Introduction to tidyverse

Objectives

This notebook will demonstrate how to:

• Use functions from the tidyverse to read and write data frames
• Implement and use tidyverse functions to wrangle data (i.e. filter, mutate, arrange, join)
• Use R pipes (|>) to combine multiple operations
• Use the apply() function to apply functions across rows or columns of a matrix

---

We’ll use the same gene expression dataset we used in the previous notebook. It is a pre-processed astrocytoma microarray dataset that we performed a set of differential expression analyses on.

More tidyverse resources:

• R for Data Science
• tidyverse documentation
  • dplyr documentation
  • readr documentation
• Cheatsheet of tidyverse data transformation
• Online tidyverse book chapter

Set Up

The tidyverse is a collection of packages that are handy for general data wrangling, analysis, and visualization. Other packages that are specifically handy for different biological analyses are found on Bioconductor. If we want to use a package’s functions we first need to install them.

Our RStudio Server already has the tidyverse group of packages installed for you. But if you needed to install it or other packages available on CRAN, you do it using the install.packages() function like this: install.packages("tidyverse").

library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.2     ✔ readr     2.1.4
✔ forcats   1.0.0     ✔ stringr   1.5.0
✔ ggplot2   3.4.2     ✔ tibble    3.2.1
✔ lubridate 1.9.2     ✔ tidyr     1.3.0
✔ purrr     1.0.1     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

Referencing a library’s function with ::

Note that if we had not imported the tidyverse set of packages using library() like above, and we wanted to use a tidyverse function like read_tsv(), we would need to tell R what package to find this function in. To do this, we would use :: to tell R to load in this function from the readr package by using readr::read_tsv(). You will see this :: method of referencing libraries within packages throughout the course. We like to use it in part to remove any ambiguity in which version of a function we are using; it is not too uncommon for different packages to use the same name for very different functions!

Managing directories

Before we can import the data we need, we should double check where R is looking for files, aka the current working directory. We can do this by using the getwd() function, which will tell us what folder we are in.

# Let's check what directory we are in:
getwd()

[1] "/__w/training-modules/training-modules/intro-to-R-tidyverse"

/__w/training-modules/training-modules/intro-to-R-tidyverse

For Rmd files, the working directory is wherever the file is located, but commands executed in the console may have a different working directory.

We will want to make a directory for our output and we will call this directory: results. But before we create the directory, we should check if it already exists. We will show two ways that we can do this.

First, we can use the dir() function to have R list the files in our working directory.

# Let's check what files are here
dir()

 [1] "00a-rstudio_guide.Rmd"                   
 [2] "00b-debugging_resources.Rmd"             
 [3] "00c-good_scientific_coding_practices.Rmd"
 [4] "01-intro_to_base_R-live.Rmd"             
 [5] "01-intro_to_base_R.nb.html"              
 [6] "01-intro_to_base_R.Rmd"                  
 [7] "02-intro_to_ggplot2-live.Rmd"            
 [8] "02-intro_to_ggplot2.nb.html"             
 [9] "02-intro_to_ggplot2.Rmd"                 
[10] "03-intro_to_tidyverse-live.Rmd"          
[11] "03-intro_to_tidyverse.nb.html"           
[12] "03-intro_to_tidyverse.Rmd"               
[13] "data"                                    
[14] "diagrams"                                
[15] "exercise_01-intro_to_base_R.Rmd"         
[16] "exercise_02-intro_to_R.Rmd"              
[17] "exercise_03a-intro_to_tidyverse.Rmd"     
[18] "exercise_03b-intro_to_tidyverse.Rmd"     
[19] "plots"                                   
[20] "README.md"                               
[21] "screenshots"                             
[22] "scripts"                                 

00a-rstudio_guide.Rmd

00b-debugging_resources.Rmd

00c-good_scientific_coding_practices.Rmd

01-intro_to_base_R-live.Rmd

01-intro_to_base_R.nb.html

01-intro_to_base_R.Rmd

02-intro_to_ggplot2-live.Rmd

02-intro_to_ggplot2.nb.html

02-intro_to_ggplot2.Rmd

03-intro_to_tidyverse-live.Rmd

03-intro_to_tidyverse.nb.html

03-intro_to_tidyverse.Rmd

data

diagrams

exercise_01-intro_to_base_R.Rmd

exercise_02-intro_to_R.Rmd

exercise_03a-intro_to_tidyverse.Rmd

exercise_03b-intro_to_tidyverse.Rmd

plots

README.md

screenshots

scripts

This shows us there is no folder called “results” yet.

If we want to more pointedly look for “results” in our working directory we can use the dir.exists() function.

# Check if the results directory exists
dir.exists("results")

[1] FALSE

If the above says FALSE that means we will need to create a results directory. We’ve previously seen that we can make directories in R using the base R function dir.create(). But we’ve also seen that this function will throw an error if you try to create a directory that already exists, which can be frustrating if you are re-running code! A different option is to use the fs package, which provides functions for you to interact with your computer’s file system with a more consistent behavior than the base R functions. One function from this package is fs::dir_create() (note that it has an underscore, not a period), and much like the base R dir.create(), it creates directories. It has some other helpful features too: - It will simply do nothing if that directory already exists; no errors, and nothing will get overwritten - It allows creating nested directories by default, i.e. in one call make directories inside of other directories

Let’s go ahead and use it to create our results directory:

# Make a directory within the working directory called 'results'
fs::dir_create("results")

After creating the results directory above, let’s re-run dir.exists() to see if now it exists.

# Re-check if the results directory exists
dir.exists("results")

[1] TRUE

The dir.exists() function will not work on files themselves. In that case, there is an analogous function called file.exists().

Try using the file.exists() function to see if the file gene_results_GSE44971.tsv exists in the current directory. Use the code chunk we set up for you below. Note that in our notebooks (and sometimes elsewhere), wherever you see a <FILL_IN_THE_BLANK> like in the chunk below, that is meant for you to replace (including the angle brackets) with the correct phrase before you run the chunk (otherwise you will get an error).

# Replace the <PUT_FILE_NAME_HERE> with the name of the file you are looking for
# Remember to use quotes to make it a character string
file.exists(<PUT_FILE_NAME_HERE>)

It doesn’t seem that file exists in our current directory, but that doesn’t mean it doesn’t exist it all. In fact, this file is inside the relative path data/, so let’s check again if the whole relative path to that file exists.

# This time, use file.path() to form your argument to file.exists()
file.exists(<PUT_PATH_TO_FILE_HERE>)

With the right relative path, we can confirm this file exists.

Read a TSV file

Declare the name of the directory where we will read in the data.

data_dir <- "data"

Although base R has functions to read in data files, the functions in the readr package (part of the tidyverse) are faster and more straightforward to use so we are going to use those here. Because the file we are reading in is a TSV (tab separated values) file we will be using the read_tsv function. There are analogous functions for CSV (comma separated values) files (read_csv()) and other files types.

Read in the differential expression analysis results file

stats_df <- readr::read_tsv(
  file.path(data_dir,
            "gene_results_GSE44971.tsv")
  )

Rows: 6804 Columns: 8
── Column specification ────────────────────────────────────────────────────────
Delimiter: "\t"
chr (3): ensembl_id, gene_symbol, contrast
dbl (5): log_fold_change, avg_expression, t_statistic, p_value, adj_p_value

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Following the template of the previous chunk, use this chunk to read in the file GSE44971.tsv that is in the data folder and save it in the variable gene_df.

# Use this chunk to read in data from the file `GSE44971.tsv`
gene_df <- readr::read_tsv(
  file.path(data_dir,
            "GSE44971.tsv")
  )

Rows: 20056 Columns: 59
── Column specification ────────────────────────────────────────────────────────
Delimiter: "\t"
chr  (1): Gene
dbl (58): GSM1094814, GSM1094815, GSM1094816, GSM1094817, GSM1094818, GSM109...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Use this chunk to explore what gene_df looks like.

# Explore `gene_df`

What information is contained in gene_df?

R pipes

One nifty feature that was added to R in version 4.1 is the pipe: |>. Pipes are very handy things that allow you to funnel the result of one expression to the next, making your code more streamlined and fluently expressing the flow of data through a series of operations.

Note: If you are using a version of R prior to 4.1 (or looking at older code), pipe functionality was available through the magrittr package , which used a pipe that looked like this: %>%. That pipe was the inspiration for the native R pipe we are using here. While there are some minor differences, you can mostly treat them interchangeably as long as you load the magrittr package or dplyr, which also loads that version of the pipe.

For example, the output from this:

filter(stats_df, contrast == "male_female")

…is the same as the output from this:

stats_df |> filter(contrast == "male_female")

This can make your code cleaner and easier to follow a series of related commands. Let’s look at an example with our stats of of how the same functions look with or without pipes:

Example 1: without pipes:

stats_arranged <- arrange(stats_df, t_statistic)
stats_filtered <- filter(stats_arranged, avg_expression > 50)
stats_nopipe <- select(stats_filtered, contrast, log_fold_change, p_value)

UGH, we have to keep track of all of those different intermediate data frames and type their names so many times here! We could maybe streamline things by using the same variable name at each stage, but even then there is a lot of extra typing, and it is easy to get confused about what has been done where. It’s annoying and makes it harder for people to read.

Example 2: Same result as 1 but with pipes!

# Example of the same modifications as above but with pipes!
stats_pipe  <- stats_df |>
               arrange(t_statistic) |>
               filter(avg_expression > 50) |>
               select(contrast, log_fold_change, p_value)

What the |> (pipe) is doing here is feeding the result of the expression on its left into the first argument of the next function (to its right, or on the next line here). We can then skip that first argument (the data in these cases), and move right on to the part we care about at that step: what we are arranging, filtering, or selecting in this case. The key insight that makes the pipe work here is to recognize that each of these functions (arrange, filter, and select) are fundamental dplyr (a tidyverse package) functions which work as “data in, data out.” In other words, these functions operate on data frames, and return data frames; you give them a data frame, and they give you back a data frame. Because these functions all follow a “data in, data out” framework, we can chain them together with pipe and send data all the way through the…pipeline!

Let’s double check that these versions with and without pipe yield the same solution by using the base R function all.equal().

all.equal(stats_nopipe, stats_pipe)

[1] TRUE

all.equal() is letting us know that these two objects are the same.

Now that hopefully you are convinced that the tidyverse can help you make your code neater and easier to use and read, let’s go through some of the popular tidyverse functions and so we can create pipelines like this.

Common tidyverse functions

Let’s say we wanted to filter this gene expression dataset to particular sample groups. In order to do this, we would use the function filter() as well as a logic statement (usually one that refers to a column or columns in the data frame).

# Here let's filter stats_df to only keep the gene_symbol "SNCA"
stats_df |>
  filter(gene_symbol == "SNCA")

We can use filter() similarly for numeric statements.

# Here let's filter the data to rows with average expression values above 50
stats_df |>
  filter(avg_expression > 50)

We can apply multiple filters at once, which will require all of them to be satisfied for every row in the results:

# filter to highly expressed genes with contrast "male_female"
stats_df |>
  filter(contrast == "male_female",
         avg_expression > 50)

When we are filtering, the %in% operator can come in handy if we have multiple items we would like to match. Let’s take a look at what using %in% does.

genes_of_interest <- c("SNCA", "CDKN1A")
# Are these genes present in the `gene_symbol` column in stats_df?
stats_df$gene_symbol %in% genes_of_interest

%in% returns a logical vector that now we can use in dplyr::filter.

# filter to keep only genes of interest
stats_df |>
  filter(gene_symbol %in% c("SNCA", "CDKN1A"))

Let’s return to our first filter() and build on to it. This time, let’s keep only some of the columns from the data frame using the select() function. Let’s also save this as a new data frame called stats_filtered_df.

# filter to highly expressed "male_female"
# and select gene_symbol, log_fold_change and t_statistic
stats_filtered_df <- stats_df |>
  filter(contrast == "male_female",
         avg_expression > 50) |>
  select(log_fold_change, t_statistic)

Let’s say we wanted to arrange this dataset so that the genes are arranged by the smallest p values to the largest. In order to do this, we would use the function arrange() as well as the column we would like to sort by (in this case p_value).

stats_df |>
  arrange(p_value)

What if we want to sort from largest to smallest? Like if we want to see the genes with the highest average expression? We can use the same function, but instead use the desc() function and now we are using avg_expression column.

# arrange descending by avg_expression
stats_df |>
  arrange(desc(avg_expression))

What if we would like to create a new column of values? For that we use mutate() function.

stats_df |>
  mutate(log10_p_value = -log10(p_value))

What if we want to obtain summary statistics for a column or columns? The summarize function allows us to calculate summary statistics for a column. Here we will use summarize to calculate two summary statistics of log-fold change across all genes: mean (function mean()) and standard deviation (function sd()).

stats_df |>
  summarize(mean(log_fold_change),
            sd(log_fold_change))

What if we’d like to obtain a summary statistics but have them for various groups? Conveniently named, there’s a function called group_by() that seamlessly allows us to do this. Also note that group_by() allows us to group by multiple variables at a time if you want to.

stats_summary_df <- stats_df |>
      group_by(contrast) |>
      summarize(mean(log_fold_change),
                sd(log_fold_change))

Let’s look at a preview of what we made:

stats_summary_df

Here we have the mean log fold change expression per each contrast we made.

A brief intro to the apply family of functions

In base R, the apply family of functions can be an alternative methods for performing transformations across a data frame, matrix or other object structures.

One of this family is (shockingly) the function apply(), which operates on matrices.

A matrix is similar to a data frame in that it is a rectangular table of data, but it has an additional constraint: rather than each column having a type, ALL data in a matrix has the same type.

The first argument to apply() is the data object we want to work on. The third argument is the function we will apply to each row or column of the data object. The second argument in specifies whether we are applying the function across rows or across columns (1 for rows, 2 for columns).

Remember that gene_df is a gene x sample gene expression data frame that has columns of two different types, character and numeric. Converting it to a matrix will require us to make them all the same type. We can coerce it into a matrix using as.matrix(), in which case R will pick a type that it can convert everything to. What does it choose?

# Coerce `gene_df` into a matrix
gene_matrix <- as.matrix(gene_df)

# Explore the structure of the `gene_matrix` object
str(gene_matrix)

 chr [1:20056, 1:59] "ENSG00000000003" "ENSG00000000005" "ENSG00000000419" ...
 - attr(*, "dimnames")=List of 2
  ..$ : NULL
  ..$ : chr [1:59] "Gene" "GSM1094814" "GSM1094815" "GSM1094816" ...

While that worked, it is rare that we want numbers converted to text, so we are going to select only the columns with numeric values before converting it to a matrix. We can do this most easily by removing the first column, which contains the gene names stored as character values.

# Let's save a new matrix object names `gene_num_matrix` containing only
# the numeric values
gene_num_matrix <- as.matrix(gene_df[, -1])

# Explore the structure of the `gene_num_matrix` object
str(gene_num_matrix)

 num [1:20056, 1:58] 9.5951 -0.0436 8.5246 1.6013 0.6189 ...
 - attr(*, "dimnames")=List of 2
  ..$ : NULL
  ..$ : chr [1:58] "GSM1094814" "GSM1094815" "GSM1094816" "GSM1094817" ...

Why do we have a [, -1] after gene_df in the above chunk?

Now that the matrix is all numbers, we can do things like calculate the column or row statistics using apply().

# Calculate row means
gene_means <- apply(gene_num_matrix, 1, mean) # Notice we are using 1 here

# How long will `gene_means` be?
length(gene_means)

[1] 20056

Note that we can obtain the same results if we select just the columns with numeric values from the gene_df data frame. This allows R to do the as.matrix() coercion automatically, and can be a handy shortcut if you have a mostly numeric data frame.

# Calculate row means using the `gene_df` object after removing the character column
# apply() converts this to a matrix internally
gene_means_from_df <- apply(gene_df[, -1], 1, mean)

# Let's check that the two gene means objects are equal
all.equal(gene_means, gene_means_from_df)

[1] TRUE

Now let’s investigate the same set up, but use 2 to apply over the columns of our matrix.

# Calculate sample means
sample_means <- apply(gene_num_matrix, 2, mean) # Notice we use 2 here

# How long will `sample_means` be?
length(sample_means)

[1] 58

We can put the gene names back into the numeric matrix object by assigning them as rownames.

# Assign the gene names from gene_df$Gene to the `gene_num_matrix` object using
# the `rownames()` function
rownames(gene_num_matrix) <- gene_df$Gene

# Explore the `gene_num_matrix` object
head(gene_num_matrix)

                 GSM1094814 GSM1094815 GSM1094816   GSM1094817  GSM1094818
ENSG00000000003  9.59510150  8.4785070 12.6802129  8.677614838 10.75552946
                 GSM1094819  GSM1094820 GSM1094821  GSM1094822 GSM1094823
ENSG00000000003  6.37470691  9.10028584  7.3546860  8.51847190  9.4216113
                GSM1094824  GSM1094825 GSM1094826  GSM1094827 GSM1094828
ENSG00000000003  5.0239629  7.89737460  8.1126876  7.03444640  9.6984918
                 GSM1094829 GSM1094830 GSM1094831 GSM1094832  GSM1094833
ENSG00000000003 13.98689230 10.5868331  7.6836223  8.3862587 11.18932763
                GSM1094834 GSM1094835  GSM1094836 GSM1094837 GSM1094838
ENSG00000000003  9.7562003  9.6984918 10.56891510  9.9391025  7.8738131
                GSM1094839  GSM1094840 GSM1094841 GSM1094842 GSM1094843
ENSG00000000003  8.6311353  8.58077557  9.1579585  6.3317019 10.1939387
                 GSM1094844  GSM1094845  GSM1094846 GSM1094847  GSM1094848
ENSG00000000003 10.44364159  9.62435722 16.05075944  6.9334508  8.55180910
                 GSM1094849 GSM1094850 GSM1094851  GSM1094852  GSM1094853
ENSG00000000003  9.29497760  7.5027098  6.9593119  8.33588532  8.16826110
                GSM1094854 GSM1094855 GSM1094856 GSM1094857  GSM1094858
ENSG00000000003  9.8020077 7.92580451  8.5122426  8.5300217  6.45774124
                 GSM1094859  GSM1094860 GSM1094861 GSM1094862 GSM1094863
ENSG00000000003  8.06834906  6.29704946 9.59510150  8.2198571  6.0207988
                 GSM1094864  GSM1094865  GSM1094866  GSM1094867  GSM1094868
ENSG00000000003 10.60783176 10.23536609 9.031964212  7.66629540  1.06494502
                GSM1094869 GSM1094870 GSM1094871
ENSG00000000003  1.0408332  1.7262079  1.0292255
 [ reached getOption("max.print") -- omitted 5 rows ]

Row names like this can be very convenient for keeping matrices organized, but row names (and column names) can be lost or misordered if you are not careful, especially during input and output, so treat them with care.

Although the apply functions may not be as easy to use as the tidyverse functions, for some applications, apply methods can be better suited. In this workshop, we will not delve too deeply into the various other apply functions (tapply(), lapply(), etc.) but you can read more information about them here.

The dplyr::join functions

Let’s say we have a scenario where we have two data frames that we would like to combine. Recall that stats_df and gene_df are data frames that contain information about some of the same genes. The dplyr::join family of functions are useful for various scenarios of combining data frames. For a visual explanation, the tidyexplain project has some helpful animations of joins.

For now, we will focus on inner_join(), which will combine data frames by only keeping information about matching rows that are in both data frames. We need to use the by argument to designate what column(s) should be used as a key to match the data frames. In this case we want to match the gene information between the two, so we will specify that we want to compare values in the ensembl_id column from stats_df to the Gene column from gene_df.

stats_df |>
  # Join based on their shared column
  # Called ensembl_id in stats_df and called Gene in gene_df
  inner_join(gene_df, by = c('ensembl_id' = 'Gene'))

Save data to files

Save to TSV files

Let’s write some of the data frames we created to a file. To do this, we can use the readr library of _write() functions. The first argument of write_tsv() is the data we want to write, and the second argument is a character string that describes the path to the new file we would like to create. Remember that we created a results directory to put our output in, but if we want to save our data to a directory other than our working directory, we need to specify this. This is what we will use the file.path() function for. Let’s look in a bit more detail what file.path() does, by examining the results of the function in the examples below.

# Which of these file paths is what we want to use to save our data to the
# results directory we created at the beginning of this notebook?
file.path("docker-install", "stats_summary.tsv")

[1] "docker-install/stats_summary.tsv"

docker-install/stats_summary.tsv

file.path("results", "stats_summary.tsv")

[1] "results/stats_summary.tsv"

results/stats_summary.tsv

file.path("stats_summary.tsv", "results")

[1] "stats_summary.tsv/results"

stats_summary.tsv/results

Replace <NEW_FILE_PATH> below with the file.path() statement from above that will successfully save our file to the results folder.

# Write our data frame to a TSV file
readr::write_tsv(stats_summary_df, <NEW_FILE_PATH>)

Check in your results directory to see if your new file has successfully saved.

Save to RDS files

For this example we have been working with data frames, which are conveniently represented as TSV or CSV tables. However, in other situations we may want to save more complicated or very large data structures, RDS (R Data Serialized/Single) files may be a better option for saving our data. RDS is R’s special file format for holding data exactly as you have it in your R environment. RDS files can also be compressed, meaning they will take up less space on your computer. Let’s save our data to an RDS file in our results folder. You will need to replace the .tsv with .RDS, but you can use what we determined as our file path for the last chunk as your template.

# Write your object to an RDS file
readr::write_rds(stats_summary_df, <PUT_CORRECT_FILE_PATH_HERE>)

Read an RDS file

Since now you have learned the readr functions: read_tsv(), write_tsv(), and now, write_rds(), what do you suppose the function you will need to read your RDS file is called? Use that function here to re-import your data in the chunk we set up for you below.

# Read in your RDS file
reimport_df <- <PUT_FUNCTION_NAME>(file.path("results", "stats_summary.RDS"))

As is good practice, we will end this session by printing out our session info.

Session Info

# Print out the versions and packages we are using in this session
sessionInfo()

R version 4.2.3 (2023-03-15)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 22.04.2 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.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] lubridate_1.9.2 forcats_1.0.0   stringr_1.5.0   dplyr_1.1.2    
 [5] purrr_1.0.1     readr_2.1.4     tidyr_1.3.0     tibble_3.2.1   
 [9] ggplot2_3.4.2   tidyverse_2.0.0 optparse_1.7.3 

loaded via a namespace (and not attached):
 [1] bslib_0.4.2      compiler_4.2.3   pillar_1.9.0     jquerylib_0.1.4 
 [5] tools_4.2.3      bit_4.0.5        digest_0.6.31    timechange_0.2.0
 [9] jsonlite_1.8.4   evaluate_0.20    lifecycle_1.0.3  gtable_0.3.3    
[13] pkgconfig_2.0.3  rlang_1.1.0      cli_3.6.1        parallel_4.2.3  
[17] yaml_2.3.7       xfun_0.39        fastmap_1.1.1    withr_2.5.0     
[21] knitr_1.42       fs_1.6.1         hms_1.1.3        generics_0.1.3  
[25] vctrs_0.6.2      sass_0.4.5       bit64_4.0.5      grid_4.2.3      
[29] getopt_1.20.3    tidyselect_1.2.0 glue_1.6.2       R6_2.5.1        
[33] fansi_1.0.4      vroom_1.6.1      rmarkdown_2.21   tzdb_0.3.0      
[37] magrittr_2.0.3   scales_1.2.1     htmltools_0.5.5  colorspace_2.1-0
[41] utf8_1.2.3       stringi_1.7.12   munsell_0.5.0    cachem_1.0.7    
[45] crayon_1.5.2