How can I get the value of a kernel density estimate at specific points?

Question

I am experimenting with ways to deal with overplotting in R, and one thing I want to try is to plot individual points but color them by the density of their neighborhood. In order to do this I would need to compute a 2D kernel density estimate at each point. However, it seems that the standard kernel density estimation functions are all grid-based. Is there a function for computing 2D kernel density estimates at specific points that I specify? I would imagine a function that takes x and y vectors as arguments and returns a vector of density estimates.

Answer 1

I eventually found the precise function I was looking for: interp.surface from the fields package. From the help text:

Uses bilinear weights to interpolate values on a rectangular grid to arbitrary locations or to another grid.

Answer 2

If I understand what you want to do, it could be achieved by fitting a smoothing model to the grid density estimate and then using that to predict the density at each point you are interested in. For example:

# Simulate some data and put in data frame DF
n <- 100
x <- rnorm(n)
y <- 3 + 2* x * rexp(n) + rnorm(n)
# add some outliers
y[sample(1:n,20)] <- rnorm(20,20,20)
DF <- data.frame(x,y)

# Calculate 2d density over a grid
library(MASS)
dens <- kde2d(x,y)

# create a new data frame of that 2d density grid
# (needs checking that I haven't stuffed up the order here of z?)
gr <- data.frame(with(dens, expand.grid(x,y)), as.vector(dens$z))
names(gr) <- c("xgr", "ygr", "zgr")

# Fit a model
mod <- loess(zgr~xgr*ygr, data=gr)

# Apply the model to the original data to estimate density at that point
DF$pointdens <- predict(mod, newdata=data.frame(xgr=x, ygr=y))

# Draw plot
library(ggplot2)
ggplot(DF, aes(x=x,y=y, color=pointdens)) + geom_point()

Or, if I just change n 10^6 we get