# Collapsing Data¶

summary: 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)

Loading required package: dplyr

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

filter, lag

The following objects are masked from ‘package:base’:

intersect, setdiff, setequal, union



## 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))

schoolmean(sat_score)
berkley 732.5
stanford742.5

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))

schoolmean_sat
berkley 732.5
stanford742.5

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))

schoolmean_sat
berkley 732.5
stanford742.5

## 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)
)

studentschoolclassofsat_score
al stanford2017 750
bo stanford2017 730
cindy stanford2018 690
dan stanford2018 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))

schoolclassofmean_sat
berkley 2017 750
berkley 2018 715
stanford2017 740
stanford2018 745

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))

schoolmean_sat
berkley 750
stanford740

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)

schoolmean_satmean_sat_strd
berkley 732.5 91.5625
stanford742.5 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)

schoolmedian_satsd_satmin_satmax_satdif_maxmin
berkley 725 34.03430700 780 80
stanford740 45.73474690 800 110

Here’s an example of using your own function:

:

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

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

schooldif_maxmin
berkley 80
stanford110

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())

schoolno_obs
berkley 4
stanford4

## 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.
: