# Missing values {#missing-values}

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

## 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).
Now we'll come back to them in more depth, so you can learn more of the details.

We'll start by discussing some general tools for working with missing values recorded as `NA`s.
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 related discussion 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 missing explicit values, i.e. cells where you see an `NA`.

### Last observation carried forward

A common use for missing values is as a data entry convenience.
Sometimes data that has been entered by hand, missing values indicate that the value in the previous row has been repeated:

```{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 where you want missing values to be replaced by last observation carried forward:

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

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 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 to 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 value should actually be treated as a missing value.
This typically arises in data generated by older software which doesn't have an explicit way to represent missing values, so it uses some special sentinel 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)
```

And 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 with missing values that are **explicitly** missing, i.e. you can see them in your data as an `NA`.
But missing values can also be **implicitly** missing, if an entire row of data is simply absent from the data.
Let's illustrate this idea with a simple data set, which records the price of a stock in 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 2021 is explicitly missing, because its value is `NA`.

-   The `price` for the first quarter of 2022 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.

It's often useful to make implicit missings explicit so you have something physical that you can work with.
In other cases, explicit missings are forced upon you by the structure of the data.
The following sections discuss some tools for moving between implicit and explict.

### 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 in tidy data by providing a set of variables that generates all rows that should exist:

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

Typically, you'll call `complete()` with names of variables that already exist, filling in their missing combinations.
However, sometimes the individual variables are themselves incomplete, so you can also provide your own data.
For example, you might know that this 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 with `complete()`.
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 empty groups, groups that don't contain any observation, 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()`.
You can request that all factor levels be preserved with `.drop = TRUE`:

```{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 we are a summarizing an empty group, so the summary functions are applied to zero-length vectors.
Zero-length vectors are empty, not missing:

```{r}
x1 <- c(NA, NA)
length(x1)

x2 <- numeric()
length(x2)
```

Summary functions do 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 min or max of the new data.

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.
