geom_density (ggplot2): one density plot with different groups

[Edit] I have realized that geom_density may not be the best way to go for conveying the message I wanted. The plot was meant to visualize that 1) 50m has fewer event occurrences and 2) for 100m and 200m, the peaks of event occurrence are at 12. Would there be a better way to represent the data? The first plot @Alan has kindly provided is almost perfect for conveying such messages - but it fails when the data for 50m are too close to each other due to the kernel smoothing @r2evans has mentioned.

I am trying to plot a density plot using geom_density under ggplot2 that shows the number of times (proportion) an event occurs at different times at different distances. Below is the mock data.

data.frame(
  distance = c(rep("50", 4), rep("100", 98), rep("200", 98)),
  time = c(7,8,8,9, rnorm(196, 12, 2))

this df has 200 datapoints, 4 at 50m, 98 at 100m, and 98 at 200m. When I use geom_density with the df:

data.frame(
  distance = c(rep("50", 4), rep("100", 98), rep("200", 98)),
  time = c(7,8,8,9, rnorm(196, 12, 2))) |>
  ggplot(aes(x = time, fill = distance, color = distance)) +
  geom_density(alpha = 0.1)

However, looking at this plot, gives the impression that 50m is a lot more prevalent. Why is this happening? I wondered the function calculated the density per distance, but having the peak close to 0.8 for the 50m does not really make sense to me.

Is it possible to calculate the density such that the overall area is 1 i.e., the 50m curve will have an area of 0.02?

You can use aes(y = after_stat(density * n/nrow(df)) if you want the summed areas under all 3 curves to add to 1. Since you are piping the data frame, you will need to do after_stat(density * n/200) (i.e. enter the denominator manually).

set.seed(1)

data.frame(
  distance = c(rep("50", 4), rep("100", 98), rep("200", 98)),
  time = c(7,8,8,9, rnorm(196, 12, 2))) |>
  ggplot(aes(x = time, fill = distance, color = distance)) +
  geom_density(alpha = 0.1, aes(y = after_stat(density * n/200)), bw = 0.5) 

We can see this is correct by stacking the three densities on top of each other. This should give an identical result to plotting the density of the whole column without splitting into different color groups (here we show the overall density as a dashed black line):

set.seed(1)

data.frame(
  distance = c(rep("50", 4), rep("100", 98), rep("200", 98)),
  time = c(7,8,8,9, rnorm(196, 12, 2))) |>
  ggplot(aes(x = time, fill = distance, color = distance)) +
  geom_density(alpha = 0.1, aes(y = after_stat(density * n/200)), 
               position = 'stack', bw = 0.5) +
  geom_density(color = 'black', fill = NA, linetype = 2, bw = 0.5)

You could make the density values ahead of time with density() (or something else if you like) then scale the y-values by the proportion of the distance values in the dataset:

library(dplyr)
library(ggplot2)
library(tidyr)
data.frame(
  distance = c(rep("50", 4), rep("100", 98), rep("200", 98)),
  time = c(7,8,8,9, rnorm(196, 12, 2))) |>
  group_by(distance) %>% 
  mutate(n = n()) |> 
  ungroup() |>
  mutate(scale = n/n()) |> 
  group_by(distance) |> 
  reframe(scale = first(scale), 
          d = list(broom::tidy(density(time)))) |> 
  unnest(d) |> 
  mutate(y_scaled = y*scale) |> 
  ggplot(aes(x=x, y=y_scaled, colour=distance)) + 
  geom_area(aes(fill=distance), position="identity", alpha=.2) + 
  labs(x="Time", y="Density (scaled)")

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^{Created on 2023-03-09 with reprex v2.0.2}