# 19  Joins

You are reading the work-in-progress second edition of R for Data Science. This chapter should be readable but is currently undergoing final polishing. You can find the complete first edition at https://r4ds.had.co.nz.

## 19.1 Introduction

It’s rare that a data analysis involves only a single data frame. Typically you have many data frames, and you must join them together to answer the questions that you’re interested in. This chapter will introduce you to two important types of joins:

• Mutating joins, which add new variables to one data frame from matching observations in another.
• Filtering joins, which filter observations from one data frame based on whether or not they match an observation in another.

We’ll begin by discussing keys, the variables used to connect a pair of data frames in a join. We cement the theory with an examination of the keys in the nycflights13 datasets, then use that knowledge to start joining data frames together. Next we’ll discuss how joins work, focusing on their action on the rows. We’ll finish up with a discussion of non-equi-joins, a family of joins that provide a more flexible way of matching keys than the default equality relationship.

### 19.1.1 Prerequisites

In this chapter, we’ll explore the five related datasets from nycflights13 using the join functions from dplyr.

``````library(tidyverse)
library(nycflights13)``````

## 19.2 Keys

To understand joins, you need to first understand how two tables can be connected through a pair of keys, with on each table. In this section, you’ll learn about the two types of key and see examples of both in the datasets of the nycflights13 package. You’ll also learn how to check that your keys are valid, and what to do if your table lacks a key.

### 19.2.1 Primary and foreign keys

Every join involves a pair of keys: a primary key and a foreign key. A primary key is a variable or set of variables that uniquely identifies each observation. When more than one variable is needed, the key is called a compound key. For example, in nycfights13:

• `airlines` records two pieces of data about each airline: its carrier code and its full name. You can identify an airline with its two letter carrier code, making `carrier` the primary key.

``````airlines
#> # A tibble: 16 × 2
#>   carrier name
#>   <chr>   <chr>
#> 1 9E      Endeavor Air Inc.
#> 2 AA      American Airlines Inc.
#> 3 AS      Alaska Airlines Inc.
#> 4 B6      JetBlue Airways
#> 5 DL      Delta Air Lines Inc.
#> 6 EV      ExpressJet Airlines Inc.
#> # … with 10 more rows``````
• `airports` records data about each airport. You can identify each airport by its three letter airport code, making `faa` the primary key.

``````airports
#> # A tibble: 1,458 × 8
#>   faa   name                             lat   lon   alt    tz dst   tzone
#>   <chr> <chr>                          <dbl> <dbl> <dbl> <dbl> <chr> <chr>
#> 1 04G   Lansdowne Airport               41.1 -80.6  1044    -5 A     America…
#> 2 06A   Moton Field Municipal Airport   32.5 -85.7   264    -6 A     America…
#> 3 06C   Schaumburg Regional             42.0 -88.1   801    -6 A     America…
#> 4 06N   Randall Airport                 41.4 -74.4   523    -5 A     America…
#> 5 09J   Jekyll Island Airport           31.1 -81.4    11    -5 A     America…
#> 6 0A9   Elizabethton Municipal Airport  36.4 -82.2  1593    -5 A     America…
#> # … with 1,452 more rows``````
• `planes` records data about each plane. You can identify a plane by its tail number, making `tailnum` the primary key.

``````planes
#> # A tibble: 3,322 × 9
#>   tailnum  year type                 manuf…¹ model engines seats speed engine
#>   <chr>   <int> <chr>                <chr>   <chr>   <int> <int> <int> <chr>
#> 1 N10156   2004 Fixed wing multi en… EMBRAER EMB-…       2    55    NA Turbo…
#> 2 N102UW   1998 Fixed wing multi en… AIRBUS… A320…       2   182    NA Turbo…
#> 3 N103US   1999 Fixed wing multi en… AIRBUS… A320…       2   182    NA Turbo…
#> 4 N104UW   1999 Fixed wing multi en… AIRBUS… A320…       2   182    NA Turbo…
#> 5 N10575   2002 Fixed wing multi en… EMBRAER EMB-…       2    55    NA Turbo…
#> 6 N105UW   1999 Fixed wing multi en… AIRBUS… A320…       2   182    NA Turbo…
#> # … with 3,316 more rows, and abbreviated variable name ¹​manufacturer``````
• `weather` records data about the weather at the origin airports. You can identify each observation by the combination of location and time, making `origin` and `time_hour` the compound primary key.

``````weather
#> # A tibble: 26,115 × 15
#>   origin  year month   day  hour  temp  dewp humid wind_dir wind_sp…¹ wind_…²
#>   <chr>  <int> <int> <int> <int> <dbl> <dbl> <dbl>    <dbl>     <dbl>   <dbl>
#> 1 EWR     2013     1     1     1  39.0  26.1  59.4      270     10.4       NA
#> 2 EWR     2013     1     1     2  39.0  27.0  61.6      250      8.06      NA
#> 3 EWR     2013     1     1     3  39.0  28.0  64.4      240     11.5       NA
#> 4 EWR     2013     1     1     4  39.9  28.0  62.2      250     12.7       NA
#> 5 EWR     2013     1     1     5  39.0  28.0  64.4      260     12.7       NA
#> 6 EWR     2013     1     1     6  37.9  28.0  67.2      240     11.5       NA
#> # … with 26,109 more rows, 4 more variables: precip <dbl>, pressure <dbl>,
#> #   visib <dbl>, time_hour <dttm>, and abbreviated variable names
#> #   ¹​wind_speed, ²​wind_gust``````

A foreign key is a variable (or set of variables) that corresponds to a primary key in another table. For example:

• `flights\$tailnum` is a foreign key that corresponds to the primary key `planes\$tailnum`.
• `flights\$carrier` is a foreign key that corresponds to the primary key `airlines\$carrier`.
• `flights\$origin` is a foreign key that corresponds to the primary key `airports\$faa`.
• `flights\$dest` is a foreign key that corresponds to the primary key `airports\$faa` .
• `flights\$origin`-`flights\$time_hour` is a compound foreign key that corresponds to the compound primary key `weather\$origin`-`weather\$time_hour`.

These relationships are summarized visually in Figure 19.1.

You’ll notice a nice feature in the design of these keys: the primary and foreign keys almost always have the same names, which, as you’ll see shortly, will make your joining life much easier. It’s also worth noting the opposite relationship: almost every variable name used in multiple tables has the same meaning in each place. There’s only one exception: `year` means year of departure in `flights` and year of manufacturer in `planes`. This will become important when we start actually joining tables together.

### 19.2.2 Checking primary keys

Now that that we’ve identified the primary keys in each table, it’s good practice to verify that they do indeed uniquely identify each observation. One way to do that is to `count()` the primary keys and look for entries where `n` is greater than one. This reveals that `planes` and `weather` both look good:

``````planes |>
count(tailnum) |>
filter(n > 1)
#> # A tibble: 0 × 2
#> # … with 2 variables: tailnum <chr>, n <int>

weather |>
count(time_hour, origin) |>
filter(n > 1)
#> # A tibble: 0 × 3
#> # … with 3 variables: time_hour <dttm>, origin <chr>, n <int>``````

You should also check for missing values in your primary keys — if a value is missing then it can’t identify an observation!

``````planes |>
filter(is.na(tailnum))
#> # A tibble: 0 × 9
#> # … with 9 variables: tailnum <chr>, year <int>, type <chr>,
#> #   manufacturer <chr>, model <chr>, engines <int>, seats <int>,
#> #   speed <int>, engine <chr>

weather |>
filter(is.na(time_hour) | is.na(origin))
#> # A tibble: 0 × 15
#> # … with 15 variables: origin <chr>, year <int>, month <int>, day <int>,
#> #   hour <int>, temp <dbl>, dewp <dbl>, humid <dbl>, wind_dir <dbl>,
#> #   wind_speed <dbl>, wind_gust <dbl>, precip <dbl>, pressure <dbl>,
#> #   visib <dbl>, time_hour <dttm>``````

### 19.2.3 Surrogate keys

So far we haven’t talked about the primary key for `flights`. It’s not super important here, because there are no data frames that use it as a foreign key, but it’s still useful to consider because it’s easier to work with observations if have some way to describe them to others.

After a little thinking and experimentation, we determined that there are three variables that together uniquely identify each flight:

``````flights |>
count(time_hour, carrier, flight) |>
filter(n > 1)
#> # A tibble: 0 × 4
#> # … with 4 variables: time_hour <dttm>, carrier <chr>, flight <int>, n <int>``````

Does the absence of duplicates automatically make `time_hour`-`carrier`-`flight` a primary key? It’s certainly a good start, but it doesn’t guarantee it. For example, are altitude and latitude a good primary key for `airports`?

``````airports |>
count(alt, lat) |>
filter(n > 1)
#> # A tibble: 1 × 3
#>     alt   lat     n
#>   <dbl> <dbl> <int>
#> 1    13  40.6     2``````

Identifying an airport by it’s altitude and latitude is clearly a bad idea, and in general it’s not possible to know from the data alone whether or not a combination of variables makes a good a primary key. But for flights, the combination of `time_hour`, `carrier`, and `flight` seems reasonable because it would be really confusing for an airline and its customers if there were multiple flights with the same flight number in the air at the same time.

That said, we might be better off introducing a simple numeric surrogate key using the row number:

``````flights2 <- flights |>
mutate(id = row_number(), .before = 1)
flights2
#> # A tibble: 336,776 × 20
#>      id  year month   day dep_time sched_de…¹ dep_d…² arr_t…³ sched…⁴ arr_d…⁵
#>   <int> <int> <int> <int>    <int>      <int>   <dbl>   <int>   <int>   <dbl>
#> 1     1  2013     1     1      517        515       2     830     819      11
#> 2     2  2013     1     1      533        529       4     850     830      20
#> 3     3  2013     1     1      542        540       2     923     850      33
#> 4     4  2013     1     1      544        545      -1    1004    1022     -18
#> 5     5  2013     1     1      554        600      -6     812     837     -25
#> 6     6  2013     1     1      554        558      -4     740     728      12
#> # … with 336,770 more rows, 10 more variables: carrier <chr>, flight <int>,
#> #   tailnum <chr>, origin <chr>, dest <chr>, air_time <dbl>, distance <dbl>,
#> #   hour <dbl>, minute <dbl>, time_hour <dttm>, and abbreviated variable
#> #   names ¹​sched_dep_time, ²​dep_delay, ³​arr_time, ⁴​sched_arr_time,
#> #   ⁵​arr_delay``````

Surrogate keys can be particular useful when communicating to other humans: it’s much easier to tell someone to take a look at flight 2001 than to say look at UA430 which departed 9am 2013-01-03.

### 19.2.4 Exercises

1. We forgot to draw the relationship between `weather` and `airports` in Figure 19.1. What is the relationship and how should it appear in the diagram?

2. `weather` only contains information for the three origin airports in NYC. If it contained weather records for all airports in the USA, what additional connection would it make to `flights`?

3. The `year`, `month`, `day`, `hour`, and `origin` variables almost form a compound key for `weather`, but there’s one hour that has duplicate observations. Can you figure out what’s special about that hour?

4. We know that some days of the year are special and fewer people than usual fly on them (e.g. Christmas eve and Christmas day). How might you represent that data as a data frame? What would be the primary key? How would it connect to the existing data frames?

5. Draw a diagram illustrating the connections between the `Batting`, `People`, and `Salaries` data frames in the Lahman package. Draw another diagram that shows the relationship between `People`, `Managers`, `AwardsManagers`. How would you characterise the relationship between the `Batting`, `Pitching`, and `Fielding` data frames?

## 19.3 Basic joins

Now that you understand how data frames are connected via keys, we can start using joins to better understand the `flights` dataset. dplyr provides six join functions: `left_join()`, `inner_join()`, `right_join()`, `semi_join()`, and `anti_join()`. They all have the same interface: they take a pair of data frames (`x` and `y`) and return a data frame. The order of the rows and columns in the output is primarily determined by `x`.

In this section, you’ll learn how to use one mutating join, `left_join()`, and two filtering joins, `semi_join()` and `anti_join()`. In the next section, you’ll learn exactly how these functions work, and about the remaining `inner_join()`, `right_join()` and `full_join()`.

### 19.3.1 Mutating joins

A mutating join allows you to combine variables from two data frames: it first matches observations by their keys, then copies across variables from one data frame to the other. Like `mutate()`, the join functions add variables to the right, so if your dataset has many variables, you won’t see the new ones. For these examples, we’ll make it easier to see what’s going on by creating a narrower dataset with just six variables1:

``````flights2 <- flights |>
select(year, time_hour, origin, dest, tailnum, carrier)
flights2
#> # A tibble: 336,776 × 6
#>    year time_hour           origin dest  tailnum carrier
#>   <int> <dttm>              <chr>  <chr> <chr>   <chr>
#> 1  2013 2013-01-01 05:00:00 EWR    IAH   N14228  UA
#> 2  2013 2013-01-01 05:00:00 LGA    IAH   N24211  UA
#> 3  2013 2013-01-01 05:00:00 JFK    MIA   N619AA  AA
#> 4  2013 2013-01-01 05:00:00 JFK    BQN   N804JB  B6
#> 5  2013 2013-01-01 06:00:00 LGA    ATL   N668DN  DL
#> 6  2013 2013-01-01 05:00:00 EWR    ORD   N39463  UA
#> # … with 336,770 more rows``````

There are four types of mutating join, but there’s one that you’ll use almost all of the time: `left_join()`. It’s special because the output will always have the same rows as `x`2. The primary use of `left_join()` is to add in additional metadata. For example, we can use `left_join()` to add the full airline name to the `flights2` data:

``````flights2 |>
left_join(airlines)
#> Joining with `by = join_by(carrier)`
#> # A tibble: 336,776 × 7
#>    year time_hour           origin dest  tailnum carrier name
#>   <int> <dttm>              <chr>  <chr> <chr>   <chr>   <chr>
#> 1  2013 2013-01-01 05:00:00 EWR    IAH   N14228  UA      United Air Lines In…
#> 2  2013 2013-01-01 05:00:00 LGA    IAH   N24211  UA      United Air Lines In…
#> 3  2013 2013-01-01 05:00:00 JFK    MIA   N619AA  AA      American Airlines I…
#> 4  2013 2013-01-01 05:00:00 JFK    BQN   N804JB  B6      JetBlue Airways
#> 5  2013 2013-01-01 06:00:00 LGA    ATL   N668DN  DL      Delta Air Lines Inc.
#> 6  2013 2013-01-01 05:00:00 EWR    ORD   N39463  UA      United Air Lines In…
#> # … with 336,770 more rows``````

Or we could find out the temperature and wind speed when each plane departed:

``````flights2 |>
left_join(weather |> select(origin, time_hour, temp, wind_speed))
#> Joining with `by = join_by(time_hour, origin)`
#> # A tibble: 336,776 × 8
#>    year time_hour           origin dest  tailnum carrier  temp wind_speed
#>   <int> <dttm>              <chr>  <chr> <chr>   <chr>   <dbl>      <dbl>
#> 1  2013 2013-01-01 05:00:00 EWR    IAH   N14228  UA       39.0       12.7
#> 2  2013 2013-01-01 05:00:00 LGA    IAH   N24211  UA       39.9       15.0
#> 3  2013 2013-01-01 05:00:00 JFK    MIA   N619AA  AA       39.0       15.0
#> 4  2013 2013-01-01 05:00:00 JFK    BQN   N804JB  B6       39.0       15.0
#> 5  2013 2013-01-01 06:00:00 LGA    ATL   N668DN  DL       39.9       16.1
#> 6  2013 2013-01-01 05:00:00 EWR    ORD   N39463  UA       39.0       12.7
#> # … with 336,770 more rows``````

Or what size of plane was flying:

``````flights2 |>
left_join(planes |> select(tailnum, type, engines, seats))
#> Joining with `by = join_by(tailnum)`
#> # A tibble: 336,776 × 9
#>    year time_hour           origin dest  tailnum carrier type   engines seats
#>   <int> <dttm>              <chr>  <chr> <chr>   <chr>   <chr>    <int> <int>
#> 1  2013 2013-01-01 05:00:00 EWR    IAH   N14228  UA      Fixed…       2   149
#> 2  2013 2013-01-01 05:00:00 LGA    IAH   N24211  UA      Fixed…       2   149
#> 3  2013 2013-01-01 05:00:00 JFK    MIA   N619AA  AA      Fixed…       2   178
#> 4  2013 2013-01-01 05:00:00 JFK    BQN   N804JB  B6      Fixed…       2   200
#> 5  2013 2013-01-01 06:00:00 LGA    ATL   N668DN  DL      Fixed…       2   178
#> 6  2013 2013-01-01 05:00:00 EWR    ORD   N39463  UA      Fixed…       2   191
#> # … with 336,770 more rows``````

When `left_join()` fails to find a match for a row in `x`, it fills in the new variables with missing values. For example, there’s no information about the plane with tail number `N3ALAA` so the `type`, `engines`, and `seats` will be missing:

``````flights2 |>
filter(tailnum == "N3ALAA") |>
left_join(planes |> select(tailnum, type, engines, seats))
#> Joining with `by = join_by(tailnum)`
#> # A tibble: 63 × 9
#>    year time_hour           origin dest  tailnum carrier type  engines seats
#>   <int> <dttm>              <chr>  <chr> <chr>   <chr>   <chr>   <int> <int>
#> 1  2013 2013-01-01 06:00:00 LGA    ORD   N3ALAA  AA      <NA>       NA    NA
#> 2  2013 2013-01-02 18:00:00 LGA    ORD   N3ALAA  AA      <NA>       NA    NA
#> 3  2013 2013-01-03 06:00:00 LGA    ORD   N3ALAA  AA      <NA>       NA    NA
#> 4  2013 2013-01-07 19:00:00 LGA    ORD   N3ALAA  AA      <NA>       NA    NA
#> 5  2013 2013-01-08 17:00:00 JFK    ORD   N3ALAA  AA      <NA>       NA    NA
#> 6  2013 2013-01-16 06:00:00 LGA    ORD   N3ALAA  AA      <NA>       NA    NA
#> # … with 57 more rows``````

We’ll come back to this problem a few times in the rest of the chapter.

### 19.3.2 Specifying join keys

By default, `left_join()` will use all variables that appear in both data frames as the join key, the so called natural join. This is a useful heuristic, but it doesn’t always work. For example, what happens if we try to join `flights2` with the complete `planes` dataset?

``````flights2 |>
left_join(planes)
#> Joining with `by = join_by(year, tailnum)`
#> # A tibble: 336,776 × 13
#>    year time_hour           origin dest  tailnum carrier type  manufa…¹ model
#>   <int> <dttm>              <chr>  <chr> <chr>   <chr>   <chr> <chr>    <chr>
#> 1  2013 2013-01-01 05:00:00 EWR    IAH   N14228  UA      <NA>  <NA>     <NA>
#> 2  2013 2013-01-01 05:00:00 LGA    IAH   N24211  UA      <NA>  <NA>     <NA>
#> 3  2013 2013-01-01 05:00:00 JFK    MIA   N619AA  AA      <NA>  <NA>     <NA>
#> 4  2013 2013-01-01 05:00:00 JFK    BQN   N804JB  B6      <NA>  <NA>     <NA>
#> 5  2013 2013-01-01 06:00:00 LGA    ATL   N668DN  DL      <NA>  <NA>     <NA>
#> 6  2013 2013-01-01 05:00:00 EWR    ORD   N39463  UA      <NA>  <NA>     <NA>
#> # … with 336,770 more rows, 4 more variables: engines <int>, seats <int>,
#> #   speed <int>, engine <chr>, and abbreviated variable name ¹​manufacturer``````

We get a lot of missing matches because our join is trying to use `tailnum` and `year` as a compound key. Both `flights` and `planes` have a `year` column but they mean different things: `flights\$year` is year the flight occurred and `planes\$year` is the year the plane was built. We only want to join on `tailnum` so we need to provide an explicit specification with `join_by()`:

``````flights2 |>
left_join(planes, join_by(tailnum))
#> # A tibble: 336,776 × 14
#>   year.x time_hour           origin dest  tailnum carrier year.y type
#>    <int> <dttm>              <chr>  <chr> <chr>   <chr>    <int> <chr>
#> 1   2013 2013-01-01 05:00:00 EWR    IAH   N14228  UA        1999 Fixed wing …
#> 2   2013 2013-01-01 05:00:00 LGA    IAH   N24211  UA        1998 Fixed wing …
#> 3   2013 2013-01-01 05:00:00 JFK    MIA   N619AA  AA        1990 Fixed wing …
#> 4   2013 2013-01-01 05:00:00 JFK    BQN   N804JB  B6        2012 Fixed wing …
#> 5   2013 2013-01-01 06:00:00 LGA    ATL   N668DN  DL        1991 Fixed wing …
#> 6   2013 2013-01-01 05:00:00 EWR    ORD   N39463  UA        2012 Fixed wing …
#> # … with 336,770 more rows, and 6 more variables: manufacturer <chr>,
#> #   model <chr>, engines <int>, seats <int>, speed <int>, engine <chr>``````

Note that the `year` variables are disambiguated in the output with a suffix (`year.x` and `year.y`), which tells you whether the variable came from the `x` or `y` argument. You can override the default suffixes with the `suffix` argument.

`join_by(tailnum)` is short for `join_by(tailnum == tailnum)`. It’s important to know about this fuller form for two reasons. Firstly, it describes the relationship between the two tables: the keys must be equal. That’s why this type of join is often called an equi-join. You’ll learn about non-equi-joins in Section 19.4.4.

Secondly, it’s how you specify different join keys in each table. For example, there are two ways to join the `flight2` and `airports` table: either by `dest` or `origin`:

``````flights2 |>
left_join(airports, join_by(dest == faa))
#> # A tibble: 336,776 × 13
#>    year time_hour           origin dest  tailnum carrier name       lat   lon
#>   <int> <dttm>              <chr>  <chr> <chr>   <chr>   <chr>    <dbl> <dbl>
#> 1  2013 2013-01-01 05:00:00 EWR    IAH   N14228  UA      George …  30.0 -95.3
#> 2  2013 2013-01-01 05:00:00 LGA    IAH   N24211  UA      George …  30.0 -95.3
#> 3  2013 2013-01-01 05:00:00 JFK    MIA   N619AA  AA      Miami I…  25.8 -80.3
#> 4  2013 2013-01-01 05:00:00 JFK    BQN   N804JB  B6      <NA>      NA    NA
#> 5  2013 2013-01-01 06:00:00 LGA    ATL   N668DN  DL      Hartsfi…  33.6 -84.4
#> 6  2013 2013-01-01 05:00:00 EWR    ORD   N39463  UA      Chicago…  42.0 -87.9
#> # … with 336,770 more rows, and 4 more variables: alt <dbl>, tz <dbl>,
#> #   dst <chr>, tzone <chr>

flights2 |>
left_join(airports, join_by(origin == faa))
#> # A tibble: 336,776 × 13
#>    year time_hour           origin dest  tailnum carrier name       lat   lon
#>   <int> <dttm>              <chr>  <chr> <chr>   <chr>   <chr>    <dbl> <dbl>
#> 1  2013 2013-01-01 05:00:00 EWR    IAH   N14228  UA      Newark …  40.7 -74.2
#> 2  2013 2013-01-01 05:00:00 LGA    IAH   N24211  UA      La Guar…  40.8 -73.9
#> 3  2013 2013-01-01 05:00:00 JFK    MIA   N619AA  AA      John F …  40.6 -73.8
#> 4  2013 2013-01-01 05:00:00 JFK    BQN   N804JB  B6      John F …  40.6 -73.8
#> 5  2013 2013-01-01 06:00:00 LGA    ATL   N668DN  DL      La Guar…  40.8 -73.9
#> 6  2013 2013-01-01 05:00:00 EWR    ORD   N39463  UA      Newark …  40.7 -74.2
#> # … with 336,770 more rows, and 4 more variables: alt <dbl>, tz <dbl>,
#> #   dst <chr>, tzone <chr>``````

In older code you might see a different way of specifying the join keys, using a character vector:

• `by = "x"` corresponds to `join_by(x)`.
• `by = c("a" = "x")` corresponds to `join_by(a == x)`.

Now that it exists, we prefer `join_by()` since it provides a clearer and more flexible specification.

### 19.3.3 Filtering joins

As you might guess the primary action of a filtering join is to filter the rows. There are two types: semi-joins and anti-joins. Semi-joins keep all rows in `x` that have a match in `y`. For example, we could use a semi-join to filter the `airports` dataset to show just the origin airports:

``````airports |>
semi_join(flights2, join_by(faa == origin))
#> # A tibble: 3 × 8
#>   faa   name                  lat   lon   alt    tz dst   tzone
#>   <chr> <chr>               <dbl> <dbl> <dbl> <dbl> <chr> <chr>
#> 1 EWR   Newark Liberty Intl  40.7 -74.2    18    -5 A     America/New_York
#> 2 JFK   John F Kennedy Intl  40.6 -73.8    13    -5 A     America/New_York
#> 3 LGA   La Guardia           40.8 -73.9    22    -5 A     America/New_York``````

Or just the destinations:

``````airports |>
semi_join(flights2, join_by(faa == dest))
#> # A tibble: 101 × 8
#>   faa   name                               lat    lon   alt    tz dst   tzone
#>   <chr> <chr>                            <dbl>  <dbl> <dbl> <dbl> <chr> <chr>
#> 1 ABQ   Albuquerque International Sunpo…  35.0 -107.   5355    -7 A     Amer…
#> 2 ACK   Nantucket Mem                     41.3  -70.1    48    -5 A     Amer…
#> 3 ALB   Albany Intl                       42.7  -73.8   285    -5 A     Amer…
#> 4 ANC   Ted Stevens Anchorage Intl        61.2 -150.    152    -9 A     Amer…
#> 5 ATL   Hartsfield Jackson Atlanta Intl   33.6  -84.4  1026    -5 A     Amer…
#> 6 AUS   Austin Bergstrom Intl             30.2  -97.7   542    -6 A     Amer…
#> # … with 95 more rows``````

Anti-joins are the opposite: they return all rows in `x` that don’t have a match in `y`. They’re useful for finding missing values that are implicit in the data, the topic of Section 18.3. Implicitly missing values don’t show up as `NA`s but instead only exist as an absence. For example, we can find rows that as missing from `airports` by looking for flights that don’t have a matching destination airport:

``````flights2 |>
anti_join(airports, join_by(dest == faa)) |>
distinct(dest)
#> # A tibble: 4 × 1
#>   dest
#>   <chr>
#> 1 BQN
#> 2 SJU
#> 3 STT
#> 4 PSE``````

Or we can find which `tailnum`s are missing from `planes`:

``````flights2 |>
anti_join(planes, join_by(tailnum)) |>
distinct(tailnum)
#> # A tibble: 722 × 1
#>   tailnum
#>   <chr>
#> 1 N3ALAA
#> 2 N3DUAA
#> 3 N542MQ
#> 4 N730MQ
#> 5 N9EAMQ
#> 6 N532UA
#> # … with 716 more rows``````

### 19.3.4 Exercises

1. Find the 48 hours (over the course of the whole year) that have the worst delays. Cross-reference it with the `weather` data. Can you see any patterns?

2. Imagine you’ve found the top 10 most popular destinations using this code:

``````top_dest <- flights2 |>
count(dest, sort = TRUE) |>

How can you find all flights to those destinations?

3. Does every departing flight have corresponding weather data for that hour?

4. What do the tail numbers that don’t have a matching record in `planes` have in common? (Hint: one variable explains ~90% of the problems.)

5. Add a column to `planes` that lists every `carrier` that has flown that plane. You might expect that there’s an implicit relationship between plane and airline, because each plane is flown by a single airline. Confirm or reject this hypothesis using the tools you’ve learned in previous chapters.

6. Add the latitude and the longitude of the origin and destination airport to `flights`. Is it easier to rename the columns before or after the join?

7. Compute the average delay by destination, then join on the `airports` data frame so you can show the spatial distribution of delays. Here’s an easy way to draw a map of the United States:

``````airports |>
semi_join(flights, join_by(faa == dest)) |>
ggplot(aes(lon, lat)) +
borders("state") +
geom_point() +
coord_quickmap()``````

You might want to use the `size` or `colour` of the points to display the average delay for each airport.

8. What happened on June 13 2013? Draw a map of the delays, and then use Google to cross-reference with the weather.

## 19.4 How do joins work?

Now that you’ve used joins a few times it’s time to learn more about how they work, focusing on how each row in `x` matches rows in `y`. We’ll begin by using Figure 19.2 to introduce a visual representation of the two simple tibbles defined below. In these examples we’ll use a single key called `key` and a single value column (`val_x` and `val_y`), but the ideas all generalize to multiple keys and multiple values.

``````x <- tribble(
~key, ~val_x,
1, "x1",
2, "x2",
3, "x3"
)
y <- tribble(
~key, ~val_y,
1, "y1",
2, "y2",
4, "y3"
)``````

Figure 19.3 shows all potential matches between `x` and `y` as the intersection between lines drawn from each row of `x` and each row of `y`. The rows and columns in the output are primarily determined by `x`, so the `x` table is horizontal and lines up with the output.

In an actual join, matches will be indicated with dots, as in Figure 19.4. The number of dots equals the number of matches, which in turn equals the number of rows in the output, a new data frame that contains the key, the x values, and the y values. The join shown here is a so-called equi inner join, where rows match if the keys are equal, so that the output contains only the rows with keys that appear in both `x` and `y`. Equi-joins are the most common type of join, so we’ll typically omit the equi prefix, and just call it an inner join. We’ll come back to non-equi joins in Section 19.4.4.

An outer join keeps observations that appear in at least one of the data frames. These joins work by adding an additional “virtual” observation to each data frame. This observation has a key that matches if no other key matches, and values filled with `NA`. There are three types of outer joins:

• A left join keeps all observations in `x`, Figure 19.5. Every row of `x` is preserved in the output because it can fall back to matching a row of `NA`s in `y`.

• A right join keeps all observations in `y`, Figure 19.6. Every row of `y` is preserved in the output because it can fall back to matching a row of `NA`s in `x`. The output still matches `x` as much as possible; any extra rows from `y` are added to the end.

• A full join keeps all observations that appear in `x` or `y`, Figure 19.7. Every row of `x` and `y` is included in the output because both `x` and `y` have a fall back row of `NA`s. Again, the output starts with all rows from `x`, followed by the remaining unmatched `y` rows.

Another way to show how the types of outer join differ is with a Venn diagram, as in Figure 19.8. However, this is not a great representation because while it might jog your memory about which rows are preserved, it fails to illustrate what’s happening with the columns.

### 19.4.1 Row matching

So far we’ve explored what happens if a row in `x` matches zero or one rows in `y`. What happens if it matches more than one row? To understand what’s going let’s first narrow our focus to the `inner_join()` and then draw a picture, Figure 19.9.

There are three possible outcomes for a row in `x`:

• If it doesn’t match anything, it’s dropped.
• If it matches 1 row in `y`, it’s preserved.
• If it matches more than 1 row in `y`, it’s duplicated once for each match.

In principle, this means that there’s no guaranteed correspondence between the rows in the output and the rows in the `x`:

• There might be fewer rows if some rows in `x` don’t match any rows in `y`.
• There might be more rows if some rows in `x` match multiple rows in `y`.
• There might be the same number of rows if every row in `x` matches one row in `y`.
• There might be the same number of rows if some rows don’t match any rows, and exactly the same number of rows match two rows in `y`!!

Row expansion is a fundamental property of joins, but it’s dangerous because it might happen without you realizing it. To avoid this problem, dplyr will warn whenever there are multiple matches:

``````df1 <- tibble(key = c(1, 2, 3), val_x = c("x1", "x2", "x3"))
df2 <- tibble(key = c(1, 2, 2), val_y = c("y1", "y2", "y3"))

df1 |>
inner_join(df2, join_by(key))
#> Warning in inner_join(df1, df2, join_by(key)): Each row in `x` is expected to match at most 1 row in `y`.
#> ℹ Row 2 of `x` matches multiple rows.
#> ℹ If multiple matches are expected, set `multiple = "all"` to silence this
#>   warning.
#> # A tibble: 3 × 3
#>     key val_x val_y
#>   <dbl> <chr> <chr>
#> 1     1 x1    y1
#> 2     2 x2    y2
#> 3     2 x2    y3``````

This is one reason we like `left_join()` — if it runs without warning, you know that each row of the output matches the row in the same position in `x`.

You can gain further control over row matching with two arguments:

• `unmatched` controls what happens when a row in `x` fails to match any rows in `y`. It defaults to `"drop"` which will silently drop any unmatched rows.
• `multiple` controls what happens when a row in `x` matches more than one row in `y`. For equi-joins, it defaults to `"warn"` which emits a warning message if any rows have multiple matches.

There are two common cases in which you might want to override these defaults: enforcing a one-to-one mapping or deliberately allowing the rows to increase.

### 19.4.2 One-to-one mapping

Both `unmatched` and `multiple` can take value `"error"` which means that the join will fail unless each row in `x` matches exactly one row in `y`:

``````df1 <- tibble(x = 1)
df2 <- tibble(x = c(1, 1))
df3 <- tibble(x = 3)

df1 |>
inner_join(df2, join_by(x), unmatched = "error", multiple = "error")
#> Error in `inner_join()`:
#> ! Each row in `x` must match at most 1 row in `y`.
#> ℹ Row 1 of `x` matches multiple rows.
df1 |>
inner_join(df3, join_by(x), unmatched = "error", multiple = "error")
#> Error in `inner_join()`:
#> ! Each row of `x` must have a match in `y`.
#> ℹ Row 1 of `x` does not have a match.``````

Note that `unmatched = "error"` is not useful with `left_join()` because, as described above, every row in `x` has a fallback match to a virtual row in `y`.

### 19.4.3 Allow multiple rows

Sometimes it’s useful to deliberately expand the number of rows in the output. This can come about naturally if you “flip” the direction of the question you’re asking. For example, as we’ve seen above, it’s natural to supplement the `flights` data with information about the plane that flew each flight:

``````flights2 |>
left_join(planes, by = "tailnum")``````

But it’s also reasonable to ask what flights did each plane fly:

``````plane_flights <- planes |>
select(tailnum, type, engines, seats) |>
left_join(flights2, by = "tailnum")
#> Warning in left_join(select(planes, tailnum, type, engines, seats), flights2, : Each row in `x` is expected to match at most 1 row in `y`.
#> ℹ Row 1 of `x` matches multiple rows.
#> ℹ If multiple matches are expected, set `multiple = "all"` to silence this
#>   warning.``````

Since this duplicates rows in `x` (the planes), we need to explicitly say that we’re ok with the multiple matches by setting `multiple = "all"`:

``````plane_flights <- planes |>
select(tailnum, type, engines, seats) |>
left_join(flights2, by = "tailnum", multiple = "all")

plane_flights
#> # A tibble: 284,170 × 9
#>   tailnum type   engines seats  year time_hour           origin dest  carrier
#>   <chr>   <chr>    <int> <int> <int> <dttm>              <chr>  <chr> <chr>
#> 1 N10156  Fixed…       2    55  2013 2013-01-10 06:00:00 EWR    PIT   EV
#> 2 N10156  Fixed…       2    55  2013 2013-01-10 10:00:00 EWR    CHS   EV
#> 3 N10156  Fixed…       2    55  2013 2013-01-10 15:00:00 EWR    MSP   EV
#> 4 N10156  Fixed…       2    55  2013 2013-01-11 06:00:00 EWR    CMH   EV
#> 5 N10156  Fixed…       2    55  2013 2013-01-11 11:00:00 EWR    MCI   EV
#> 6 N10156  Fixed…       2    55  2013 2013-01-11 18:00:00 EWR    PWM   EV
#> # … with 284,164 more rows``````

### 19.4.4 Filtering joins

The number of matches also determines the behavior of the filtering joins. The semi-join keeps rows in `x` that have one or more matches in `y`, as in Figure 19.10. The anti-join keeps rows in `x` that match zero rows in `y`, as in Figure 19.11. In both cases, only the existence of a match is important; it doesn’t matter how many times it matches. This means that filtering joins never duplicate rows like mutating joins do.

## 19.5 Non-equi joins

So far you’ve only seen equi-joins, joins where the rows match if the `x` key equals the `y` key. Now we’re going to relax that restriction and discuss other ways of determining if a pair of rows match.

But before we can do that, we need to revisit a simplification we made above. In equi-joins the `x` keys and `y` are always equal, so we only need to show one in the output. We can request that dplyr keep both keys with `keep = TRUE`, leading to the code below and the re-drawn `inner_join()` in Figure 19.12.

``````x |> left_join(y, by = "key", keep = TRUE)
#> # A tibble: 3 × 4
#>   key.x val_x key.y val_y
#>   <dbl> <chr> <dbl> <chr>
#> 1     1 x1        1 y1
#> 2     2 x2        2 y2
#> 3     3 x3       NA <NA>``````

When we move away from equi-joins we’ll always show the keys, because the key values will often be different. For example, instead of matching only when the `x\$key` and `y\$key` are equal, we could match whenever the `x\$key` is greater than or equal to the `y\$key`, leading to Figure 19.13. dplyr’s join functions understand this distinction equi and non-equi joins so will always show both keys when you perform a non-equi join.

Non-equi-join isn’t a particularly useful term because it only tells you what the join is not, not what it is. dplyr helps by identifying four particularly useful types of non-equi-join:

• Cross joins match every pair of rows.
• Inequality joins use `<`, `<=`, `>`, and `>=` instead of `==`.
• Rolling joins are similar to inequality joins but only find the closest match.
• Overlap joins are a special type of inequality join designed to work with ranges.

Each of these is described in more detail in the following sections.

### 19.5.1 Cross joins

A cross join matches everything, as in Figure 19.14, generating the Cartesian product of rows. This means the output will have `nrow(x) * nrow(y)` rows.

Cross joins are useful when generating permutations. For example, the code below generates every possible pair of names. Since we’re joining `df` to itself, this is sometimes called a self-join.

``````df <- tibble(name = c("John", "Simon", "Tracy", "Max"))
df |> left_join(df, join_by())
#> # A tibble: 16 × 2
#>   name.x name.y
#>   <chr>  <chr>
#> 1 John   John
#> 2 John   Simon
#> 3 John   Tracy
#> 4 John   Max
#> 5 Simon  John
#> 6 Simon  Simon
#> # … with 10 more rows``````

### 19.5.2 Inequality joins

Inequality joins use `<`, `<=`, `>=`, or `>` to restrict the set of possible matches, as in Figure 19.13 and Figure 19.15.

Inequality joins are extremely general, so general that it’s hard to come up with meaningful specific use cases. One small useful technique is to use them to restrict the cross join so that instead of generating all permutations, we generate all combinations:

``````df <- tibble(id = 1:4, name = c("John", "Simon", "Tracy", "Max"))

df |> left_join(df, join_by(id < id))
#> # A tibble: 7 × 4
#>    id.x name.x  id.y name.y
#>   <int> <chr>  <int> <chr>
#> 1     1 John       2 Simon
#> 2     1 John       3 Tracy
#> 3     1 John       4 Max
#> 4     2 Simon      3 Tracy
#> 5     2 Simon      4 Max
#> 6     3 Tracy      4 Max
#> # … with 1 more row``````

### 19.5.3 Rolling joins

Rolling joins are a special type of inequality join where instead of getting every row that satisfies the inequality, you get just the closest row, as in Figure 19.16. You can turn any inequality join into a rolling join by adding `closest()`. For example `join_by(closest(x <= y))` matches the smallest `y` that’s greater than or equal to x, and `join_by(closest(x > y))` matches the biggest `y` that’s less than `x`.

Rolling joins are particularly useful when you have two tables of dates that don’t perfectly line up and you want to find (e.g.) the closest date in table 1 that comes before (or after) some date in table 2.

For example, imagine that you’re in charge of the party planning commission for your office. Your company is rather cheap so instead of having individual parties, you only have a party once each quarter. The rules for determining when a party will be held are a little complex: parties are always on a Monday, you skip the first week of January since a lot of people are on holiday, and the first Monday of Q3 2022 is July 4, so that has to be pushed back a week. That leads to the following party days:

``````parties <- tibble(
q = 1:4,
party = lubridate::ymd(c("2022-01-10", "2022-04-04", "2022-07-11", "2022-10-03"))
)``````

Now imagine that you have a table of employee birthdays:

``````employees <- tibble(
name = wakefield::name(100),
birthday = lubridate::ymd("2022-01-01") + (sample(365, 100, replace = TRUE) - 1)
)
employees
#> # A tibble: 100 × 2
#>   name       birthday
#>   <variable> <date>
#> 1 Lindzy     2022-08-11
#> 2 Santania   2022-03-01
#> 3 Gardell    2022-03-04
#> 4 Cyrille    2022-11-15
#> 5 Kynli      2022-07-09
#> 6 Sever      2022-02-03
#> # … with 94 more rows``````

And for each employee we want to find the first party date that comes after (or on) their birthday. We can express that with a rolling join:

``````employees |>
left_join(parties, join_by(closest(birthday >= party)))
#> # A tibble: 100 × 4
#>   name       birthday       q party
#>   <variable> <date>     <int> <date>
#> 1 Lindzy     2022-08-11     3 2022-07-11
#> 2 Santania   2022-03-01     1 2022-01-10
#> 3 Gardell    2022-03-04     1 2022-01-10
#> 4 Cyrille    2022-11-15     4 2022-10-03
#> 5 Kynli      2022-07-09     2 2022-04-04
#> 6 Sever      2022-02-03     1 2022-01-10
#> # … with 94 more rows``````

There is, however, one problem with this approach: the folks with birthdays before January 10 don’t get a party:

``````employees |>
anti_join(parties, join_by(closest(birthday >= party)))
#> # A tibble: 4 × 2
#>   name       birthday
#>   <variable> <date>
#> 1 Janeida    2022-01-04
#> 2 Aires      2022-01-07
#> 3 Mikalya    2022-01-06
#> 4 Carlynn    2022-01-08``````

To resolve that issue we’ll need to tackle the problem a different way, with overlap joins.

### 19.5.4 Overlap joins

Overlap joins provide three helpers that use inequality joins to make it easier to work with intervals:

• `between(x, y_lower, y_upper)` is short for `x >= y_lower, x <= y_upper`.
• `within(x_lower, x_upper, y_lower, y_upper)` is short for `x_lower >= y_lower, x_upper <= y_upper`.
• `overlaps(x_lower, x_upper, y_lower, y_upper)` is short for `x_lower <= y_upper, x_upper >= y_lower`.

Let’s continue the birthday example to see how you might use them. There’s one problem with the strategy we used above: there’s no party preceding the birthdays Jan 1-9. So it might be better to to be explicit about the date ranges that each party spans, and make a special case for those early birthdays:

``````parties <- tibble(
q = 1:4,
party = lubridate::ymd(c("2022-01-10", "2022-04-04", "2022-07-11", "2022-10-03")),
start = lubridate::ymd(c("2022-01-01", "2022-04-04", "2022-07-11", "2022-10-03")),
end = lubridate::ymd(c("2022-04-03", "2022-07-11", "2022-10-02", "2022-12-31"))
)
parties
#> # A tibble: 4 × 4
#>       q party      start      end
#>   <int> <date>     <date>     <date>
#> 1     1 2022-01-10 2022-01-01 2022-04-03
#> 2     2 2022-04-04 2022-04-04 2022-07-11
#> 3     3 2022-07-11 2022-07-11 2022-10-02
#> 4     4 2022-10-03 2022-10-03 2022-12-31``````

Hadley is hopelessly bad at data entry so he also wanted to check that the party periods don’t overlap. One way to do this is by using a self-join to check to if any start-end interval overlap with another:

``````parties |>
inner_join(parties, join_by(overlaps(start, end, start, end), q < q)) |>
select(start.x, end.x, start.y, end.y)
#> # A tibble: 1 × 4
#>   start.x    end.x      start.y    end.y
#>   <date>     <date>     <date>     <date>
#> 1 2022-04-04 2022-07-11 2022-07-11 2022-10-02``````

Ooops, there is an overlap, so let’s fix that problem and continue:

``````parties <- tibble(
q = 1:4,
party = lubridate::ymd(c("2022-01-10", "2022-04-04", "2022-07-11", "2022-10-03")),
start = lubridate::ymd(c("2022-01-01", "2022-04-04", "2022-07-11", "2022-10-03")),
end = lubridate::ymd(c("2022-04-03", "2022-07-10", "2022-10-02", "2022-12-31"))
)``````

Now we can match each employee to their party. This is a good place to use `unmatched = "error"` because we want to quickly find out if any employees didn’t get assigned a party.

``````employees |>
inner_join(parties, join_by(between(birthday, start, end)), unmatched = "error")
#> # A tibble: 100 × 6
#>   name       birthday       q party      start      end
#>   <variable> <date>     <int> <date>     <date>     <date>
#> 1 Lindzy     2022-08-11     3 2022-07-11 2022-07-11 2022-10-02
#> 2 Santania   2022-03-01     1 2022-01-10 2022-01-01 2022-04-03
#> 3 Gardell    2022-03-04     1 2022-01-10 2022-01-01 2022-04-03
#> 4 Cyrille    2022-11-15     4 2022-10-03 2022-10-03 2022-12-31
#> 5 Kynli      2022-07-09     2 2022-04-04 2022-04-04 2022-07-10
#> 6 Sever      2022-02-03     1 2022-01-10 2022-01-01 2022-04-03
#> # … with 94 more rows``````

### 19.5.5 Exercises

1. Can you explain what’s happening with the keys in this equi-join? Why are they different?

``````x |> full_join(y, by = "key")
#> # A tibble: 4 × 3
#>     key val_x val_y
#>   <dbl> <chr> <chr>
#> 1     1 x1    y1
#> 2     2 x2    y2
#> 3     3 x3    <NA>
#> 4     4 <NA>  y3

x |> full_join(y, by = "key", keep = TRUE)
#> # A tibble: 4 × 4
#>   key.x val_x key.y val_y
#>   <dbl> <chr> <dbl> <chr>
#> 1     1 x1        1 y1
#> 2     2 x2        2 y2
#> 3     3 x3       NA <NA>
#> 4    NA <NA>      4 y3``````
2. When finding if any party period overlapped with another party period we used `q < q` in the `join_by()`? Why? What happens if you remove this inequality?

## 19.6 Summary

In this chapter, you’ve learned how to use mutating and filtering joins to combine data from a pair of data frames. Along the way you learned how to identify keys, and the difference between primary and foreign keys. You also understand how joins work and how to figure out how many rows the output will have. Finally, you’ve gained a glimpse into the power of non-equi-joins and seen a few interesting use cases.

This chapter concludes the “Transform” part of the book where the focus was on the tools you could use with individual columns and tibbles. You learned about dplyr and base functions for working with logical vectors, numbers, and complete tables, stringr functions for working strings, lubridate functions for working with date-times, and forcats functions for working with factors.

In the next part of the book, you’ll learn more about getting various types of data into R in a tidy form.

1. Remember that in RStudio you can also use `View()` to avoid this problem.↩︎

2. That’s not 100% true, but you’ll get a warning whenever it isn’t.↩︎