factors.Rmd

# Factors

## Introduction

In R, factors are used to work with categorical variables, variables that have a fixed and known set of possible values. They are also useful when you want to display character vectors in a non-alphabetical order.

Historically, factors were much easier to work with than characters. As a result, many of the functions in base R automatically convert characters to factors. This means that factors often crop up in places where they're not actually helpful. Fortunately, you don't need to worry about that in the tidyverse, and can focus on situations where factors are genuinely useful.

For more historical context on factors, I recommend [_stringsAsFactors: An unauthorized biography_](http://simplystatistics.org/2015/07/24/stringsasfactors-an-unauthorized-biography/) by Roger Peng, and [_stringsAsFactors = \<sigh\>_](http://notstatschat.tumblr.com/post/124987394001/stringsasfactors-sigh) by Thomas Lumley.


### Prerequisites

To work with factors, we'll use the __forcats__ package, which provides tools for dealing with **cat**egorical variables (and it's an anagram of factors!). It provides a wide range of helpers for working with factors. We'll also need dplyr for some data manipulation, and ggplot2 for visualisation.

```{r setup, message = FALSE}
library(forcats)
library(ggplot2)
library(dplyr)
```

## Creating factors

Typically you'll convert a factor from a character vector, using `factor()`. Apart from the character input, the most important argument is the list of valid __levels__:

```{r}
x <- c("pear", "apple", "banana", "apple", "pear", "apple")
factor(x, levels = c("apple", "banana", "pear"))
```

Any values not in the list of levels will be silently converted to `NA`:

```{r}
factor(x, levels = c("apple", "banana"))
```

If you omit the levels, they'll be taken from the data in alphabetical order:

```{r}
factor(x)
```

Sometimes you'd prefer that the order of the levels match the order of the first appearance in the data. You can do that when creating the factor by setting levels to `unique(x)`, or after the fact, with `fct_inorder()`:

```{r}
f1 <- factor(x, levels = unique(x))
f1

f2 <- x %>% factor() %>% fct_inorder()
f2
```

If you ever need to access the set of valid levels directly, you can do so with `levels()`:

```{r}
levels(f2)
```

## General Social Survey

For the rest of this chapter, we're going to focus on `forcats::gss_cat`. It's a sample of data from the [General Social Survey](http://gss.norc.org), which is a long-running US survey conducted by the independent research organization NORC at the University of Chicago. The survey has thousands of questions, so in `gss_cat` I've selected a handful that will illustrate some common challenges you'll encounter when working with factors.

```{r}
gss_cat
```

(Remember, since this dataset is provided by a package, you can get more information about the variables with `?gss_cat`.)

When factors are stored in a tibble, you can't see their levels so easily. One way to see them is with `count()`:

```{r}
gss_cat %>%
  count(race)
```

Or with a bar chart:

```{r}
ggplot(gss_cat, aes(race)) +
  geom_bar()
```

By default, ggplot2 will drop levels that don't have any values. You can force them to display with:

```{r}
ggplot(gss_cat, aes(race)) +
  geom_bar() +
  scale_x_discrete(drop = FALSE)
```

These levels represent valid values that simply did not occur in this dataset. Unfortunately, dplyr doesn't yet have a `drop` option, but it will in the future.

When working with factors, the two most common operations are changing the order of the levels, and changing the values of the levels. Those operations are described in the sections below.

### Exercise

1.  Explore the distribution of `rincome` (reported income). What makes the
    default bar chart hard to understand? How could you improve the plot?

1.  What is the most common `religion` in this survey? What's the most
    common `partyid`?

1.  Which `religion` does `denom` (denomination) apply to? How can you find
    out with a table? How can you find out with a visualisation?

## Modifying factor order

It's often useful to change the order of the factor levels in a visualisation. For example, imagine you want to explore the average number of hours spent watching TV per day across religions:

```{r}
relig <- gss_cat %>%
  group_by(relig) %>%
  summarise(
    age = mean(age, na.rm = TRUE),
    tvhours = mean(tvhours, na.rm = TRUE),
    n = n()
  )

ggplot(relig, aes(tvhours, relig)) + geom_point()
```

It is difficult to interpret this plot because there's no overall pattern. We can improve it by reordering the levels of `relig` using `fct_reorder()`. `fct_reorder()` takes three arguments:

* `f`, the factor whose levels you want to modify.
* `x`, a numeric vector that you want to use to reorder the levels.
* Optionally, `fun`, a function that's used if there are multiple values of
  `x` for each value of `f`. The default value is `median`.

```{r}
ggplot(relig, aes(tvhours, fct_reorder(relig, tvhours))) +
  geom_point()
```

Reordering religion makes it much easier to see that people in the "Don't know" category watch much more TV, and Hinduism & Other Eastern religions watch much less.

As you start making more complicated transformations, I'd recommend moving them out of `aes()` and into a separate `mutate()` step. For example, you could rewrite the plot above as:

```{r, eval = FALSE}
relig %>%
  mutate(relig = fct_reorder(relig, tvhours)) %>%
  ggplot(aes(tvhours, relig)) +
    geom_point()
```
What if we create a similar plot looking at how average age varies across reported income level?

```{r}
rincome <- gss_cat %>%
  group_by(rincome) %>%
  summarise(
    age = mean(age, na.rm = TRUE),
    tvhours = mean(tvhours, na.rm = TRUE),
    n = n()
  )

ggplot(rincome, aes(age, fct_reorder(rincome, age))) + geom_point()
```

Here, arbitrarily reordering the levels isn't a good idea! That's because `rincome` already has a principled order that we shouldn't mess with. Reserve `fct_reorder()` for factors whose levels are arbitrarily ordered.

However, it does make sense to pull "Not applicable" to the front with the other special levels. You can use `fct_relevel()`. It takes a factor, `f`, and then any number of levels that you want to move to the front of the line.

```{r}
ggplot(rincome, aes(age, fct_relevel(rincome, "Not applicable"))) +
  geom_point()
```

Why do you think the average age for "Not applicable" is so high?

Another type of reordering is useful when you are colouring the lines on a plot. `fct_reorder2()` reorders the factor by the `y` values associated with the largest `x` values. This makes the plot easier to read because the line colours line up with the legend.

```{r, fig.align = "default", out.width = "50%", fig.width = 4}
by_age <- gss_cat %>%
  filter(!is.na(age)) %>%
  group_by(age, marital) %>%
  count() %>%
  mutate(prop = n / sum(n))

ggplot(by_age, aes(age, prop, colour = marital)) +
  geom_line(na.rm = TRUE)

ggplot(by_age, aes(age, prop, colour = fct_reorder2(marital, age, prop))) +
  geom_line() +
  labs(colour = "marital")
```

Finally, for bar plots, you can use `fct_infreq()` to order levels in increasing frequency: this is the simplest type of reordering because it doesn't need any extra variables. You may want to combine with `fct_rev()`.

```{r}
gss_cat %>%
  mutate(marital = marital %>% fct_infreq() %>% fct_rev()) %>%
  ggplot(aes(marital)) +
    geom_bar()
```

### Exercises

1.  There are some suspiciously high numbers in `tvhours`. Is the mean a good
    summary?

1.  For each factor in `gss_cat` identify whether the order of the levels is
    arbitrary or principled.

1.  Why did moving "Not applicable" to the front of the levels move it to the
    bottom of the plot?

1.  Recreate the display of marital status by age, using `geom_area()` instead
    of `geom_line()`. What do you need to change to the plot? How might you
    tweak the levels?

## Modifying factor levels

More powerful than changing the orders of the levels is changing their values. This allows you to clarify labels for publication, and collapse levels for high-level displays. The most general and powerful tool is `fct_recode()`. It allows you to recode, or change, the value of each level. For example, take the `gss_cat$partyid`:

```{r}
gss_cat %>% count(partyid)
```

The levels are terse and inconsistent. Let's tweak them to be longer and use a parallel construction.

```{r}
gss_cat %>%
  mutate(partyid = fct_recode(partyid,
    "Republican, strong"    = "Strong republican",
    "Republican, weak"      = "Not str republican",
    "Independent, near rep" = "Ind,near rep",
    "Independent, near dem" = "Ind,near dem",
    "Democrat, weak"        = "Not str democrat",
    "Democrat, strong"      = "Strong democrat"
  )) %>%
  count(partyid)
```

`fct_recode()` will leave levels that aren't explicitly mentioned as is, and will warn you if you accidentally refer to a level that doesn't exist.

To combine groups, you can assign multiple old levels to the same new level:

```{r}
gss_cat %>%
  mutate(partyid = fct_recode(partyid,
    "Republican, strong"    = "Strong republican",
    "Republican, weak"      = "Not str republican",
    "Independent, near rep" = "Ind,near rep",
    "Independent, near dem" = "Ind,near dem",
    "Democrat, weak"        = "Not str democrat",
    "Democrat, strong"      = "Strong democrat",
    "Other"                 = "No answer",
    "Other"                 = "Don't know",
    "Other"                 = "Other party"
  )) %>%
  count(partyid)
```

You must use this technique with care: if you group together categories that are truly different you will end up with misleading results.

If you want to collapse a lot of levels, `fct_collapse()` is a useful variant of `fct_recode()`. For each new variable, you can provide a vector of old levels:

```{r}
gss_cat %>%
  mutate(partyid = fct_collapse(partyid,
    other = c("No answer", "Don't know", "Other party"),
    rep = c("Strong republican", "Not str republican"),
    ind = c("Ind,near rep", "Independent", "Ind,near dem"),
    dem = c("Not str democrat", "Strong democrat")
  )) %>%
  count(partyid)
```

Sometimes you just want to lump together all the small groups to make a plot or table simpler. That's the job of `fct_lump()`:

```{r}
gss_cat %>%
  mutate(relig = fct_lump(relig)) %>%
  count(relig)
```

The default behaviour is to progressively lump together the smallest groups, ensuring that the aggregate is still the smallest group. In this case it's not very helpful: it is true that the majority of Americans in this survey are Protestant, but we've probably over collapsed.

Instead, we can use the `n` parameter to specify how many groups (excluding other) we want to keep:

```{r}
gss_cat %>%
  mutate(relig = fct_lump(relig, n = 10)) %>%
  count(relig, sort = TRUE) %>%
  print(n = Inf)
```

### Exercises

1.  How have the proportions of people identifying as Democrat, Republican, and
    Independent changed over time?

1.  Display the joint distribution of the  `relig` and `denom` variables in
    a single plot.

1.  How could you collapse `rincome` into a small set of categories?