Context

I recently had the opportunity to teach some R coding to colleagues and classmates in a series of workshops. Some had already dabbled in R or other programming languages, but it was the first time that the majority of participants had written a single line of code.

A few things happened in the week following the last session that I didn’t expect.

First, I saw a bit of R code written on a campus whiteboard that had nothing to do with me, but was straight out of the workshop. It may have come from some of my data-centric colleagues who use R, so I didn’t think too much of it.

Then, I overheard a conversation involving R from those in a program that doesn’t require any data-related coursework. Many folks are familiar with the name as the school’s primary data analysis course uses the {Rcmdr} GUI for statistical analysis, but these students would not have necessarily taken the course. I wondered if there was a connection.

Finally, a student who didn’t even attend came to my office hours asking for resources. Why exactly? Some of his work colleagues attended. It turns out that they are now trying to incorporate some R-powered analysis in their work and he doesn’t want to miss out.

The workshop consisted of 3 consecutive Fridays lasting 90 minutes each. That’s only a total of 4.5 hours.

That’s relatively tiny amount of time.

Wait. Scratch that.

That’s a negligible amount of time.

… but it was enough to convince some participants and non-participants that they should take advantage of the power that a bit of data-centric coding can offer.

Reflection

I taught a similar 90 minute workshop last spring using R, but focused on base R and a few data types. 10 minutes in, I’m trying to explain the difference between a data.frame and a matrix and the person asking the question says something along the lines of “I guess I’m kinda dumb. Don’t worry about it.”

For context, these were international policy graduate students. While some have completed a bit of quantitative coursework, most don’t have a hardcore math or science background and programming is seen as something akin to wizardry. However, they hold domain expertise in some rather important subjects. These include WMD nonproliferation, international development, economic diplomacy, conflict studies, and environmental policy. Nearly half of the participants were international students and everyone is proficient in at least a second natural language. Most have already tackled big, complicated problems in their careers and the others are on their way to doing so following graduation. In a nutshell, they’re not dumb. The way I was teaching was dumb. They knew that they’re supposed to want to learn new skills, but they didn’t know why. Focusing on the “basics” didn’t show them anything immediately useful. It didn’t show them the why.

After the workshop, I never heard anyone mention R outside my circle of fellow data folks.

Since that time, I started using R more. Like, a lot more. I have found a way to use R in nearly everything I’ve done since May 2017. As a policy student myself, that has not always been very straightforward and I was still avoiding the strange “tidy” code I’d encounter on Stack Overflow and elsewhere. I realized the error of my ways when I came across Julia Silge and David Robinson’s Text Mining with R. It was like discovering that you’re still in the stone age while most people are off partying on spaceships.

In preparation for this workshop series, I found a lot of inspiration in Michael Levy’s presentation on teaching R, which itself echoes principles preached by other tidyverse advocates.

A huge takeaway: live coding works.

Writing code in real time shows every single step we make from opening the IDE, to reshaping the data, to debugging inevitable errors, to rendering a final report.

Within a few short weeks of learning to code, it might be surprising how many tiny steps become automatic and taken for granted. Tack on a couple more months and newcomers will think you’re speaking in an entirely different language because you’re explaining something requiring context they simply haven’t yet encountered. Add a few years and… yeesh.

Something that frustrated me when I first started is that code explanations often seem to be written in such a way that dismisses how difficult establishing the basics can be. I’m half-convinced that, for some folks, the trauma was so great that they have simply blocked it from memory. Code is intimidating enough, but if an instructor doesn’t make a conscious effort to empathize, students will question their ability to learn. The goal is empowerment, not intimidation.

Live coding enforces a maximum speed in moving through exercises, which not only gives students more time to digest what you’re doing. It also provides more opportunities for them to ask questions on details you might find trivial, but only because you already suffered through them.

I also think that the benefits of live coding extend to the instructor as well. I found myself answering questions that framed things in ways that I had not even considered, but were exactly how multiple participants saw the task. Additionally, I have a better sense of which concepts need to be covered in more detail, as they weren’t necessarily as intuitive for others as they were for me. On the flip-side, concepts with which I remember struggling may not be difficult at all for others to understand.

… and now that we got the bloggyness of a blog post out of the way…

Here is the workflow I used for the first session. The goal was to introduce the primary {dplyr} verbs, functions that accomplish tasks necessary in nearly every project. Between each section is an exercise using {ggplot}.

tidyverse::tidyverse_logo()
## * __  _    __   .    o           *  . 
##  / /_(_)__/ /_ ___  _____ _______ ___ 
## / __/ / _  / // / |/ / -_) __(_-</ -_)
## \__/_/\_,_/\_, /|___/\__/_/ /___/\__/ 
##      *  . /___/      o      .       *

# install.packages("tidyverse")
library(tidyverse)

# install.packages("gapminder")
library(gapminder)
# loads the gapminder data set

## just to prettify printed tables when knitting
# install.packages("kableExtra")
library(knitr)
library(kableExtra)

Resources Up Front

gm.data.frame <- as.data.frame(gapminder)

gm_df <- gapminder

tibble

class(gm.data.frame)
## [1] "data.frame"
class(gm_df)
## [1] "tbl_df"     "tbl"        "data.frame"

tibbles are opinionated data.frames that keep everything that is helpful about data.frames, changes some of their quirks, and adds methods that makes them even more useful.

Printing gm.data.frame dumps the whole data set to the console, typically requiring head() to limit the output.

head(gm.data.frame)
##       country continent year lifeExp      pop gdpPercap
## 1 Afghanistan      Asia 1952  28.801  8425333  779.4453
## 2 Afghanistan      Asia 1957  30.332  9240934  820.8530
## 3 Afghanistan      Asia 1962  31.997 10267083  853.1007
## 4 Afghanistan      Asia 1967  34.020 11537966  836.1971
## 5 Afghanistan      Asia 1972  36.088 13079460  739.9811
## 6 Afghanistan      Asia 1977  38.438 14880372  786.1134

gm_df
## # A tibble: 1,704 x 6
##    country     continent  year lifeExp      pop gdpPercap
##    <fct>       <fct>     <int>   <dbl>    <int>     <dbl>
##  1 Afghanistan Asia       1952    28.8  8425333      779.
##  2 Afghanistan Asia       1957    30.3  9240934      821.
##  3 Afghanistan Asia       1962    32.0 10267083      853.
##  4 Afghanistan Asia       1967    34.0 11537966      836.
##  5 Afghanistan Asia       1972    36.1 13079460      740.
##  6 Afghanistan Asia       1977    38.4 14880372      786.
##  7 Afghanistan Asia       1982    39.9 12881816      978.
##  8 Afghanistan Asia       1987    40.8 13867957      852.
##  9 Afghanistan Asia       1992    41.7 16317921      649.
## 10 Afghanistan Asia       1997    41.8 22227415      635.
## # ... with 1,694 more rows

%>%

The pipe (%>%) is used to chain operations together. Underneath the hood, it’s taking the value on the left-hand side of %>% and using it as the first argument of the function on the right-hand side of %>%.

For example, these 2 lines are doing the exact same thing.

head(gm_df)
## # A tibble: 6 x 6
##   country     continent  year lifeExp      pop gdpPercap
##   <fct>       <fct>     <int>   <dbl>    <int>     <dbl>
## 1 Afghanistan Asia       1952    28.8  8425333      779.
## 2 Afghanistan Asia       1957    30.3  9240934      821.
## 3 Afghanistan Asia       1962    32.0 10267083      853.
## 4 Afghanistan Asia       1967    34.0 11537966      836.
## 5 Afghanistan Asia       1972    36.1 13079460      740.
## 6 Afghanistan Asia       1977    38.4 14880372      786.
gm_df %>% head()
## # A tibble: 6 x 6
##   country     continent  year lifeExp      pop gdpPercap
##   <fct>       <fct>     <int>   <dbl>    <int>     <dbl>
## 1 Afghanistan Asia       1952    28.8  8425333      779.
## 2 Afghanistan Asia       1957    30.3  9240934      821.
## 3 Afghanistan Asia       1962    32.0 10267083      853.
## 4 Afghanistan Asia       1967    34.0 11537966      836.
## 5 Afghanistan Asia       1972    36.1 13079460      740.
## 6 Afghanistan Asia       1977    38.4 14880372      786.

For simple operations involving 1 function, %>% is only (arguably) beneficial in that it improves readability as the flow of operations go from left to right.

%>% become truly useful when you need to perform multiple operations in succession, which is the vast majority of data carpentry.

As an arbitrary example, let’s say that we want to select the head() (first 6 rows) of gm.data.frame and convert it to a tibble.

Without %>%, we can do this in a few ways.

1. Use intermediate variables.
   • get gm.data.frame’s head() and assign it to no_pipe_1
   • convert no_pipe_1 to a tibble with as_tibble() and assign it to no_pipe_2

no_pipe_1 <- head(gm.data.frame)

no_pipe_2 <- as_tibble(no_pipe_1)

no_pipe_2
## # A tibble: 6 x 6
##   country     continent  year lifeExp      pop gdpPercap
## * <fct>       <fct>     <int>   <dbl>    <int>     <dbl>
## 1 Afghanistan Asia       1952    28.8  8425333      779.
## 2 Afghanistan Asia       1957    30.3  9240934      821.
## 3 Afghanistan Asia       1962    32.0 10267083      853.
## 4 Afghanistan Asia       1967    34.0 11537966      836.
## 5 Afghanistan Asia       1972    36.1 13079460      740.
## 6 Afghanistan Asia       1977    38.4 14880372      786.

2. Nest gm.data.frame inside of head(), which is itself nested inside of as_tibble().

as_tibble(head(gm.data.frame))
## # A tibble: 6 x 6
##   country     continent  year lifeExp      pop gdpPercap
## * <fct>       <fct>     <int>   <dbl>    <int>     <dbl>
## 1 Afghanistan Asia       1952    28.8  8425333      779.
## 2 Afghanistan Asia       1957    30.3  9240934      821.
## 3 Afghanistan Asia       1962    32.0 10267083      853.
## 4 Afghanistan Asia       1967    34.0 11537966      836.
## 5 Afghanistan Asia       1972    36.1 13079460      740.
## 6 Afghanistan Asia       1977    38.4 14880372      786.

With %>%, we can chain these actions together in the order in which they occur, which is also the way we read English.

• Here, we do the same thing by:
  • taking gm_df
  • piping it to head() (keeping the top 6 rows)
  • piping it to as_tibble() (converting it to a tibble data frame)

gm_df %>% head() %>% as_tibble()
## # A tibble: 6 x 6
##   country     continent  year lifeExp      pop gdpPercap
##   <fct>       <fct>     <int>   <dbl>    <int>     <dbl>
## 1 Afghanistan Asia       1952    28.8  8425333      779.
## 2 Afghanistan Asia       1957    30.3  9240934      821.
## 3 Afghanistan Asia       1962    32.0 10267083      853.
## 4 Afghanistan Asia       1967    34.0 11537966      836.
## 5 Afghanistan Asia       1972    36.1 13079460      740.
## 6 Afghanistan Asia       1977    38.4 14880372      786.

In practice, it’s usually best to place each of the functions on a separate line as it facilitates debugging and further improves readability.

gm_df %>%
  as_tibble() %>%
  head()
## # A tibble: 6 x 6
##   country     continent  year lifeExp      pop gdpPercap
##   <fct>       <fct>     <int>   <dbl>    <int>     <dbl>
## 1 Afghanistan Asia       1952    28.8  8425333      779.
## 2 Afghanistan Asia       1957    30.3  9240934      821.
## 3 Afghanistan Asia       1962    32.0 10267083      853.
## 4 Afghanistan Asia       1967    34.0 11537966      836.
## 5 Afghanistan Asia       1972    36.1 13079460      740.
## 6 Afghanistan Asia       1977    38.4 14880372      786.

From here on, you’ll notice prettify(). This is only being used to print tables in a clean format when the document is knit()ted.

I’m choosing to include it here as I often find myself reading similar pages where I come across a really effective way to format some output. I understand why the author chooses to set echo=FALSE, but it can be nice to see the underlying code without having to hunt through their GitHub.

data.frames will print a default maximum of 3 rows while tibbles will print a default maximum of 10 rows.

prettify <- function(df, n = NULL, cols_changed = NULL, rows_changed = NULL){
  if(is.null(n)) n <- ifelse(is.tibble(df), 10, 3)
  pretty_df <- df %>%
    head(n) %>%
    kable(format = "html") %>%
    kable_styling(bootstrap_options = c("striped", "bordered", "condensed",
                                        "hover", "responsive"),
                  full_width = FALSE)
  
  if(!is.null(cols_changed)){
    pretty_df <- pretty_df %>%
      column_spec(cols_changed, bold = T, color = "black", background = "#C8FAE3")
  }
  
  if(!is.null(rows_changed)){
    pretty_df <- pretty_df %>%
      row_spec(rows_changed, bold = T, color = "black", background = "#C8FAE3")
  }
  
  return(pretty_df)
}
gm.data.frame %>%
  prettify()

gm_df %>%
  prettify()

sample_countries <- c("Tunisia", "Nicaragua", "Singapore", "Hungary",
                      "New Zealand", "Nigeria", "Brazil", "Sri Lanka",
                      "Ireland", "Australia")
  
sample_df <- gm_df %>%
  filter(year == 2007,
         country %in% sample_countries)

sample_df %>%     
  prettify()

“Tidy” Data

If you’re unsure of what “Tidy” data is actually describing and want to learn more, you can read Hadley Wickham’s article here. Otherwise, these graphics are likely the most concise explanation you’ll find.

With tibbles, %>%, and the concept of tidy data covered, let’s take a dive.

summary(gm.data.frame)
##         country        continent        year         lifeExp     
##  Afghanistan:  12   Africa  :624   Min.   :1952   Min.   :23.60  
##  Albania    :  12   Americas:300   1st Qu.:1966   1st Qu.:48.20  
##  Algeria    :  12   Asia    :396   Median :1980   Median :60.71  
##  Angola     :  12   Europe  :360   Mean   :1980   Mean   :59.47  
##  Argentina  :  12   Oceania : 24   3rd Qu.:1993   3rd Qu.:70.85  
##  Australia  :  12                  Max.   :2007   Max.   :82.60  
##  (Other)    :1632                                                
##       pop              gdpPercap       
##  Min.   :6.001e+04   Min.   :   241.2  
##  1st Qu.:2.794e+06   1st Qu.:  1202.1  
##  Median :7.024e+06   Median :  3531.8  
##  Mean   :2.960e+07   Mean   :  7215.3  
##  3rd Qu.:1.959e+07   3rd Qu.:  9325.5  
##  Max.   :1.319e+09   Max.   :113523.1  
## 
dim(gm.data.frame)
## [1] 1704    6
str(gm.data.frame)
## 'data.frame':    1704 obs. of  6 variables:
##  $ country  : Factor w/ 142 levels "Afghanistan",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ continent: Factor w/ 5 levels "Africa","Americas",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ year     : int  1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 ...
##  $ lifeExp  : num  28.8 30.3 32 34 36.1 ...
##  $ pop      : int  8425333 9240934 10267083 11537966 13079460 14880372 12881816 13867957 16317921 22227415 ...
##  $ gdpPercap: num  779 821 853 836 740 ...
glimpse(gm_df)
## Observations: 1,704
## Variables: 6
## $ country   <fct> Afghanistan, Afghanistan, Afghanistan, Afghanistan, ...
## $ continent <fct> Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia, Asia...
## $ year      <int> 1952, 1957, 1962, 1967, 1972, 1977, 1982, 1987, 1992...
## $ lifeExp   <dbl> 28.801, 30.332, 31.997, 34.020, 36.088, 38.438, 39.8...
## $ pop       <int> 8425333, 9240934, 10267083, 11537966, 13079460, 1488...
## $ gdpPercap <dbl> 779.4453, 820.8530, 853.1007, 836.1971, 739.9811, 78...

select() columns

sample_df %>%
  prettify()

sample_df %>%
  select(country, pop) %>%
  prettify()

gm_df %>%
  select(country, year, pop) %>%            # select columns by specific names
  prettify()

gm_df %>%
  select(continent, lifeExp:gdpPercap) %>%  # select columns name range
  prettify()

gm_df %>%
  select(-lifeExp) %>%                      # deselect column by name
  prettify()

gm_df %>%
  select(-c(lifeExp:gdpPercap)) %>%         # deselect column by name range
  prettify()

gm_df %>%
  select(4) %>%                             # select column by index
  prettify()

gm_df %>%
  select(-4) %>%                         # deselect column by index
  prettify()

gm_df %>%
  select(-c(3:5)) %>%                    # deselect columns by index range
  prettify()

ggplot() Exercise 1

{ggplot2} is monster of a package used for data visualization that follows The Grammar of Graphics.

{ggplot2} takes R’s powerful graphics capabilities and makes them more accessible by taking care of many plotting tasks that are often tedious, while still allowing for lower-level customization.

• Basic Setup

ggplot(your data, aes(x =x values, y =y values)) +
geom_boxplot() the type of plot geometry desired

Steps

1. Using gm_df, select the lifeExp column
2. Pipe (%>%) the result to ggplot()
3. Select the plot’s aes()thetic values
   • lifeExp for the x values
     • a histogram’s y are counts of its x values, so we don’t provide them here
4. Add geom_histogram() as the geometry of the plot

gm_df %>%                                     # data frame: Data
  select(lifeExp) %>%                         # columns to keep: Data
  ggplot(aes(x = lifeExp)) +                  # x values: Aesthetics
  geom_histogram()                            # histogram: Geometries

Figure 1: Figure 1

filter() Rows

sample_df %>%
  select(country, lifeExp) %>%
  prettify()

sample_df %>%
  select(country, lifeExp) %>%
  filter(lifeExp > 75) %>%
  prettify(cols_changed = 2)

gm_df %>%
  filter(gdpPercap < 500) %>%
  prettify(cols_changed = 6)

gm_df %>%
  filter(year > 1990, lifeExp < 40) %>%
  prettify(cols_changed = 3:4)

gm_df %>%
  filter(pop < 10000 | gdpPercap > 100000) %>%
  prettify(cols_changed = 5:6)

gm_df %>%
  filter(year == 1997 & continent == "Europe") %>%
  prettify(cols_changed = 2:3)

gm_df %>%                                         # data frame: Data
  select(continent, country, gdpPercap) %>%       # columns to keep: Data
  filter(continent == "Oceania") %>%              # rows to keep: Data
  ggplot(aes(x = country, y = gdpPercap)) +       # x and y values: Aesthetics
  geom_boxplot()                                  # box plot: Geometries

mutate() Columns

sample_df %>%
  select(country, pop) %>%
  prettify()

sample_df %>%
  select(country, pop) %>%
  mutate(pop_in_thousands = pop / 1000) %>%
  prettify(cols_changed = 3)

gm_df %>%
  mutate(planet = "Earth") %>%
  prettify(cols_changed = 7)

gm_df %>%
  mutate(total_GDP = pop * gdpPercap) %>%
  prettify(cols_changed = 7)

gm_df %>%
  filter(year == 1977) %>%
  mutate(gdp_per_cap_z_score = (gdpPercap - mean(gdpPercap)) / sd(gdpPercap)) %>%
  prettify(cols_changed = 7)

gm_df %>%
  filter(country %in% c("Korea, Rep.", "Korea, Dem. Rep.", "Japan", "China")) %>%
  mutate(total_GDP = pop * gdpPercap) %>%
  ggplot(aes(x = year, y = gdpPercap, color = country)) +
  geom_line() +
  labs(title = "GDP Over Time")

arrange() Rows

sample_df %>%
  select(country, gdpPercap) %>%
  prettify()

sample_df %>%
  select(country, gdpPercap)%>%
  arrange(gdpPercap) %>%
  prettify(cols_changed = 2)

gm_df %>%
  arrange(pop) %>%
  prettify(cols_changed = 5)

gm_df %>%
  arrange(desc(lifeExp)) %>%
  prettify(cols_changed = 4)

gm_df %>%
  filter(year == 2007, continent == "Americas") %>%
  arrange(country) %>%
  prettify(cols_changed = 2:3)

group_by() for Grouped Data

sample_df %>%
  select(country, continent, pop) %>%
  prettify()

sample_df %>%
  select(country, continent, pop) %>%
  group_by(continent) %>%
  mutate(pop_by_continent = sum(pop)) %>%
  ungroup() %>%
  arrange(pop_by_continent) %>%
  prettify(cols_changed = 4)

gm_df %>%
  group_by(country) %>%
  mutate(mean_gdp_per_cap = median(gdpPercap)) %>% 
  ungroup() %>%
  distinct(country, mean_gdp_per_cap) %>% 
  prettify(cols_changed = 2)

gm_df %>%
  group_by(year, continent) %>%
  mutate(mean_gdp = mean(gdpPercap)) %>%
  ungroup() %>%
  distinct(continent, year, mean_gdp) %>%
  ggplot(aes(x = year, y = mean_gdp, color = continent)) +
  geom_line() +
  labs(title = "Mean GDPs by Continent Over Time",
       caption = "Source: Free material from www.gapminder.org")

summarize()

sample_df %>%
  select(country, continent, lifeExp, pop) %>%
  prettify()

sample_df %>%
  select(country, continent, lifeExp, pop) %>%
  group_by(continent) %>%
  summarise(max_pop = max(pop),
            mean_life_exp = mean(lifeExp)) %>%
  prettify(cols_changed = 2:3)

gm_df %>%
  group_by(continent) %>%
  summarise(count = n(),
            mean_pop = mean(pop),
            max_gdp_per_cap = max(gdpPercap)) %>%
  prettify(cols_changed = 2:4)

gm_df %>%
  filter(continent != "Oceania") %>%
  group_by(continent, year) %>%
  summarise(mean_pop = mean(pop)) %>%
  ungroup() %>%
  ggplot(aes(x = year, y = mean_pop,
             color = continent)) +
  geom_line() +
  geom_point() +
  theme_minimal() +
  facet_wrap(~ continent) +
  labs(title = "Mean Continent Populations over Time",
       caption = "Source: Free material from www.gapminder.org")

sessionInfo()
## R version 3.5.1 (2018-07-02)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 17134)
## 
## Matrix products: default
## 
## locale:
## [1] LC_COLLATE=English_United States.1252 
## [2] LC_CTYPE=English_United States.1252   
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C                          
## [5] LC_TIME=English_United States.1252    
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] bindrcpp_0.2.2       kableExtra_0.9.0     knitr_1.20.8        
##  [4] gapminder_0.3.0      forcats_0.3.0        stringr_1.3.1       
##  [7] dplyr_0.7.6          purrr_0.2.5          readr_1.1.1         
## [10] tidyr_0.8.1          tibble_1.4.2.9004    ggplot2_3.0.0.9000  
## [13] tidyverse_1.2.1.9000
## 
## loaded via a namespace (and not attached):
##  [1] tidyselect_0.2.4  xfun_0.3          reshape2_1.4.3   
##  [4] haven_1.1.2       lattice_0.20-35   colorspace_1.3-2 
##  [7] viridisLite_0.3.0 htmltools_0.3.6   yaml_2.1.19      
## [10] utf8_1.1.4        rlang_0.2.1       pillar_1.3.0.9000
## [13] withr_2.1.2       foreign_0.8-70    glue_1.2.0       
## [16] modelr_0.1.2      readxl_1.1.0      bindr_0.1.1      
## [19] plyr_1.8.4        munsell_0.5.0     blogdown_0.7.1   
## [22] gtable_0.2.0      cellranger_1.1.0  rvest_0.3.2      
## [25] codetools_0.2-15  psych_1.8.4       evaluate_0.10.1  
## [28] labeling_0.3      parallel_3.5.1    fansi_0.2.3      
## [31] highr_0.7         broom_0.4.5       Rcpp_0.12.17     
## [34] scales_0.5.0.9000 jsonlite_1.5      mnormt_1.5-5     
## [37] hms_0.4.2         digest_0.6.15     stringi_1.2.3    
## [40] bookdown_0.7      grid_3.5.1        cli_1.0.0        
## [43] tools_3.5.1       magrittr_1.5      lazyeval_0.2.1   
## [46] crayon_1.3.4      pkgconfig_2.0.1   xml2_1.2.0       
## [49] lubridate_1.7.4   assertthat_0.2.0  rmarkdown_1.10.7 
## [52] httr_1.3.1        rstudioapi_0.7    htmldeps_0.1.0   
## [55] R6_2.2.2          nlme_3.1-137      compiler_3.5.1