Bandwidth when plotting densities in R

Question

When I plot the density for wind direction using circular package, I get an error. The error is shown below. Can someone explain the bw (bandwidth) that I need for the amount of data?

plot(density(dirCir))
Error in density.circular(dirCir) : 
  argument "bw" is missing, with no default

This is the actual code that I have.

library (circular)
dir <-c(308,351,330,16,3,346,345,345,287,359,345,358,336,335,346,16,325,354,5,354,322,340,6,278,354,343,261,353,288,8) 
dirCir <- circular(dir, units ="degrees", template = "geographics")
mean(dirCir)
var(dirCir)
summary(dirCir)
plot(dirCir)
plot(density(dirCir))
rose.diag(dirCir, main = 'dir Data')
points(dirCir)

Answer 1

When you run density on an object of class circular , it appears that you have to include a value for bw (bandwidth) explicitly (as the error message indicates). Try this:

plot(density(dirCir, kernel="wrappednormal", bw=0.02), ylim=c(-1,5))

See below for the graph. The ylim range is so that the plot fits inside the plot area without clipping. See the help for density.circular for more info on running the density function on circular objects.

Answer 2

As @eipi10 says, bw has to be explicitly chosen. Depending on the kernel that you choose large and small values of this bandwidth parameter may produce spiky density estimates as well as very smooth ones.

Common practice is to try several values and choose the one that seems to describe the data best. However, note that the following functions provide more objective ways of selecting the bw :

# bw.cv.mse.circular(dirCir)
[1] 21.32236
# bw.cv.mse.circular(dirCir, kernel = "wrappednormal")
[1] 16.97266
# bw.cv.ml.circular(dirCir)
[1] 19.71197
# bw.cv.ml.circular(dirCir, kernel = "wrappednormal")
[1] 0.2280636
# bw.nrd.circular(dirCir)
[1] 14.63382