Collapsing Data

PRELIMINARY SITE DRAFT. MUCH WORK TO BE DONE!

This tutorial explains how to collapse data in R. Collapsing means using one or several grouping variables to find summary statistics — mean, median, etc. — for different categories in your data. For example, if you have yearly income data for the 50 U.S. states over a 10-year period (i.e., you have 500 data points), you may want to know what the mean income was in each state (collapsing the data to 50 data points) or in each year (10 data points). Or you may want to collapse the data by year and U.S. region, say, South v. non-South (20 data points). Like the tutorial on modifying data this tutorial draws on a set of intuitive and elegant functions from the dplyr package.

Before we begin, let’s load the dplyr package. We’ll make particular use of two functions from this package: group_by and summarize. We’ll also make use of chaining, which you can read more about in the tutorial on modifying data.

require(dplyr)

One grouping variable

To illustrate how collapsing works, let’s create a data frame with three variables: student (an id variable that uniquely identifies each row); school (a grouping variable indicating the student’s school); and sat_score (the student’s SAT score).

grades <- data.frame(
    student = c("al", "bo", "cindy", "dan", "ella", "frank", "gina", "henry"),
    school = c(rep("stanford", 4), rep("berkley", 4)),
    sat_score = c(750, 730, 690, 800, 780, 720, 730, 700)
    )

Which school — Stanford or Berkley — attracts students with a higher SAT score? Based on my (in reality-not-so-random) random assignment of scores, it appears to be Stanford:

grades %>%
    group_by(school) %>%
    summarize(mean(sat_score))

A tibble: 2 × 2

school	mean(sat_score)
<chr>	<dbl>
berkley	732.5
stanford	742.5

In words, the mean SAT score for Berkley students is 732.5, and the mean for Stanford students is 742.5. (dplyr also outputs some information about the new data frame for us, such as its dimensions and the class of each of its variables.)

To be clear, here’s how group_by() and summarize() work. First, group_by() specifies the grouping variable, i.e., the variable that classifies observations into different clusters. In this case, we’re classifying students by the school they attend. Second, summarize() specifies what to do with the data points within each cluster. In this case, we’re finding the mean SAT score in each cluster.

It’s often useful to assign a name to the collapsed variable:

grades %>%
    group_by(school) %>%
    summarize(mean_sat = mean(sat_score))

A tibble: 2 × 2

school	mean_sat
<chr>	<dbl>
berkley	732.5
stanford	742.5

Also note that you’d often want to save the resulting collapsed data frame to R’s memory. Here’s how to do this, creating a new object called grades_clps with the collapsed data:

grades_clps <- grades %>%
    group_by(school) %>%
    summarize(mean_sat = mean(sat_score))
grades_clps

A tibble: 2 × 2

school	mean_sat
<chr>	<dbl>
berkley	732.5
stanford	742.5

Several grouping variables

In the previous example we collapsed the data using only one grouping variable. Collapsing can also be done using several grouping variables. Let’s modify the grades data frame to illustrate:

grades <- data.frame(
    student = c("al", "bo", "cindy", "dan", "ella", "frank", "gina", "henry"),
    school = c(rep("stanford", 4), rep("berkley", 4)),
    classof = rep(c(2017, 2017, 2018, 2018), 2),
    sat_score = c(750, 730, 690, 800, 780, 720, 730, 700)
    )
grades

A data.frame: 8 × 4

student	school	classof	sat_score
<chr>	<chr>	<dbl>	<dbl>
al	stanford	2017	750
bo	stanford	2017	730
cindy	stanford	2018	690
dan	stanford	2018	800
ella	berkley	2017	780
frank	berkley	2017	720
gina	berkley	2018	730
henry	berkley	2018	700

We now have two grouping variables: school and classof. The latter specifies the expected graduation year for each student.

Collapsing by these two grouping variables follows the same logic as above. Just specify the variables to collapse by inside group_by().

grades %>%
    group_by(school, classof) %>%
    summarize(mean_sat = mean(sat_score))

`summarise()` has grouped output by 'school'. You can override using the `.groups` argument.

A grouped_df: 4 × 3

school	classof	mean_sat
<chr>	<dbl>	<dbl>
berkley	2017	750
berkley	2018	715
stanford	2017	740
stanford	2018	745

Additional manipulation

One nice thing about using dplyr functions for collapsing data is that you can combine them with other data manipulation functions, many of which are covered in a separate tutorial on modifying data. The result is elegant code that is easy to debug and relatively quick to execute. Here’s an example in which I’m filtering the grades data frame to class of 2017 and then collapsing:

grades %>%
    filter(classof == 2017) %>%
    group_by(school) %>%
    summarize(mean_sat = mean(sat_score))

A tibble: 2 × 2

school	mean_sat
<chr>	<dbl>
berkley	750
stanford	740

Here’s an example that adds a variable after the collapse (rescaling the mean SAT scores to be between 0 and 100, assuming 800 is the maximum possible score):

grades %>%
    group_by(school) %>%
    summarize(mean_sat = mean(sat_score)) %>%
    mutate(mean_sat_strd = (mean_sat / 800) * 100)

A tibble: 2 × 3

school	mean_sat	mean_sat_strd
<chr>	<dbl>	<dbl>
berkley	732.5	91.5625
stanford	742.5	92.8125

Different functions

In all the examples above I’ve used mean() inside summarize(). Of course you’re by no means limited to finding the mean. You can use all of R’s built-in functions or write your own function. Here are examples that make use of other common functions:

grades %>%
    group_by(school) %>%
    summarize(median_sat = median(sat_score),
              sd_sat = sd(sat_score),
              min_sat = min(sat_score),
              max_sat = max(sat_score),
              dif_maxmin = max_sat - min_sat)

A tibble: 2 × 6

school	median_sat	sd_sat	min_sat	max_sat	dif_maxmin
<chr>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>
berkley	725	34.03430	700	780	80
stanford	740	45.73474	690	800	110

Here’s an example of using your own function:

maxmindif <- function(x) max(x) - min(x)

grades %>%
    group_by(school) %>%
    summarize(dif_maxmin = maxmindif(sat_score))

A tibble: 2 × 2

school	dif_maxmin
<chr>	<dbl>
berkley	80
stanford	110

Lastly, dplyr provides a few special functions that can be used within summarize(). One very useful special function is n(), which provides the number of observations in each cluster:

grades %>%
    group_by(school) %>%
    summarize(no_obs = n())

A tibble: 2 × 2

school	no_obs
<chr>	<int>
berkley	4
stanford	4

Exercises

1. Read the world-small.csv dataset (available here) into R. Get to know the structure of this dataset using functions like dim(), head(), and summary().

2. Find the mean and median GDP per capita and Polity IV score, by region (that is, for each region in the dataset). Also find the number of countries by region.

3. Find the mean and median GDP per capita, by region and whether a country is a “democracy” or not. For the purpose of this exercise, a country is a “democracy” if it has a Polity IV score of 15 or higher.