---
layout: default
title: Relational data
---

# Relational data {#relation-data}

```{r setup-relation, include = FALSE}
library(dplyr)
library(nycflights13)
library(ggplot2)
source("common.R")
options(dplyr.print_min = 6, dplyr.print_max = 6)
knitr::opts_chunk$set(fig.path = "figures/", cache = TRUE)
```

It's rare that a data analysis involves only a single table of data. Typically you have many tables of data, and you have to combine them to answer the questions that you're interested in. This type of data is called __relational__ because it concerns the relations between multiple datasets. 

Relations are always defined between a pair of tables. The relationships of three or more tables are always a property of the relations between each pair. To work with relational data you need verbs that work with pairs of tables. There are three families of verbs design to work with relational data:

* __Mutating joins__, which add new variables to one data frame from matching 
  rows in another.

* __Filtering joins__, which filter observations from one data frame based on 
  whether or not they match an observation in the other table.

* __Set operations__, which treat observations like they were set elements.

The most common place to find relational data is in a relational database management system, or RDBMS for short. If you've worked with an RDBMS you'll have used SQL to communicate with it. If you've used SQL before you're probably familiar with the mutating joins (these are the classic left join, right join, etc), but you might not know about the filtering joins (semi and anti joins) or the set operations.

## nycflights13 {#nycflights13-relational}

As well as the `flights` dataset that we've worked so far, nycflights13 contains a four related data frames:

*   `airlines` lets you look up the full carrier name from its abbreviated 
    code:
    
    ```{r}
    airlines
    ```

*   `planes` gives information about each plane, identified by its `tailnum`:

    ```{r}
    planes
    ```

*   `airports` gives information about each airport, identified by the `faa`
    airport code:
    
    ```{r}
    airports
    ```
  
*   `weather` gives the weather at each NYC airport for each hour:

    ```{r}
    weather
    ```

One way to show the relationships between the different tables is with a diagram:

```{r, echo = FALSE, out.width = "75%"}
knitr::include_graphics("diagrams/relational-nycflights.png")
```

This diagram is a little overwhelming, and it's simple compared to some you'll see in the wild. The key to understanding diagrams like this is to remember each relation always concerns a pair of tables. You don't need to understand the whole diagram; you just need the understand the chain of relations between the tables that you are interested in. For these tables:

* `flights` connects to `planes` via single variable, `tailnum`. `flights`
  connect `airlines` with the `carrier` variable.

* `flights` connects to `airports` in two ways: via the `origin` or the 
  `dest`.
  
* `flights` connects to `weather` via `origin` (the location), and
  `year`, `month`, `day` and `hour` (the time).

The variables used to connect each pair of tables are called __keys__. The __primary key__ uniquely identifies an observation. For example, each plane is uniquely identified by `tailnum`. In other cases, you might need multiple keys to uniquely identify an observation. For example, to identify an observation in `weather` you need five variables: `year`, `month`, `day`, `hour`, and `origin`. Primary keys are coloured grey. The __foreign key__ is the corresponding variable in another table.

All relations are implicitly one-to-many. For example, each flight has one plane, but each plane has many flights. In other data, you'll occassionaly see a 1-to-1 relationship. You can think of this as a special case of 1-to-many. It's possible to model many-to-many relations with a many-to-1 relation plus a 1-to-many relation. For example, in this data there's a many-to-many relationship between airlines and airports: each airport flies to many airlines; each airport hosts many airlines.

### Exercise

1.  Imagine you want to draw (approximately) the route each plane flies from
    its origin to its destination. What variables would you need? What tables
    would you need to combine?

1.  There's a relationship between `weather` and `airports` that I forgot to 
    draw. What is it?
    
1.  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 data.

1.  We know that some days of the year are "special", and fewer people than
    usual fly on them. What new table could you store that data in? What would
    the primary keys be? How would it connect to the existing tables?

## Mutating joins {#mutating-joins}

The first tool we'll look at for combining a pair of tables is the mutating join. Mutating joins allow you to combine variables from multiple tables. They match observations using keys, and then add variables from one table to the other. To explore matching joins with the flights data, we'll first create a smaller dataset. Like `mutate()`, the join functions add variables to the right, so the new variables might not fit on the screen if you have a lot. (Remember, when you're in RStudio you can use `View()` to avoid this problem).

```{r}
# Drop unimportant variables so it's easier to understand the join results.
flights2 <- flights %>% select(year:day, hour, origin, dest, tailnum, carrier)
flights2
```

For example, imagine you want to add the full airline name to the `flights` data. You can combine the `airlines` and `carrier` data frames with `left_join()`:

```{r}
flights2 %>% 
  left_join(airlines, by = "carrier")
```

The result of joining airlines on to flights is an additional variable: `carrier`. This is why I call this type of join a mutating join.

In this case, you could have created achieved the same result using `mutate()` and basic subsetting:

```{r}
flights2 %>% 
  mutate(carrier = airlines$name[match(carrier, airlines$carrier)])
```

But this is hard to generalise when you need to match multiple variables, and doesn't as clearly communicate the action of joining as using an explicit join function.

There are three important things you need to understand about mutating joins work:

1. The different types of matches (1-to-1, 1-to-many, many-to-many).

1. What happens when a row doesn't match.

1. How you control which variables (keys) are used to match observations.

To help you built up an intuition for how joins work and how the various options affect behaviour I'm going to use a visual abstraction of a table: 

```{r, echo = FALSE, out.width = "10%"}
knitr::include_graphics("diagrams/join-setup.png")
```
```{r}
data_frame(key = 1:5, value = paste0("x", 1:5))
```

The coloured column represents the "key" variable: these are used to match the rows between the tables. The labelled column represents the "value" columns that are carried along for the ride. The same basic idea generalised to any number of key and value columns.

[Insert basic explanation of joins]

### Missing matches {#join-types}

You might also wonder what happens when there isn't a match. This is controlled by the type of "join": inner, left, right, or full I'll show each type of join with a picture, and the corresponding R code. Here are the tables we will use:

```{r, echo = FALSE, out.width = "25%"}
knitr::include_graphics("diagrams/join-setup2.png")
```
```{r}
(x <- data_frame(key = c(1, 2, 3), val_x = c("x1", "x2", "x3")))
(y <- data_frame(key = c(1, 2, 4), val_y = c("y1", "y2", "y3")))
```

The left, right and full joins are collectively known as __outer joins__. When a row doesn't match in an outer join, the new variables are filled in with missing values. You can also think about joins heuristically as set operations on the rows of the tables:

```{r, echo = FALSE}
knitr::include_graphics("diagrams/join-venn.png")
```

#### Inner join

In an inner join, only rows that have matching keys are retained:

```{r, echo = FALSE, out.width = "50%"}
knitr::include_graphics("diagrams/join-inner.png")
```

```{r}
x %>% inner_join(y, by = "key")
```

#### Left join

In a left join, every row in `x` is kept.  A left join effectively works by adding a "default" match: if a row in `x` doesn't match a row in `y`, it falls back to matching a row that contains only missing values.

```{r, echo = FALSE, out.width = "50%"}
knitr::include_graphics("diagrams/join-left.png")
```
```{r}
x %>% left_join(y, by = "key")
```

This is the most commonly used join because it ensures that you don't lose
observations from your primary table.

#### Right join

A right join is the complement of a left join: every row in `y` is kept.

```{r, echo = FALSE, out.width = "50%"}
knitr::include_graphics("diagrams/join-right.png")
```
```{r}
x %>% right_join(y, by = "key")
```

#### Full join

A full join is combines a left join and a right join, keeping every 
row in both `x` and `y`.

```{r, echo = FALSE, out.width = "50%"}
knitr::include_graphics("diagrams/join-full.png")
```
```{r}
x %>% full_join(y, by = "key")
```

### Matches {#join-matches}

There are three ways that the keys might match: one-to-one, one-to-many, and many-to-many.

*    In a one-to-one match, each key in `x` matches one key in `y`. This sort of
     match is useful when you two tables that have data about the same thing and
     you want to align the rows.

    ```{r, echo = FALSE, out.width = "100%"}
    knitr::include_graphics("diagrams/join-one-to-one.png")
    ```
    
    ```{r}
    x <- data_frame(key = 1:5, val_x = paste0("x", 1:5))
    y <- data_frame(key = c(3, 5, 2, 4, 1), val_y = paste0("y", 1:5))
    inner_join(x, y, by = "key")
    ```
    
*   In a one-to-many match, each key in `x` matches multiple keys in `y`. This
    is useful when you want to add in additional information.
    
    ```{r, echo = FALSE, out.width = "100%"}
    knitr::include_graphics("diagrams/join-one-to-many.png")
    ```
    
    ```{r}
    x <- data_frame(key = c(3, 3, 1, 4, 4), val_x = paste0("x", 1:5))
    y <- data_frame(key = 1:4, val_y = paste0("y", 1:4))
    inner_join(x, y, by = "key")
    ```

*   Finally, you can have a many-to-many match, where there are duplicated
    keys in `x` and duplicate keys in `y`. When this happens, every possible
    combination is created in the output.

    ```{r, echo = FALSE, out.width = "100%"}
    knitr::include_graphics("diagrams/join-many-to-many.png")
    ```
    ```{r}
    x <- data_frame(key = c(1, 2, 2, 4), val_x = paste0("x", 1:4))
    y <- data_frame(key = c(1, 2, 2, 4), val_y = paste0("y", 1:4))
    inner_join(x, y, by = "key")
    ```    

### Controlling how the tables are matched {#join-by}

When joining multiple tables of data, it's useful to think about the "key", the combination of variables that uniquely identifies each observation. Sometimes that's a single variable. For example each airport is uniquely identified by a three letter `faa` code, each carrier is uniquely identified by its two letter abbreviation, and each plane by its `tailnum`. `weather` is more complex: to uniquely identify an observation you need to know when (`year`, `month`, `day`, `hour`) and where it happened (`origin`).

When you combine two tables of data, you do so by matching the keys in each table. You can control the matching behaviour using the `by` argument:

  * The default, `by = NULL`, uses all variables that appear in both tables, 
    the so called __natural__ join. For example, the flights and weather tables 
    match on their common variables: `year`, `month`, `day`, `hour` and
    `origin`.
    
    ```{r}
    flights2 %>% left_join(weather)
    ```
    
  * A character vector, `by = "x"`. This is like a natural join, but uses only 
    some of the common variables. For example, `flights` and `planes` have 
    `year` variables, but they mean different things so we only want to join by 
    `tailnum`.
    
    ```{r}
    flights2 %>% left_join(planes, by = "tailnum")
    ```
    
    Note that the `year` variables (which appear in both input data frames,
    but are not constrained to be equal) are disambiguated in the output with 
    a suffix.

  * A named character vector: `by = c("a" = "b")`. This will
    match variable `a` in table `x` to variable `y` in table `b`. The 
    variables from `x` will be used in the output.
    
    For example, if we want to draw a map we need to combine the flights data
    with the airports data which contains the location (`lat` and `long`) of
    each airport. Each flight has an origin and destination `airport`, so we 
    need to specify which one we want to join to:
    
    ```{r}
    flights2 %>% left_join(airports, c("dest" = "faa"))
    flights2 %>% left_join(airports, c("origin" = "faa"))
    ```

### Exercises

1.  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:
    
    ```{r, include = FALSE}
    airports %>% 
      semi_join(flights, c("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.

1.  Is there a relationship between the age of a plane and its delays?

1.  What weather conditions make it more likely to see a delay?
    
1.  What happened on June 13 2013? Display the spatial pattern of delays,
    and then use google to cross-reference with the weather.
    
    ```{r, eval = FALSE, include = FALSE}
    worst <- filter(not_cancelled, month == 6, day == 13)
    worst %>% 
      group_by(dest) %>% 
      summarise(delay = mean(arr_delay), n = n()) %>% 
      filter(n > 5) %>% 
      inner_join(airports, by = c("dest" = "faa")) %>% 
      ggplot(aes(lon, lat)) +
        borders("state") +
        geom_point(aes(size = n, colour = delay)) +
        coord_quickmap()
    ```

### Other joins

`base::merge()` can perform all four types of mutating join: 

dplyr              | merge
-------------------|-------------------------------------------
`inner_join(x, y)` | `merge(x, y)`
`left_join(x, y)`  | `merge(x, y, all.x = TRUE)`
`right_join(x, y)` | `merge(x, y, all.y = TRUE)`,
`full_join(x, y)`  | `merge(x, y, all.x = TRUE), all.y = TRUE)`

The advantages of the specific dplyr verbs is that they more clearly convey the intent of your code: the difference between the joins is really important but concealed in the arguments of `merge()`. dplyr's joins are considerably faster and don't mess with the order of the rows.

SQL is the inspiration for dplyr's conventions, so the translation is straightforward:

dplyr                        | SQL
-----------------------------|-------------------------------------------
`inner_join(x, y, by = "z")` | `SELECT * FROM x INNER JOIN y USING (z)`
`left_join(x, y, by = "z")`  | `SELECT * FROM x LEFT OUTER JOIN USING (z)`
`right_join(x, y, by = "z")` | `SELECT * FROM x RIGHT OUTER JOIN USING (z)`
`full_join(x, y, by = "z")`  | `SELECT * FROM x FULL OUTER JOIN USING (z)`

Note that "INNER" and "OUTER" are optional, and often ommitted. 

Joining different variables between the tables, e.g. `inner_join(x, y, by = c("a" = "b"))` uses a slightly different syntax: `SELECT * FROM x INNER JOIN y ON x.a = y.b`. As this syntax suggests SQL supports a wide range of join types than dplyr because you can connect the tables using constraints other than equiality (sometimes called non-equijoins).

## Filtering joins {#filtering-joins}

Filtering joins match obserations in the same way as mutating joins, but affect the observations, not the variables. There are two types:

* `semi_join(x, y)` __keeps__ all observations in `x` that have a match in `y`.
* `anti_join(x, y)` __drops__ all observations in `x` that have a match in `y`.

Semi joins are useful for matching filtered summary tables back to the original rows. For example, imagine you've found the top ten most popular destinations:

```{r}
top_dest <- flights %>% 
  count(dest, sort = TRUE) %>%
  head(10)
top_dest
```

Now you want to find each flight that went to one of those destinations. You could construct a filter yourself:

```{r}
flights %>% filter(dest %in% top_dest$dest)
```

But it's difficult to extend that approach to multiple variables. For example, imagine that you'd found the 10 days with highest average delays. How would you construct the filter statement that used `year`, `month`, and `day` to match it back to `flights`?

Instead you can use a semi join, which connects the two tables like a mutating join, but instead of adding new columns, only keeps the rows in `x` that have a match in `y`:

```{r}
flights %>% semi_join(top_dest)
```

The inverse of a semi join is an anti join. An anti join keeps the rows that _don't_ have a match, and are useful for diagnosing join mismatches. For example, when connecting `flights` and `planes`, you might be interested to know that there are many `flights` that don't have a match in `planes`:

```{r}
flights %>% 
  anti_join(planes, by = "tailnum") %>% 
  count(tailnum, sort = TRUE)
```

### Exercises

1.  What does it mean for a flight to have a missing `tailnum`? What do the 
    tail numbers that don't have a matching record in `planes` have in common?
    (Hint: one variable explains ~90% of the problem.)

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? 
    
1.  What does `anti_join(flights, airports, by = c("dest" = "faa"))` tell you?
    What does `anti_join(airports, flights, by = c("dest" = "faa"))` tell you?

## Set operations {#set-operations}

The final type of two-table verb is set operations. Generally, I use these the least frequnetly, but they are occassionally useful when you want to break a single complex filter into simpler pieces that you then combine.

All these operations work with a complete row, comparing the values of every variable. These expect the `x` and `y` inputs to have the same variables, and treat the observations like sets:

* `intersect(x, y)`: return only observations in both `x` and `y`.
* `union(x, y)`: return unique observations in `x` and `y`.
* `setdiff(x, y)`: return observations in `x`, but not in `y`.

Given this simple data:

```{r}
(df1 <- data_frame(x = 1:2, y = c(1L, 1L)))
(df2 <- data_frame(x = 1:2, y = 1:2))
```

The four possibilities are:

```{r}
intersect(df1, df2)
# Note that we get 3 rows, not 4
union(df1, df2)
setdiff(df1, df2)
setdiff(df2, df1)
```
