species)) + geom_density(alpha=.5) + scale_fill_brewer(palette = "Set1")+ labs(title="Shannon Information Content")
Warning: Removed 1 rows containing non-finite values (stat_density).

Version Author Date
448aa08 brimittleman 2020-04-24
wilcox.test(BothResInfo$Human_Base2, BothResInfo$Chimp_Base2, alternative = "greater")

    Wilcoxon rank sum test with continuity correction

data:  BothResInfo$Human_Base2 and BothResInfo$Chimp_Base2
W = 39254000, p-value < 2.2e-16
alternative hypothesis: true location shift is greater than 0

Human shift higher, ie less density:

BothResInfo_e= BothResInfo %>% select(gene, contains("basee")) %>% gather("species", "basee", -gene)

ggplot(BothResInfo_e, aes(x=basee, fill=species)) + geom_density(alpha=.3)
Warning: Removed 1 rows containing non-finite values (stat_density).

Version Author Date
448aa08 brimittleman 2020-04-24

I want to look at this by dominance:

ggplot(BothResInfo_2,aes(x=base2, fill=species)) + geom_histogram() + facet_grid(~species)
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Warning: Removed 1 rows containing non-finite values (stat_bin).

Version Author Date
448aa08 brimittleman 2020-04-24

Plot human vs chimp:

ggplot(BothResInfo,aes(x=Human_Base2,y= Chimp_Base2 )) + geom_point() + geom_abline(slope=1, intercept = 0) + stat_cor() + geom_density_2d(col="blue")
Warning: Removed 1 rows containing non-finite values (stat_cor).
Warning: Removed 1 rows containing non-finite values (stat_density2d).
Warning: Removed 1 rows containing missing values (geom_point).

Version Author Date
448aa08 brimittleman 2020-04-24
ggplot(BothResInfo,aes(x=Human_Base2,y= Chimp_Base2 ,col=numPAS)) + geom_point(alpha=.4) + geom_abline(slope=1, intercept = 0) +labs(title="Shannon Index Colored by number of PAS")
Warning: Removed 1 rows containing missing values (geom_point).

Version Author Date
448aa08 brimittleman 2020-04-24

Does number explain:

summary(lm(BothResInfo$Human_Base2 ~BothResInfo$numPAS))

Call:
lm(formula = BothResInfo$Human_Base2 ~ BothResInfo$numPAS)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.88694 -0.20022  0.06073  0.23527  0.53990 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)        0.209838   0.008559   24.52   <2e-16 ***
BothResInfo$numPAS 0.314404   0.001527  205.93   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3166 on 8448 degrees of freedom
  (1 observation deleted due to missingness)
Multiple R-squared:  0.8339,    Adjusted R-squared:  0.8339 
F-statistic: 4.241e+04 on 1 and 8448 DF,  p-value: < 2.2e-16
summary(lm(BothResInfo$Chimp_Base2 ~BothResInfo$numPAS ))

Call:
lm(formula = BothResInfo$Chimp_Base2 ~ BothResInfo$numPAS)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.76846 -0.25131  0.06184  0.27657  0.67339 

Coefficients:
                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)        0.108685   0.010226   10.63   <2e-16 ***
BothResInfo$numPAS 0.307373   0.001824  168.49   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3784 on 8449 degrees of freedom
Multiple R-squared:  0.7706,    Adjusted R-squared:  0.7706 
F-statistic: 2.839e+04 on 1 and 8449 DF,  p-value: < 2.2e-16

So this is working but the number of PAS explains most of the variation. Maybe I can normalize this out and look at residuals:

BothResInfoRes= BothResInfo %>% mutate(HumanNorm=residuals(BothResInfo$Human_Base2~BothResInfo$numPAS),ChimpNorm=residuals(BothResInfo$Chimp_Base2~BothResInfo$numPAS))

pull in dominance:

HumanRes=read.table("../data/DomDefGreaterX/Human_AllGenes_DiffTop.txt", col.names = c("Human_PAS", "gene","Human_DiffDom"),stringsAsFactors = F)

ChimpRes=read.table("../data/DomDefGreaterX/Chimp_AllGenes_DiffTop.txt", col.names = c("Chimp_PAS", "gene","Chimp_DiffDom"),stringsAsFactors = F)

BothRes=HumanRes %>% inner_join(ChimpRes,by="gene")

BothRes_10=BothRes %>% filter(Chimp_DiffDom >=0.1 | Human_DiffDom>=0.1) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=10) 
BothRes_20=BothRes %>% filter(Chimp_DiffDom >=0.2 | Human_DiffDom>=0.2) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=20)
BothRes_30=BothRes %>% filter(Chimp_DiffDom >=0.3 | Human_DiffDom>=0.3) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=30)
BothRes_40=BothRes %>% filter(Chimp_DiffDom >=0.4 | Human_DiffDom>=0.4) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=40)
BothRes_50=BothRes %>% filter(Chimp_DiffDom >=0.5 | Human_DiffDom>=0.5) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=50)
BothRes_60=BothRes %>% filter(Chimp_DiffDom >=0.6 | Human_DiffDom>=0.6) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=60)
BothRes_70=BothRes %>% filter(Chimp_DiffDom >=0.7 | Human_DiffDom>=0.7) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=70)
BothRes_80=BothRes %>% filter(Chimp_DiffDom >=0.8 | Human_DiffDom>=0.8) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=80)
BothRes_90=BothRes %>% filter(Chimp_DiffDom >=0.9 | Human_DiffDom>=0.9) %>% mutate(Set= ifelse(Human_PAS==Chimp_PAS,"Same", "Different"),cut=90)

BothResAll=BothRes_10 %>% bind_rows(BothRes_20) %>% bind_rows(BothRes_30) %>% bind_rows(BothRes_40) %>% bind_rows(BothRes_50) %>% bind_rows(BothRes_60) %>% bind_rows(BothRes_70) %>% bind_rows(BothRes_80) %>% bind_rows(BothRes_90)

I want dominance in 1 or both at .4.

BothRes_40_each= BothRes_40 %>% mutate(Dom=ifelse(Human_DiffDom>=.4, ifelse(Chimp_DiffDom >=.4, "Both", "Human"), "Chimp"))

BothRes_40_each %>% group_by(Dom) %>% summarise(n())
# A tibble: 3 x 2
  Dom   `n()`
  <chr> <int>
1 Both   1565
2 Chimp   906
3 Human   257
BothRes_40_each %>% group_by(Set,Dom) %>% summarise(n())
# A tibble: 6 x 3
# Groups:   Set [2]
  Set       Dom   `n()`
  <chr>     <chr> <int>
1 Different Both     22
2 Different Chimp   114
3 Different Human    46
4 Same      Both   1543
5 Same      Chimp   792
6 Same      Human   211
BothRes_40_eachsm= BothRes_40_each %>% select(gene, Set, Dom)


BothResInfoDom= BothResInfo %>% full_join(BothRes_40_eachsm, by="gene", fill="None") %>%  mutate(Set= replace_na(Set, "None"),Dom= replace_na(Dom, "None"))


ggplot(BothResInfoDom,aes(x=Human_Base2,y= Chimp_Base2, col=Dom )) + geom_point(alpha=.3) + geom_abline(slope=1, intercept = 0) + scale_color_brewer(palette = "Set2") + labs(x="Human Information", y="Chimp Information", title="Shannon Information Index colored by whether gene has a dominanat PAS")
Warning: Removed 1 rows containing missing values (geom_point).

Version Author Date
448aa08 brimittleman 2020-04-24
ggplot(BothResInfoDom,aes(x=Human_Base2,y= Chimp_Base2, col=Set )) + geom_point(alpha=.3) + geom_abline(slope=1, intercept = 0) + scale_color_brewer(palette = "Set2") +geom_density2d()+ labs(x="Human Information", y="Chimp Information", title="Shannon Information Index colored by Dominance Structure ")
Warning: Removed 1 rows containing non-finite values (stat_density2d).

Warning: Removed 1 rows containing missing values (geom_point).

Version Author Date
448aa08 brimittleman 2020-04-24
BothResInfoDom$numPAS=as.factor(BothResInfoDom$numPAS)
ggplot(BothResInfoDom,aes(x=Human_Base2,y= Chimp_Base2, col=numPAS )) + geom_point(alpha=.3) + geom_abline(slope=1, intercept = 0) + labs(x="Human Information", y="Chimp Information", title="Shannon Information Index colored by Dominance Structure ") + facet_grid(~Dom)
Warning: Removed 1 rows containing missing values (geom_point).

Version Author Date
448aa08 brimittleman 2020-04-24
#+ scale_color_brewer(palette = "Spectral")

Dominance and number of PAS:

BothResInfoDom$numPAS=as.numeric(as.character(BothResInfoDom$numPAS))
ggplot(BothResInfoDom,aes(x=Dom, y=numPAS)) +geom_boxplot() +stat_compare_means() +  labs(x="Dominance Structure",y="Number of PAS", title="Number of PAS differ by dominance structure")

Version Author Date
448aa08 brimittleman 2020-04-24
ggplot(BothResInfoDom,aes(x=Set, y=numPAS)) +geom_boxplot() +stat_compare_means() +  labs(x="Dominance Structure",y="Number of PAS", title="Number of PAS differ by dominance structure")

Ratio problem!!!!

but the confounder is biological- number of PAS.

Try the simpson index.

skit-bio: http://scikit-bio.org/docs/0.1.3/math.diversity.alpha.html

\(D=\sum_{i=1}^{R}p_{i}^{2}\)

and

\(D=1-\sum_{i=1}^{R}p_{i}^{2}\)

python infoContentSimpson.py Human
python infoContentSimpson.py Chimp
SimpHuman=read.table("../data/InfoContent/Human_SimpsonInfoContent.txt", header = T, stringsAsFactors = F) %>% rename(simpson_Human=simpson) %>% mutate(simpOpp_Human=1-simpson_Human)
SimpChimp=read.table("../data/InfoContent/Chimp_SimpsonInfoContent.txt", header = T, stringsAsFactors = F)%>% rename(simpson_Chimp=simpson)%>% mutate(simpOpp_Chimp=1-simpson_Chimp)

BothSimp= SimpHuman %>% inner_join(SimpChimp, by=c("gene", "numPAS")) %>% filter(numPAS > 1)

Gather and plot:

BothSimp_g= BothSimp %>% select(-contains("Opp")) %>% gather("species", "Simpson", -gene, -numPAS)
ggplot(BothSimp_g, aes(x=Simpson, fill=species)) + geom_density(alpha=.5) + scale_fill_brewer(palette = "Set1")+labs(title="Simpson Index")

BothOppSimp_g= BothSimp %>% select(-contains("simpson")) %>% gather("species", "SimpsonOpp", -gene, -numPAS)

ggplot(BothOppSimp_g, aes(x=SimpsonOpp, fill=species)) + geom_density(alpha=.5) + scale_fill_brewer(palette = "Set1")+labs(title="Simpson Index (1-opp)")

wilcox.test(BothSimp$simpOpp_Human, BothSimp$simpOpp_Chimp, alternative = "greater")

    Wilcoxon rank sum test with continuity correction

data:  BothSimp$simpOpp_Human and BothSimp$simpOpp_Chimp
W = 40925000, p-value < 2.2e-16
alternative hypothesis: true location shift is greater than 0

Histogram:

ggplot(BothSimp_g,aes(x=Simpson, fill=species)) + geom_histogram() + facet_grid(~species)+scale_fill_brewer(palette = "Set1")
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(BothOppSimp_g, aes(x=SimpsonOpp, fill=species)) + geom_histogram() + facet_grid(~species)+scale_fill_brewer(palette = "Set1")
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

here, higher index is lower diversity= more dominance (opposite of shannon)

the opposite one is 1- sum. this is more dominance at lower values like shannon. I will go with this so the sign is the same.

BothInfoTypes=BothSimp %>% inner_join(BothResInfoRes, by=c("gene", "numPAS"))

BothInfoTypes_h=BothInfoTypes %>% select(gene,numPAS, simpOpp_Human, Human_Base2) %>% mutate(species="Human") %>% rename(Simpson= simpOpp_Human, Shannon=Human_Base2)
BothInfoTypes_c=BothInfoTypes %>% select(gene,numPAS, simpOpp_Chimp, Chimp_Base2) %>% mutate(species="Chimp")%>% rename(Simpson= simpOpp_Chimp, Shannon=Chimp_Base2)

BothInfoTypes_both=BothInfoTypes_h %>% bind_rows(BothInfoTypes_c)

ggplot(BothInfoTypes_both,aes(x=Simpson, y=Shannon, by=species, col=species)) +geom_point(alpha=.4) +geom_density2d(col="black") +  stat_cor(label.x=0) + geom_smooth(col="black",method = "lm") + facet_grid(~species) + labs(title="Correlation between Indicies") +theme(legend.position = "none")+scale_color_brewer(palette = "Set1")
Warning: Removed 1 rows containing non-finite values (stat_density2d).
Warning: Removed 1 rows containing non-finite values (stat_cor).
Warning: Removed 1 rows containing non-finite values (stat_smooth).
Warning: Removed 1 rows containing missing values (geom_point).

There is more variation at the low end here.

Compare human and chimp simpson by PAS number:

ggplot(BothInfoTypes,aes(x=simpOpp_Human,y= simpOpp_Chimp ,col=numPAS)) + geom_point(alpha=.4) + geom_abline(slope=1, intercept = 0)+labs(title="Simpson Index Colored by number of PAS")

summary(lm(BothInfoTypes$simpOpp_Human ~BothResInfo$numPAS))

Call:
lm(formula = BothInfoTypes$simpOpp_Human ~ BothResInfo$numPAS)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.94165 -0.08859  0.00961  0.10528  0.43248 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)        0.4483250  0.0046537   96.34   <2e-16 ***
BothResInfo$numPAS 0.0595955  0.0008302   71.78   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1722 on 8449 degrees of freedom
Multiple R-squared:  0.3788,    Adjusted R-squared:  0.3788 
F-statistic:  5153 on 1 and 8449 DF,  p-value: < 2.2e-16
summary(lm(BothInfoTypes$simpOpp_Chimp ~BothResInfo$numPAS ))

Call:
lm(formula = BothInfoTypes$simpOpp_Chimp ~ BothResInfo$numPAS)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.79002 -0.10111  0.01491  0.11286  0.50115 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)        0.3685223  0.0049596   74.31   <2e-16 ***
BothResInfo$numPAS 0.0651630  0.0008848   73.65   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1835 on 8449 degrees of freedom
Multiple R-squared:  0.391, Adjusted R-squared:  0.3909 
F-statistic:  5424 on 1 and 8449 DF,  p-value: < 2.2e-16

Number of PAS is less correlated with this index.

Add in the dominanace structure to compare to simpson:

BothResBothInfoDom= BothInfoTypes %>% full_join(BothRes_40_eachsm, by="gene", fill="None") %>%  mutate(Set= replace_na(Set, "None"),Dom= replace_na(Dom, "None"))


ggplot(BothResBothInfoDom,aes(x=simpOpp_Human,y= simpOpp_Chimp, col=Dom )) + geom_point(alpha=.3) + geom_abline(slope=1, intercept = 0) + scale_color_brewer(palette = "Set2") + labs(x="Human Simpson", y="Chimp Simpson", title="Simpson Information Index colored by whether gene has a dominanat PAS")

ggplot(BothResBothInfoDom,aes(x=simpOpp_Human,y= simpOpp_Chimp, col=Set )) + geom_point(alpha=.3) + geom_abline(slope=1, intercept = 0) + scale_color_brewer(palette = "Set2") +geom_density2d()+ labs(x="Human Simpson", y="Chimp Simpson", title="Simpson Information Index colored by Dominance Structure ")

BothResBothInfoDom$numPAS=as.factor(BothResBothInfoDom$numPAS)
ggplot(BothResBothInfoDom,aes(x=simpOpp_Human,y= simpOpp_Chimp, col=numPAS )) + geom_point(alpha=.3) + geom_abline(slope=1, intercept = 0) + labs(x="Human Simpson", y="Chimp Simpson", title="Simpson Information Index colored by Dominance Structure ") + facet_grid(~Dom)

#+ scale_color_brewer(palette = "Spectral")

Equitability. Shannon diversity divided by the logarithm of number of taxa. This measures the evenness with which individuals are divided among the taxa present.

Shannon’s equitability (EH) measures the evenness of a community and can be easily calculated by diving the value of H with H_max, which equals to lnS(S=number of species encountered). Its value ranges between 0 and 1, with being complete evenness. (0-1)


sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

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

other attached packages:
 [1] vegan_2.5-3     lattice_0.20-38 permute_0.9-4   workflowr_1.6.0
 [5] ggpubr_0.2      magrittr_1.5    forcats_0.3.0   stringr_1.3.1  
 [9] dplyr_0.8.0.1   purrr_0.3.2     readr_1.3.1     tidyr_0.8.3    
[13] tibble_2.1.1    ggplot2_3.1.1   tidyverse_1.2.1

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.2         lubridate_1.7.4    assertthat_0.2.0  
 [4] rprojroot_1.3-2    digest_0.6.18      utf8_1.1.4        
 [7] R6_2.3.0           cellranger_1.1.0   plyr_1.8.4        
[10] backports_1.1.2    evaluate_0.12      httr_1.3.1        
[13] pillar_1.3.1       rlang_0.4.0        lazyeval_0.2.1    
[16] readxl_1.1.0       rstudioapi_0.10    whisker_0.3-2     
[19] Matrix_1.2-15      reticulate_1.10    rmarkdown_1.10    
[22] labeling_0.3       munsell_0.5.0      broom_0.5.1       
[25] compiler_3.5.1     httpuv_1.4.5       modelr_0.1.2      
[28] pkgconfig_2.0.2    mgcv_1.8-25        htmltools_0.3.6   
[31] tidyselect_0.2.5   fansi_0.4.0        crayon_1.3.4      
[34] withr_2.1.2        later_0.7.5        MASS_7.3-51.1     
[37] grid_3.5.1         nlme_3.1-137       jsonlite_1.6      
[40] gtable_0.2.0       git2r_0.26.1       scales_1.0.0      
[43] cli_1.1.0          stringi_1.2.4      reshape2_1.4.3    
[46] fs_1.3.1           promises_1.0.1     xml2_1.2.0        
[49] generics_0.0.2     RColorBrewer_1.1-2 tools_3.5.1       
[52] glue_1.3.0         hms_0.4.2          parallel_3.5.1    
[55] yaml_2.2.0         colorspace_1.3-2   cluster_2.0.7-1   
[58] rvest_0.3.2        knitr_1.20         haven_1.1.2