How to plot a function family in ggplot2

Question

I need to plot a family of functions variying according to a set of parameters, say, a family of normal distribution curves that depend on the mean and standard deviation. I found here, a code snipet that almost do the task:

p9 <- ggplot(data.frame(x = c(0, 1)), aes(x = x)) +
    stat_function(fun = dnorm, args = list(0.2, 0.1),
                  aes(colour = "Group 1")) +
    stat_function(fun = dnorm, args = list(0.7, 0.05),
                  aes(colour = "Group 2")) +
    scale_x_continuous(name = "Probability",
                          breaks = seq(0, 1, 0.2),
                          limits=c(0, 1)) +
    scale_y_continuous(name = "Frequency") +
    ggtitle("Normal function curves of probabilities") +
    scale_colour_brewer(palette="Accent") +
    labs(colour = "Groups")
p9 

In this case, the code plots exactly two curves, as shown below:

My problem is that the number of curves in the family could be any, thus I tried to adapt the code as follows:

aa <- list(list(0.2, 0.1), list(0.7, 0.05), list(0.45, 0.2))
p9 <- ggplot(data.frame(x = c(0, 1)), aes(x = x))
for (i in 1:3) {
    p9 <- p9 + stat_function(fun = dnorm, args = aa[[i]],
                         aes(colour = paste("Group", i))
}
p9 <- p9 + 
  scale_x_continuous(name = "Probability",
                   breaks = seq(0, 1, 0.2),
                   limits=c(0, 1)) +
  scale_y_continuous(name = "Frequency") +
  ggtitle("Normal function curves of probabilities") +
  scale_colour_brewer(palette="Accent") +
  labs(colour = "Groups")
p9

The result is almost successful in that it depicts the three curves, except that it does not distinguish them by colors nor in the legend,as it is shown below:

I guess the problem arises from the manner the function aes() manages its arguments. Do you have any idea on how to rewrite my code?

Answer 1

Add a list to ggplot

A quick edit: I just learned an idiom I just learned from @BrodieG that's very applicable here: you can add a list of geoms or stats directly to a ggplot call, which allows you to avoid the convolutions of Reduce for lapply or even Map, which lets you pass as many variables in parallel as you like. Combined with @JulioSergio's aes_ approach, you get a decent plot with readable code that's easily customizable:

ggplot(data.frame(x = 0:1), aes(x)) + 
    Map(function(params, name){stat_function(mapping = aes_(color = name), 
                                             fun = dnorm, args = params)}, 
        params = aa, 
        name = paste('Group', seq_along(aa)))

---

Reduce

The structure lends itself reasonably well to Reduce with init set to the initial ggplot call. Colors can be added by indexing a palette function by the number of layers in the object at that point:

Reduce(function(x, y){
    x + stat_function(fun = dnorm, args = y, 
                      colour = scales::brewer_pal('qual', 'Set1')(length(aa))[length(x$layers) + 1])}, 
    aa, 
    init = ggplot(data.frame(x = c(0, 1)), aes(x = x)))

The disadvantage of this approach is that it does not make a nice legend, as it's hardcoding colors.

---

Precalculate

One way around this is to simply do the calculations before plotting, which makes the plotting itself very simple:

library(tidyverse)

aa <- list(list(0.2, 0.1), list(0.7, 0.05), list(0.45, 0.2))

aa %>% set_names(paste('Group', 1:3)) %>% 
    map_df(~dnorm(seq(0, 1, length = 100), .x[[1]], .x[[2]])) %>% 
    mutate(x = seq(0, 1, length = 100)) %>% 
    gather(Group, y, -x) %>% 
    ggplot(aes(x, y, color = Group)) + 
    geom_line()