原生 R 环境处理 factor

R 中储存 factor 的步骤

  1. 建立 levels 与整数的映射关系
  2. 按照映射关系,将 factor 转换为整数向量存储

levels 的排序

  1. 默认按字母顺序排序
class <- factor(c("Poor", "Improved", "Excellent"), ordered = T)
class
#> [1] Poor      Improved  Excellent
#> Levels: Excellent < Improved < Poor
  1. 通过 levels 参数人工设定因子型数据各水平的顺序
class <- factor(
  c("Poor", "Improved", "Excellent"),
  levels = c("Poor", "Improved", "Excellent"),
  ordered = T
)
class
#> [1] Poor      Improved  Excellent
#> Levels: Poor < Improved < Excellent
  1. 与 levels 出现的顺序保持一致

在创建因子时,将水平设置为unique(x);或者在创建因子后再对其使用fct_inorder()函数,需要forcats包(包含在tidyverse全家桶中)。

x <- c("A", "T", "T", "A", "C", "K")
y <- factor(x, levels = unique(x))
y
#> [1] A T T A C K
#> Levels: A T C K

x %>%
  factor() %>%
  fct_inorder()
#> [1] A T T A C K
#> Levels: A T C K

使用forcats处理factor

想要以非字母表顺序显示字符串向量时(如一个轴为离散变量的绘图),就需要用到因子。forcats 包中含有大量处理因子的函数。

当字符串向量中有很多重复元素时,用 factor (本质是整数)储存比用字符串节省空间。因此,R 基础包中的很多函数都自动将字符串转换为因子。这意味着因子经常出现在并不真正适合它们的地方。好在不用担心 tidyverse 中会出现这种问题。

library(forcats)

创建因子

要想创建一个因子,必须先创建 levels 向量:

month_levels <- c(
  "Jan", "Feb", "Mar", "Apr", "May", "Jun",
  "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"
)

因子的排序

生成因子时的顺序

## 非因子的排序遵循字母表排序
x1 <- c("Dec", "Apr", "Jan", "Mar", "Mar", "Apr")
x1
#> [1] "Dec" "Apr" "Jan" "Mar" "Mar" "Apr"
sort(x1)
#> [1] "Apr" "Apr" "Dec" "Jan" "Mar" "Mar"

## 因子:按预先声明的因子顺序排序
y1 <- factor(x1, levels = month_levels)
sort(y1)
#> [1] Jan Mar Mar Apr Apr Dec
#> Levels: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

## 因子:字母表排序
y2 <- factor(x1) # 如果省略了定义水平的这个步骤直接创建因子
sort(y2) # 会按字母顺序排序
#> [1] Apr Apr Dec Jan Mar Mar
#> Levels: Apr Dec Jan Mar

## 因子:以初始数据的出现顺序作为默认排序
# 令levels参数为unique(x),或在创建因子后使用fct_inorder()函数
y3 <- factor(x1, levels = unique(x1))
sort(y3)
#> [1] Dec Apr Apr Jan Mar Mar
#> Levels: Dec Apr Jan Mar

y4 <- factor(x1) %>% fct_inorder()
sort(y4)
#> [1] Dec Apr Apr Jan Mar Mar
#> Levels: Dec Apr Jan Mar

fct_relevel()

随时重新手动设定顺序

income <- c("low", "high", "medium", "medium", "low", "high", "high")
x <- factor(income)
x %>% fct_relevel(levels = c("high", "medium", "low"))
#> [1] low    high   medium medium low    high   high  
#> Levels: high medium low
x %>% fct_relevel(levels = c("medium"))
#> [1] low    high   medium medium low    high   high  
#> Levels: medium high low
x %>% fct_relevel("medium", after = Inf)
#> [1] low    high   medium medium low    high   high  
#> Levels: high low medium

fct_rev()

对因子逆序

d <- tibble(
  x = c("a", "a", "b", "b", "c", "c"),
  y = c(2, 2, 1, 5, 0, 3)
)

d %>%
  mutate(x = fct_rev(x)) %>%
  ggplot(aes(x = x, y = y)) +
  geom_point()

fct_reorder()

fct_reorder(x, y, .fun = , .desc = FALSE)

按 x 分类,根据每个分类变量对应 y 值的向量经过 .fun 运算后的结果来对 x 排序

d %>%
  # x轴因子的顺序为字母顺序
  ggplot(aes(x = x, y = y)) +
  geom_point()


d %>%
  # x因子的顺序变为按照每组成员的y值的中位数的降序来排序
  mutate(x = fct_reorder(x, y, .fun = median, .desc = TRUE)) %>%
  ggplot(aes(x = x, y = y)) +
  geom_point()


d %>%
  # x因子的顺序变为按照每组成员的y值的最小值的降序来排序
  mutate(x = fct_reorder(x, y, .fun = median, .desc = TRUE)) %>%
  ggplot(aes(x = x, y = y)) +
  geom_point()

排查输入错误

x2 <- c("Dec", "Apr", "Jam", "Mar")
y5 <- factor(x2, levels = month_levels)
y5 # 不再水平范围内的值自动转换为NA
#> [1] Dec  Apr  <NA> Mar 
#> Levels: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

查看水平:levels()

levels(y1)
#>  [1] "Jan" "Feb" "Mar" "Apr" "May" "Jun" "Jul" "Aug" "Sep" "Oct" "Nov" "Dec"
levels(y2)
#> [1] "Apr" "Dec" "Jan" "Mar"
levels(y3)
#> [1] "Dec" "Apr" "Jan" "Mar"

例:综合社会调查

forcats::gss_cat %>% head(n = 5) # 发现一些字段是factor
#> # A tibble: 5 x 9
#>    year marital         age race  rincome        partyid     relig denom tvhours
#>   <int> <fct>         <int> <fct> <fct>          <fct>       <fct> <fct>   <int>
#> 1  2000 Never married    26 White $8000 to 9999  Ind,near r~ Prot~ Sout~      12
#> 2  2000 Divorced         48 White $8000 to 9999  Not str re~ Prot~ Bapt~      NA
#> 3  2000 Widowed          67 White Not applicable Independent Prot~ No d~       2
#> 4  2000 Never married    39 White Not applicable Ind,near r~ Orth~ Not ~       4
#> 5  2000 Divorced         25 White Not applicable Not str de~ None  Not ~       1

## 查看因子水平
gss_cat %>% count(race) # count()函数
#> # A tibble: 3 x 2
#>   race      n
#>   <fct> <int>
#> 1 Other  1959
#> 2 Black  3129
#> 3 White 16395
ggplot(gss_cat, aes(race)) +
  geom_bar() # 条形图,不显示记数为0的水平

ggplot(gss_cat, aes(race)) +
  geom_bar() +
  scale_x_discrete(drop = FALSE) # 显示记数为0的水平

修改因子的水平

修改水平不仅可以使得图形标签更美观清晰,以满足出版发行的要求,还可以将水平汇集成更高层次的显示。

修改水平最常用、最强大的工具是 fct_recode() 函数,它可以对每个水平进行修改或重新编码,让没有明确提及的水平保持原样,如果不小心修改了一个不存在的水平,它也会给出警告。

gss_cat %>% count(partyid)
#> # A tibble: 10 x 2
#>    partyid                n
#>    <fct>              <int>
#>  1 No answer            154
#>  2 Don't know             1
#>  3 Other party          393
#>  4 Strong republican   2314
#>  5 Not str republican  3032
#>  6 Ind,near rep        1791
#>  7 Independent         4119
#>  8 Ind,near dem        2499
#>  9 Not str democrat    3690
#> 10 Strong democrat     3490

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)
#> # A tibble: 10 x 2
#>    partyid                   n
#>    <fct>                 <int>
#>  1 No answer               154
#>  2 Don't know                1
#>  3 Other party             393
#>  4 Republican, strong     2314
#>  5 Republican, weak       3032
#>  6 Independent, near rep  1791
#>  7 Independent            4119
#>  8 Independent, near dem  2499
#>  9 Democrat, weak         3690
#> 10 Democrat, strong       3490

可以将多个原水平赋给同一个新水平,这样就可以合并原来的分类:

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)
#> # A tibble: 8 x 2
#>   partyid                   n
#>   <fct>                 <int>
#> 1 Other                   548
#> 2 Republican, strong     2314
#> 3 Republican, weak       3032
#> 4 Independent, near rep  1791
#> 5 Independent            4119
#> 6 Independent, near dem  2499
#> 7 Democrat, weak         3690
#> 8 Democrat, strong       3490

也可以使用 fct_recode() 函数的变体 fct_collapse() 函数。对于每个新水平,你都可以提供一个包含原水平的向量:

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)
#> # A tibble: 4 x 2
#>   partyid     n
#>   <fct>   <int>
#> 1 other     548
#> 2 rep      5346
#> 3 ind      8409
#> 4 dem      7180
---
title: "Factor"
subtitle: ''
author: "Humoon"
date: "`r Sys.Date()`"
output:
  html_document: 
    code_download: true
    css: ["../css/style.css"]
    fig_caption: yes
    theme: united
    highlight: haddock
    number_sections: no
    toc: yes
    toc_depth: 4
    toc_float:
      collapsed: yes
      smooth_scroll: yes
documentclass: ctexart
classoption: hyperref,
---

```{r setup, include = FALSE}
source("../Rmarkdown-template/Rmarkdown_config.R")

## global options ===================================
knitr::opts_chunk$set(
  width = config$width,
  fig.width = config$fig.width,
  fig.asp = config$fig.asp,
  out.width = config$out.width,
  fig.align = config$fig.align,
  fig.path = config$fig.path,
  fig.show = config$fig.show,
  warn = config$warn,
  warning = config$warning,
  message = config$message,
  echo = config$echo,
  eval = config$eval,
  tidy = config$tidy,
  comment = config$comment,
  collapse = config$collapse,
  cache = config$cache,
  cache.comments = config$cache.comments,
  autodep = config$autodep
)

## use necessary packages ==============================
library(tidyverse)
library(data.table)
library(magrittr)
library(plotly)
library(htmlwidgets)
```



## 原生 R 环境处理 factor

### R 中储存 factor 的步骤

1. 建立 levels 与整数的映射关系
2. 按照映射关系，将 factor 转换为整数向量存储

### levels 的排序

1. 默认按字母顺序排序
```{r}
class <- factor(c("Poor", "Improved", "Excellent"), ordered = T)
class
```

2. 通过 levels 参数人工设定因子型数据各水平的顺序
```{r}
class <- factor(
  c("Poor", "Improved", "Excellent"),
  levels = c("Poor", "Improved", "Excellent"),
  ordered = T
)
class
```

3. 与 levels 出现的顺序保持一致

在创建因子时，将水平设置为`unique(x)`；或者在创建因子后再对其使用`fct_inorder()`函数，需要forcats包（包含在tidyverse全家桶中）。

```{r}
x <- c("A", "T", "T", "A", "C", "K")
y <- factor(x, levels = unique(x))
y

x %>%
  factor() %>%
  fct_inorder()
```


## 使用forcats处理factor

想要**以非字母表顺序显示字符串向量时（如一个轴为离散变量的绘图），就需要用到因子**。forcats 包中含有大量处理因子的函数。

当字符串向量中有很多重复元素时，用 factor （本质是整数）储存比用字符串节省空间。因此，R 基础包中的很多函数都自动将字符串转换为因子。这意味着因子经常出现在并不真正适合它们的地方。好在不用担心 tidyverse 中会出现这种问题。

```{r}
library(forcats)
```

### 创建因子

要想创建一个因子，必须先创建 levels 向量：

```{r}
month_levels <- c(
  "Jan", "Feb", "Mar", "Apr", "May", "Jun",
  "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"
)
```


### 因子的排序

#### 生成因子时的顺序

```{r}
## 非因子的排序遵循字母表排序
x1 <- c("Dec", "Apr", "Jan", "Mar", "Mar", "Apr")
x1
sort(x1)

## 因子：按预先声明的因子顺序排序
y1 <- factor(x1, levels = month_levels)
sort(y1)

## 因子：字母表排序
y2 <- factor(x1) # 如果省略了定义水平的这个步骤直接创建因子
sort(y2) # 会按字母顺序排序

## 因子：以初始数据的出现顺序作为默认排序
# 令levels参数为unique(x)，或在创建因子后使用fct_inorder()函数
y3 <- factor(x1, levels = unique(x1))
sort(y3)

y4 <- factor(x1) %>% fct_inorder()
sort(y4)
```

#### `fct_relevel()`

随时重新手动设定顺序

```{r}
income <- c("low", "high", "medium", "medium", "low", "high", "high")
x <- factor(income)
x %>% fct_relevel(levels = c("high", "medium", "low"))
x %>% fct_relevel(levels = c("medium"))
x %>% fct_relevel("medium", after = Inf)
```

#### `fct_rev()`

对因子逆序

```{r}
d <- tibble(
  x = c("a", "a", "b", "b", "c", "c"),
  y = c(2, 2, 1, 5, 0, 3)
)

d %>%
  mutate(x = fct_rev(x)) %>%
  ggplot(aes(x = x, y = y)) +
  geom_point()
```

#### `fct_reorder()`

`fct_reorder(x, y, .fun = , .desc = FALSE)`

按 x 分类，根据每个分类变量对应 y 值的向量经过 .fun 运算后的结果来对 x 排序

```{r}
d %>%
  # x轴因子的顺序为字母顺序
  ggplot(aes(x = x, y = y)) +
  geom_point()

d %>%
  # x因子的顺序变为按照每组成员的y值的中位数的降序来排序
  mutate(x = fct_reorder(x, y, .fun = median, .desc = TRUE)) %>%
  ggplot(aes(x = x, y = y)) +
  geom_point()

d %>%
  # x因子的顺序变为按照每组成员的y值的最小值的降序来排序
  mutate(x = fct_reorder(x, y, .fun = median, .desc = TRUE)) %>%
  ggplot(aes(x = x, y = y)) +
  geom_point()
```

### 排查输入错误

```{r}
x2 <- c("Dec", "Apr", "Jam", "Mar")
y5 <- factor(x2, levels = month_levels)
y5 # 不再水平范围内的值自动转换为NA
```

### 查看水平：levels()
```{r}
levels(y1)
levels(y2)
levels(y3)
```

### 例：综合社会调查

```{r}
forcats::gss_cat %>% head(n = 5) # 发现一些字段是factor

## 查看因子水平
gss_cat %>% count(race) # count()函数
ggplot(gss_cat, aes(race)) +
  geom_bar() # 条形图，不显示记数为0的水平
ggplot(gss_cat, aes(race)) +
  geom_bar() +
  scale_x_discrete(drop = FALSE) # 显示记数为0的水平
```

### 修改因子的水平

修改水平不仅可以使得图形标签更美观清晰，以满足出版发行的要求，还可以将水平汇集成更高层次的显示。

修改水平最常用、最强大的工具是 `fct_recode()` 函数，它可以对每个水平进行修改或重新编码，让没有明确提及的水平保持原样，如果不小心修改了一个不存在的水平，它也会给出警告。

```{r}
gss_cat %>% count(partyid)

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)
```

可以将多个原水平赋给同一个新水平，这样就可以合并原来的分类：

```{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)
```

也可以使用 fct_recode() 函数的变体 fct_collapse() 函数。对于每个新水平，你都可以提供一个包含原水平的向量：

```{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)
```
