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. (But that pair might be the same table, a so called self-join.) 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:
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.
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.
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 matching variable in another table.
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.
The first tool we'll look at for combining a pair of tables is the __mutating join__. A mutating join allows you to combine variables from two tables. It first matches observations using keys, then copies across variables from one table to the other.
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. To make it easier to see what's going on in the examples, we'll first create a smaller dataset.
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()`:
The result of joining airlines 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 got to the same place using `mutate()` and basic subsetting:
The coloured column represents the "key" variable: these are used to match the rows between the tables. The grey column represents the "value" columns that are carried along for the ride. In these examples I'll show a single key variable and single value variable, but idea generalises in a straightforward way to multiple keys and multiple values.
A join is a way of connecting each row in `x` to zero, one, or more rows in `y`. The following diagram shows each potential match as an intersection of a pair of lines.
(If you look closely, you might notice that we've switched the order of the keys and values in `x`. This is to emphasise that joins match based on the key variable; value variable is just carried along for the ride.)
(To be precise this is an inner equijoin because the keys are matched on equality. Since most joins are equijoins we usually drop that condition.)
The output of an inner join is a new data frame that contains the key, the x values, and the y values. We use `by` to tell the join which column is the key variable.
The most important property of an inner join is that rows that don't have matches don't appear in the output. This generally means that inner joins are not appropriate for use in analysis because it's too easy to lose observations.
An inner join only keeps observations that have a match in both tables. An __outer join__ keeps observations that only appear in one of the tables. There are three types of outer joins:
These joins work by adding an additional "virtual" observation to each table. This observation has a key that always matches (if no other key matches), and has missing values. Graphically, that looks like:
The most commonly used join is the left join: you use this whenever you lookup additional data out of another table, preserving the original observations even if there isn't match. The left join should be your default join: use it unless you have a strong reason to prefer one of the others.
However, this is not a great representation. It might jog your memory about which join preserves the observations in which table. But it suffers from a major limitation: it can't show what happens when keys are duplicated, the topic of the next sections.
So far all the diagrams have assumed that the keys are unique. But obviously that's not always the case. This section explains what happens when the keys are not unique. There are three possibilities:
So far, the pairs of tables have always been joined by a single variable, and that variable has the same name in both tables. That constraint was encoded by `by = "key"`. You can use other values for `by` to connect the tables in other ways:
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:
`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 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`.
