使用 ggplot 的多 x 轴来呈现 z 分数、智商分数和原始数据

Question

只是结合上下文，我从事心理测量/心理测试。我有一个由“点”、“百分位数”、“z_real”、“z_normal”、“iq”组成的数据集。我想要一个 ggplot，其中可以呈现 Z_score（来自我的原始数据）、z_score（具有基础正态分布），然后有两个带有“原始分数”和“智商分数”的补充 x 轴。这在统计中很常见，您可以在下面查看

这是目前的剧情

这是我得到的最好的解决方案

这就是想要的剧情

我正在与 tidyverse 合作，我想留在其中。以前的一些帖子对我有帮助，例如这个[一] [5]和这个[一] [6]。

谢谢。（部分）数据和代码在这里：

ask_ds <- structure(list(points = c(17, 17, 2, 16, 11, 17, 20, 16, 19, 
                                    15, 9, 14, 14, 16, 13, 13, 22, 21, 25, 17, 17, 17, 20, 6, 11, 
                                    5, 10, 23, 21, 19, 11, 15, 13, 17, 17, 17, 9, 18, 12, 22, 21, 
                                    23, 8, 12, 6, 7, 22, 12, 21, 16, 12, 5, 19, 19, 21, 13, 12, 18, 
                                    22, 13, 21, 24, 23, 4, 12, 19, 2, 22, 14, 16, 24, 19, 7, 12, 
                                    18, 14, 9, 18, 7, 22, 3, 18, 14, 22, 15, 11, 15, 19, 25, 9, 19, 
                                    16, 13, 19, 14, 15, 20, 3, 23, 9, 7, 22, 9, 22, 17, 12, 14, 11, 
                                    7, 9, 19, 16, 19, 10, 24, 14, 12, 18, 19, 24, 22, 11, 11, 15, 
                                    17, 15, 11, 11, 14, 24, 14, 21, 16, 10, 19, 21, 15, 20, 15, 20, 
                                    22, 10, 22, 16, 14, 16, 8, 16, 9, 15), percentile = c(63, 61, 
                                                                                          1, 56, 25, 59, 80, 55, 74, 49, 17, 45, 44, 57, 36, 32, 90, 85, 
                                                                                          99, 63, 63, 60, 82, 7, 24, 5, 20, 93, 83, 75, 24, 50, 35, 64, 
                                                                                          62, 61, 16, 65, 28, 90, 85, 93, 12, 28, 7, 8, 90, 26, 87, 55, 
                                                                                          30, 4, 74, 73, 87, 33, 30, 67, 91, 35, 86, 95, 93, 3, 29, 75, 
                                                                                          1, 89, 44, 55, 96, 75, 8, 27, 66, 41, 13, 68, 9, 91, 2, 65, 44, 
                                                                                          89, 51, 22, 46, 74, 98, 13, 76, 58, 37, 73, 43, 50, 79, 2, 93, 
                                                                                          17, 8, 91, 14, 92, 60, 26, 43, 25, 10, 14, 73, 57, 76, 18, 96, 
                                                                                          40, 31, 70, 73, 96, 91, 24, 23, 47, 59, 51, 24, 22, 40, 96, 45, 
                                                                                          85, 57, 17, 73, 86, 50, 79, 48, 81, 91, 21, 89, 53, 43, 58, 11, 
                                                                                          53, 14, 47), z_real = structure(c(0.36, 0.36, -2.38, 0.18, -0.73, 
                                                                                                                            0.36, 0.91, 0.18, 0.73, 0, -1.1, -0.19, -0.19, 0.18, -0.37, -0.37, 
                                                                                                                            1.28, 1.09, 1.83, 0.36, 0.36, 0.36, 0.91, -1.65, -0.73, -1.83, 
                                                                                                                            -0.92, 1.46, 1.09, 0.73, -0.73, 0, -0.37, 0.36, 0.36, 0.36, -1.1, 
                                                                                                                            0.55, -0.55, 1.28, 1.09, 1.46, -1.28, -0.55, -1.65, -1.47, 1.28, 
                                                                                                                            -0.55, 1.09, 0.18, -0.55, -1.83, 0.73, 0.73, 1.09, -0.37, -0.55, 
                                                                                                                            0.55, 1.28, -0.37, 1.09, 1.64, 1.46, -2.01, -0.55, 0.73, -2.38, 
                                                                                                                            1.28, -0.19, 0.18, 1.64, 0.73, -1.47, -0.55, 0.55, -0.19, -1.1, 
                                                                                                                            0.55, -1.47, 1.28, -2.2, 0.55, -0.19, 1.28, 0, -0.73, 0, 0.73, 
                                                                                                                            1.83, -1.1, 0.73, 0.18, -0.37, 0.73, -0.19, 0, 0.91, -2.2, 1.46, 
                                                                                                                            -1.1, -1.47, 1.28, -1.1, 1.28, 0.36, -0.55, -0.19, -0.73, -1.47, 
                                                                                                                            -1.1, 0.73, 0.18, 0.73, -0.92, 1.64, -0.19, -0.55, 0.55, 0.73, 
                                                                                                                            1.64, 1.28, -0.73, -0.73, 0, 0.36, 0, -0.73, -0.73, -0.19, 1.64, 
                                                                                                                            -0.19, 1.09, 0.18, -0.92, 0.73, 1.09, 0, 0.91, 0, 0.91, 1.28, 
                                                                                                                            -0.92, 1.28, 0.18, -0.19, 0.18, -1.28, 0.18, -1.1, 0), .Dim = c(150L, 
                                                                                                                                                                                            1L), "`\`\`\`scaled:center\`\`\``" = 15.0143288084465, "`\`\`\`scaled:scale\`\`\``" = 5.47051980922509), 
                         z_normal = c(0.33, 0.28, -2.33, 0.15, -0.67, 0.23, 0.84, 
                                      0.13, 0.64, -0.03, -0.95, -0.13, -0.15, 0.18, -0.36, -0.47, 
                                      1.28, 1.04, 2.33, 0.33, 0.33, 0.25, 0.92, -1.48, -0.71, -1.64, 
                                      -0.84, 1.48, 0.95, 0.67, -0.71, 0, -0.39, 0.36, 0.31, 0.28, 
                                      -0.99, 0.39, -0.58, 1.28, 1.04, 1.48, -1.17, -0.58, -1.48, 
                                      -1.41, 1.28, -0.64, 1.13, 0.13, -0.52, -1.75, 0.64, 0.61, 
                                      1.13, -0.44, -0.52, 0.44, 1.34, -0.39, 1.08, 1.64, 1.48, 
                                      -1.88, -0.55, 0.67, -2.33, 1.23, -0.15, 0.13, 1.75, 0.67, 
                                      -1.41, -0.61, 0.41, -0.23, -1.13, 0.47, -1.34, 1.34, -2.05, 
                                      0.39, -0.15, 1.23, 0.03, -0.77, -0.1, 0.64, 2.05, -1.13, 
                                      0.71, 0.2, -0.33, 0.61, -0.18, 0, 0.81, -2.05, 1.48, -0.95, 
                                      -1.41, 1.34, -1.08, 1.41, 0.25, -0.64, -0.18, -0.67, -1.28, 
                                      -1.08, 0.61, 0.18, 0.71, -0.92, 1.75, -0.25, -0.5, 0.52, 
                                      0.61, 1.75, 1.34, -0.71, -0.74, -0.08, 0.23, 0.03, -0.71, 
                                      -0.77, -0.25, 1.75, -0.13, 1.04, 0.18, -0.95, 0.61, 1.08, 
                                      0, 0.81, -0.05, 0.88, 1.34, -0.81, 1.23, 0.08, -0.18, 0.2, 
                                      -1.23, 0.08, -1.08, -0.08), iq = c(104.98, 104.19, 65.1, 
                                                                         102.26, 89.88, 103.41, 112.62, 101.88, 109.65, 99.62, 85.69, 
                                                                         98.12, 97.74, 102.65, 94.62, 92.98, 119.22, 115.55, 134.9, 
                                                                         104.98, 104.98, 103.8, 113.73, 77.86, 89.41, 75.33, 87.38, 
                                                                         122.14, 114.31, 110.12, 89.41, 100, 94.22, 105.38, 104.58, 
                                                                         104.19, 85.08, 105.78, 91.26, 119.22, 115.55, 122.14, 82.38, 
                                                                         91.26, 77.86, 78.92, 119.22, 90.35, 116.9, 101.88, 92.13, 
                                                                         73.74, 109.65, 109.19, 116.9, 93.4, 92.13, 106.6, 120.11, 
                                                                         94.22, 116.2, 124.67, 122.14, 71.79, 91.7, 110.12, 65.1, 
                                                                         118.4, 97.74, 101.88, 126.26, 110.12, 78.92, 90.81, 106.19, 
                                                                         96.59, 83.1, 107.02, 79.89, 120.11, 69.19, 105.78, 97.74, 
                                                                         118.4, 100.38, 88.42, 98.49, 109.65, 130.81, 83.1, 110.59, 
                                                                         103.03, 95.02, 109.19, 97.35, 100, 112.1, 69.19, 122.14, 
                                                                         85.69, 78.92, 120.11, 83.8, 121.08, 103.8, 90.35, 97.35, 
                                                                         89.88, 80.78, 83.8, 109.19, 102.65, 110.59, 86.27, 126.26, 
                                                                         96.2, 92.56, 107.87, 109.19, 126.26, 120.11, 89.41, 88.92, 
                                                                         98.87, 103.41, 100.38, 89.41, 88.42, 96.2, 126.26, 98.12, 
                                                                         115.55, 102.65, 85.69, 109.19, 116.2, 100, 112.1, 99.25, 
                                                                         113.17, 120.11, 87.9, 118.4, 101.13, 97.35, 103.03, 81.6, 
                                                                         101.13, 83.8, 98.87)), row.names = c(NA, -150L), class = c("tbl_df", 
                                                                                                                                    "tbl", "data.frame"))
ask_ds %>% 
  select(z_real, z_normal) %>% 
  pivot_longer(everything()) %>% 
  ggplot(., aes(value, fill = name)) + 
  geom_density(alpha=.2) +
  scale_x_continuous(breaks=-3:3, labels=parse(text=paste(-3:3, '*sigma')) ,
                     "Standard deviation", 
                     sec.axis = sec_axis(trans = ~.* sd(ask_ds$points) +
                                           mean(ask_ds$points), 
                                         "Raw score")) 


gridExtra::grid.arrange(ask_ds %>% 
                          select(z_real, z_normal) %>% 
                          pivot_longer(everything()) %>% 
                          ggplot(., aes(value, fill = name)) + 
                          geom_density(alpha=.2) ,
                        
                        ggplot(ask_ds, aes(points)) +
                          geom_density()
                        
)

Answer 1

我认为这里问题的核心是如何获取多个 x 轴，所以我将回答这个问题，而不是试图理解您的数据的含义。在 ggplot2 中没有“正确”的方法来引入多个 x 轴，但是，您可以通过将一堆微小的高度图放在彼此下方来解决此问题。为此我推荐 patchwork 包。

我们首先绘制我们想要说明的图，我将使用一些虚拟数据来完成此操作：

library(ggplot2)
library(patchwork)

set.seed(0)
df <- data.frame(
  x = rnorm(100, 100, 15)
)

dens <- ggplot(df, aes(x)) +
  geom_density() +
  labs(x = "IQ") +
  theme(axis.line.x = element_line())

接下来，我们将制作两个虚拟图，其中将训练 x 轴，但不绘制几何图形。此外，纵横比设置为一个较小的数字，使其看起来好像这只是轴线并且没有发生任何绘图。这通常仅在从一个轴到下一个轴的线性平移时才起作用。我不是心理测量学家，但我认为 IQ 大致为~N(100, 15)，因此我们需要将其逆变换为 Z 分数的标准正常值。

zscore_axis <- ggplot(df, aes((x - 100) / 15)) +
  labs(x = "Z-score") +
  theme(axis.line.x = element_line(),
        aspect.ratio = 1e-8)

quantile_axis <- ggplot(df, aes((x - 100) / 15)) +
  labs(x = "Quantile") +
  scale_x_continuous(breaks = qnorm(seq(0.1, 0.9, by = 0.1)),
                     labels = seq(0.1, 0.9, by = 0.1)) +
  theme(axis.line.x = element_line(),
        aspect.ratio = 1e-8)

最后，通过拼凑魔法，我们将所有三个图放在另一个图下方。

dens / zscore_axis / quantile_axis

^{由reprex 包(v0.3.0)于 2020-09-17 创建}

这就是我制作多个 x 轴的方法。我不太确定这将如何处理您的数据。您可以适应自己的指标，例如原始分数，只要它们是数据的线性转换即可。