# Missing values {#missing-values}

```{r, results = "asis", echo = FALSE}
status("polishing")
```

## Introduction

You've already learned the basics of missing values earlier in the the book: you first saw them in Section \@ref(summarize) where they interfered with computing summary statistics, and you learned about their their infectious nature and how to check for their presence in Section \@ref(na-comparison).
In this chapter, we'll come back to missing values in more depth, so you can learn more of the details.

We'll start by discussing some general tools for explicitly missing values that recorded as `NA`.
We'll then explore the idea of implicitly missing values, values are that are simply absent from your data, and show some tools you can use to make them explicit.
We'll finish off with a of empty groups, caused by factor levels that don't appear in the data.

### Prerequisites

The functions for working will missing data mostly come from dplyr and tidyr, which are core members of the tidyverse.

```{r setup, message = FALSE}
library(tidyverse)
```

## Explicit missing values

To begin, let's explore a few handy tools for creating or eliminating explicitly `NA`s.
In the following sections you'll learn how to carry the last observation forward, convert `NA`s to fixed values, convert some fixed value to `NA`s, and learn about the special variant of `NA` known as "not a number".

### Last observation carried forward

Missing values are commonly used as data entry convenience where they indicate a repeat of the value in the previous row:

```{r}
treatment <- tribble(
  ~person,           ~treatment, ~response,
  "Derrick Whitmore", 1,         7,
  NA,                 2,         10,
  NA,                 3,         NA,
  "Katherine Burke",  1,         4
)
```

You can fill in these missing values with `tidyr::fill()`.
It works like `select()`, taking a set of columns:

```{r}
treatment |>
  fill(everything())
```

This treatment is sometimes called "last observation carried forward", or **locf** for short.
You can use the `direction` argument to fill in missing values that have been generated in more exotic ways.

### Fixed values

Some times missing values represent some fixed and known value, mostly commonly 0.
You can use `dplyr::coalesce()` to replace them:

```{r}
x <- c(1, 4, 5, 7, NA)
coalesce(x, 0)
```

You could use `mutate()` together with `across()` to apply this treatment to (say) every numeric column in a data frame:

```{r, eval = FALSE}
df |> 
  mutate(across(where(is.numeric), coalesce, 0))
```

### Sentinel values

Sometimes you'll hit the opposite problem where some conrete value actually represents as a missing value.
This typically arises in data generated by older software that doesn't have a proper way to represent missing values, so it must instead use some special value like 99 or -999.

If possible, handle this when reading in the data, for example, by using the `na` argument to `readr::read_csv()`.
If you discover the problem later, or your data source doesn't provide a way to handle on it read, you can use `dplyr::na_if():`

```{r}
x <- c(1, 4, 5, 7, -99)
na_if(x, -99)
```

You could apply this transformation to every numeric column in a data frame with the following code.

```{r, eval = FALSE}
df |> 
  mutate(across(where(is.numeric), na_if, -99))
```

### NaN

Before we continue, there's one special type of missing value that you'll encounter from time-to-time: a `NaN` (pronounced "nan"), or **n**ot **a** **n**umber.
It's not that important to know about because it generally behaves just like `NA`:

```{r}
x <- c(NA, NaN)
x * 10
x == 1
is.na(x)
```

In the rare case you need to distinguish an `NA` from a `NaN`, you can use `is.nan(x)`.

You'll generally encounter a `NaN` when you perform a mathematical operation that has an indeterminate result:

```{r}
0 / 0 
0 * Inf
Inf - Inf
sqrt(-1)
```

## Implicit missing values

So far we've talked about missing values that are **explicitly** missing, i.e. you can see an `NA` in your data.
But missing values can also be **implicitly** missing, if an entire row of data is simply absent from the data.
Let's illustrate the difference with a simple data set that records the price of some stock each quarter:

```{r}
stocks <- tibble(
  year  = c(2020, 2020, 2020, 2020, 2021, 2021, 2021),
  qtr   = c(   1,    2,    3,    4,    2,    3,    4),
  price = c(1.88, 0.59, 0.35,   NA, 0.92, 0.17, 2.66)
)
```

This dataset has two missing observations:

-   The `price` in the fourth quarter of 2020 is explicitly missing, because its value is `NA`.

-   The `price` for the first quarter of 2021 is implicitly missing, because it simply does not appear in the dataset.

One way to think about the difference is with this Zen-like koan:

> An explicit missing value is the presence of an absence.\
>
> An implicit missing value is the absence of a presence.

Sometimes you want to make implicit missings explicit in order to have something physical to work with.
In other cases, explicit missings are forced upon you by the structure of the data and you want to get rid of them.
The following sections discuss some tools for moving between implicit and explicit missingness.

### Pivoting

You've already seen one tool that can make implicit missings explicit and vice versa: pivoting.
Making data wider can make implicit missing values explicit because every combination of the rows and new columns must have some value.
For example, if we pivot `stocks` to put the `quarter` in the columns, both missing become values explicit:

```{r}
stocks |>
  pivot_wider(
    names_from = qtr, 
    values_from = price
  )
```

By default, making data longer preserves explicit missing values, but if they are structural missing values that only exist because the data is not tidy, you can drop them (make them implicit) by setting `drop_na = TRUE`.
See the examples in Chapter \@ref(tidy-data) for more details.

### Complete

`tidyr::complete()` allows you to generate explicit missing values by providing a set of variables that define the combination of rows that should exist.
For example, we know that all combinations of `year` and `qtr` should exist in the `stocks` data:

```{r}
stocks |>
  complete(year, qtr)
```

Typically, you'll call `complete()` with names of existing variables, filling in the missing combinations.
However, sometimes the individual variables are themselves incomplete, so you can instead provide your own data.
For example, you might know that the `stocks` dataset is supposed to run from 2019 to 2021, so you could explicitly supply those values for `year`:

```{r}
stocks |>
  complete(year = 2019:2021, qtr)
```

If the range of a variable is correct, but not all values are present, you could use `full_seq(x, 1)` to generate all values from `min(x)` to `max(x)` spaced out by 1.

In some cases, the complete set of observations can't be generated by a simple combination of variables.
In that case, you can do manually what `complete()` does for you: create a data frame that contains all the rows that should exist (using whatever combination of techniques you need), then combine it with your original dataset with `dplyr::full_join()`.

### Joins

This brings us to another important way of revealing implicitly missing observations: joins.
Often you can only know that values are missing when from one dataset when you go to join it to another.
`dplyr::anti_join()` is particularly useful at revealing these values.
The following example shows how two `anti_join()`s reveals that we're missing information for four airports and 722 planes.

```{r}
library(nycflights13)

flights |> 
  distinct(faa = dest) |> 
  anti_join(airports)

flights |> 
  distinct(tailnum) |> 
  anti_join(planes)
```

The default behavior of joins is to succeed if observations in `x` don't have a match in `y`.
If you're worried about this, and you have dplyr 1.1.0 or newer, you can use the new `unmatched = "error"` argument to tell joins to error if any rows in `x` don't have a match in `y`.

### Exercises

1.  Can you find any relationship between the carrier and the rows that appear to be missing from `planes`?

## Factors and empty groups

A final type of missingness is the empty group, a group that doesn't contain any observations, which can arise when working with factors.
For example, imagine we have a dataset that contains some health information about people:

```{r}
health <- tibble(
  name = c("Ikaia", "Oletta", "Leriah", "Dashay", "Tresaun"),
  smoker = factor(c("no", "no", "no", "no", "no"), levels = c("yes", "no")),
  age = c(34L, 88L, 75L, 47L, 56L),
)
```

And we want to count the number of smokers with `dplyr::count()`:

```{r}
health |> count(smoker)
```

This dataset only contains non-smokers, but we know that smokers exist; the group of non-smoker is empty.
We can request `count()` to keep all the groups, even those not seen in the data by using `.drop = FALSE`:

```{r}
health |> count(smoker, .drop = FALSE)
```

The same principle applies to ggplot2's discrete axes, which will also drop levels that don't have any values.
You can force them to display with by supplying `drop = FALSE` to the appropriate discrete axis:

```{r}
#| fig.align: default
#| out.width: "50%"
#| fig.width: 3
#| fig.alt: 
#| - >
#|   A bar chart with a single value on the x-axis, "no".
#| - >
#|   The same bar chart as the last plot, but now with two values on
#|   the x-axis, "yes" and "no". There is no bar for the "yes" category.
ggplot(health, aes(smoker)) +
  geom_bar() +
  scale_x_discrete()

ggplot(health, aes(smoker)) +
  geom_bar() +
  scale_x_discrete(drop = FALSE)
```

The same problem comes up more generally with `dplyr::group_by()`.
And again you can use `.drop = FALSE` to preserve all factor levels:

```{r}
health |> 
  group_by(smoker, .drop = FALSE) |> 
  summarise(
    n = n(),
    mean_age = mean(age),
    min_age = min(age),
    max_age = max(age),
    sd_age = sd(age)
  )
```

We get some interesting results here because when summarizing an empty group, the summary functions are applied to zero-length vectors.
There's an important distinction between empty vectors, which have length 0, and missing values, which each have length 1.

```{r}
# A vector containing two missing values
x1 <- c(NA, NA)
length(x1)

# A vector containing nothing
x2 <- numeric()
length(x2)
```

All summary functions work with zero-length vectors, but they may return results that are surprising at first glance.
Here we see `mean(age)` returning `NaN` because `mean(age)` = `sum(age)/length(age)` which here is 0/0.
`max()` and `min()` return -Inf and Inf for empty vectors so if you combine the results with a non-empty vector of new data and recompute you'll get the minimum or maximum of the new data[^missing-values-1].

[^missing-values-1]: In other words, `min(c(x, y))` is always equal to `min(min(x), min(y)).`

A sometimes simpler approach is to perform the summary and then make the implicit missings explicit with `complete()`.

```{r}
health |> 
  group_by(smoker) |> 
  summarise(
    n = n(),
    mean_age = mean(age),
    min_age = min(age),
    max_age = max(age),
    sd_age = sd(age)
  ) |> 
  complete(smoker)
```

The main drawback of this approach is that you get an `NA` for the count, even though you know that it should be zero.
