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 _relational_ database management system, which encompasses almost all modern databases. If you've used a database before, you've almost certainly used SQL. If so, you should find the concepts in this chapter familiar, although their expression in dplyr is little different. Generally, dplyr is a little easier to use than SQL because it's specialised to data analysis: it makes common data analysis operations easier, at the expense of making it difficult to do other things.
You'll learn about relational data with other data from nycflights13. As well as the `flights` table that you've worked with so far, nycflights13 contains a four related data frames:
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 thing; 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 in the current table.
* The __foreign key__ uniquely identifies an observation in another table.
In simple cases, a single variable is sufficient to identify an observation. For example, each plane is uniquely identified by its `tailnum`. In other cases, multiple variables may be needed. For example, to identify an observation in `weather` you need five variables: `year`, `month`, `day`, `hour`, and `origin`.
Each relation (an arrow) matches a primary keys (coloured grey) with the corresponding foreign key (the arrowhead) 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 by their keys, then copies across variables from one table to the other.
Like `mutate()`, the join functions add variables to the right, so if you have a lot of variables already, the new variables won't get printed out. For these examples, we'll make it easier to see what's going on in the examples by creating a narrower 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 following sections explain, in detail, how mutating joins work. You'll start by learning a useful visual representation of joins. We'll then use that to explain the four mutating join functions: the inner join, and the three outer joins. When working with real data, keys don't always uniquely identify observations, so next we'll talk about what happens when there isn't a unique match. Finally, you'll learn how to tell dplyr which variables are the keys for a given join.
The coloured column represents the "key" variable: these are used to match the rows between the tables. The grey column represents the "value" column that is 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.)
In an actual join, matches will be indicated with dots. The colour of the dots match the colour of the keys to remind that that's what important. Then the number of dots = the number of matches = the number of rows in the output.
(To be precise, this is an inner __equijoin__ because the keys are matched using the equality operator. 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 dplyr which variable is the key:
The most important property of an inner join is that unmatched rows are dropped. This means that generally inner joins are not appropriate for use in analysis because it's too easy to lose observations.
An inner join keeps observations that appear in both tables. An __outer join__ keeps observations that appear in at least 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 a value filled with `NA`.
The most commonly used join is the left join: you use this when ever you lookup additional data out of another table, becasuse it preserves the original observations even when there isn't a 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. A Venn diagram can't show what happens when keys don't uniquely identify an observation.
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 two possibilities:
Once you've identified the primary keys in your tables, it's good practice to verify that they do indeed uniquely identify each observation. One way to do that is `count()` the primary keys and look for entries where `n` is greater than one:
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:
Joining different variables between the tables, e.g. `inner_join(x, y, by = c("a" = "b"))` uses a slightly different syntax in SQL: `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).
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:
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`:
Only the existence of a match is important; it doesn't match what observation is matched. This means that filtering joins never duplicate rows like mutating joins do:
The inverse of a semi-join is an anti-join. An anti-join keeps the rows that _don't_ have a match:
```{r, echo = FALSE, out.width = "50%"}
knitr::include_graphics("diagrams/join-anti.png")
```
Anti-joins are 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`:
The final type of two-table verb is set operations. Generally, I use these the least frequently, 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`.
