Area under a density plot not equal to 1

Question

I am trying to chart a probability density plot using ggplot. My problem is that the area under the curve is not equal to one. Advice appreciated.

Sample chart... the code that produced this chart follows... The Y axis looks like it is a count for small sized bins, rather than a probability for falling into that bin. The example code here, is one of the sources I drew on in the preparation of this chart.

Sample code... most of which is data... the key bit of code is at the bottom...

library(ggplot2)
library(reshape)
library(plyr)
library(scales)

Date <- as.Date(
    c("1976-01-16", "1976-02-15", "1976-03-16", "1976-04-15", "1976-05-16",
      "1976-06-15", "1976-07-16", "1976-08-16", "1976-09-15", "1976-10-16",
      "1976-11-15", "1976-12-16", "1977-01-16", "1977-02-14", "1977-03-16",
      "1977-04-15", "1977-05-16", "1977-06-15", "1977-07-16", "1977-08-16",
      "1977-09-15", "1977-10-16", "1977-11-15", "1977-12-16", "1978-01-16",
      "1978-02-14", "1978-03-16", "1978-04-15", "1978-05-16", "1978-06-15",
      "1978-07-16", "1978-08-16", "1978-09-15", "1978-10-16", "1978-11-15",
      "1978-12-16", "1979-01-16", "1979-02-14", "1979-03-16", "1979-04-15",
      "1979-05-16", "1979-06-15", "1979-07-16", "1979-08-16", "1979-09-15",
      "1979-10-16", "1979-11-15", "1979-12-16", "1980-01-16", "1980-02-15",
      "1980-03-16", "1980-04-15", "1980-05-16", "1980-06-15", "1980-07-16",
      "1980-08-16", "1980-09-15", "1980-10-16", "1980-11-15", "1980-12-16",
      "1981-01-16", "1981-02-14", "1981-03-16", "1981-04-15", "1981-05-16",
      "1981-06-15", "1981-07-16", "1981-08-16", "1981-09-15", "1981-10-16",
      "1981-11-15", "1981-12-16", "1982-01-16", "1982-02-14", "1982-03-16",
      "1982-04-15", "1982-05-16", "1982-06-15", "1982-07-16", "1982-08-16",
      "1982-09-15", "1982-10-16", "1982-11-15", "1982-12-16", "1983-01-16",
      "1983-02-14", "1983-03-16", "1983-04-15", "1983-05-16", "1983-06-15",
      "1983-07-16", "1983-08-16", "1983-09-15", "1983-10-16", "1983-11-15",
      "1983-12-16", "1984-01-16", "1984-02-15", "1984-03-16", "1984-04-15",
      "1984-05-16", "1984-06-15", "1984-07-16", "1984-08-16", "1984-09-15",
      "1984-10-16", "1984-11-15", "1984-12-16", "1985-01-16", "1985-02-14",
      "1985-03-16", "1985-04-15", "1985-05-16", "1985-06-15", "1985-07-16",
      "1985-08-16", "1985-09-15", "1985-10-16", "1985-11-15", "1985-12-16"))

GOLD <- c(
  -0.104,  0.051,  0.011, -0.035, -0.008, -0.010, -0.065, -0.067,  0.041,  0.017,
   0.126,  0.023, -0.011,  0.029,  0.087,  0.007, -0.016, -0.044,  0.048, -0.013,
   0.030,  0.062, -0.029,  0.042,  0.078,  0.028,  0.031, -0.045,  0.005,  0.043,
   0.028,  0.090,  0.030,  0.072, -0.094,  0.009,  0.093,  0.080, -0.014, -0.013,
   0.077,  0.084,  0.058,  0.021,  0.184,  0.097,  0.002,  0.169,  0.474, -0.014,
  -0.168, -0.067, -0.007,  0.169,  0.071, -0.025,  0.077, -0.022, -0.059, -0.044,
  -0.063, -0.103, -0.003, -0.008, -0.031, -0.040, -0.113,  0.005,  0.081, -0.014,
  -0.057, -0.009, -0.062, -0.026, -0.117,  0.061, -0.046, -0.058,  0.080,  0.076,
   0.190, -0.031, -0.019,  0.074,  0.079,  0.022, -0.144,  0.030,  0.013, -0.057,
   0.026, -0.017, -0.012, -0.042, -0.030,  0.015, -0.043,  0.041,  0.022, -0.032,
  -0.011,  0.001, -0.083,  0.004, -0.019, -0.002,  0.003, -0.065, -0.063,  0.017,
  -0.044,  0.134, -0.022, -0.014, -0.008,  0.033, -0.014,  0.017, -0.004, -0.023)

df <- data.frame(Date=Date, GOLD=GOLD)

p <- ggplot(data=df, aes(x=GOLD, y=..density..)) +
    stat_density(fill='grey50') +
    xlab('Percent change on previous month') +
    ylab('Density') +
    opts(title='Change in Gold Price in the US')
ggsave(p, width=8, height=4, filename='plot.png', dpi=125)

Answer 1

I don't think this is a problem with ggplot, but with your understanding of the y-axis in a density plot. The base plotting functions in R plot the same thing. You can set the call to y=..scaled.. to give you a relative density, but if you use stat_bin() you'll see the actual histogram and notice it's not the counts. If you want you could normalize your data with something like this:

GOLD_N <- (GOLD- mean(GOLD))/sd(GOLD)
df <- data.frame(Date=Date, GOLD=GOLD,GOLD_N=GOLD_N)

Then run your plot it will look something like this:

You should watch this video about how to interpret density functions http://www.youtube.com/watch?v=Fvi9A_tEmXQ But normalizing your data will give you the plot that's a bit more intuitive if you're used to staring at PDF's and will sum to 1. But don't misinterpret the y axis. y IS NOT the probability of a randomly drawn value from the density being equal to x.