Is there an sf (or df) based alternative to kernelUD to estimate bivariate normal kernel density?

Question

I am switching from sp to sf but have some analysis which uses kernelUD from adehabitatHR which requires my data to be SpatialPoints. Is there an equivalent which does not use sp, perhaps instead using sf or a regular dataframe, which offers similar bandwidth options?

A snippet of my original code using Genetta genetta as an example:

library(adehabitatHR)

G_genetta <- as.data.frame(matrix(c(0.5519758, 0.27524548,
                                    0.5725632, 0.12309273,
                                    0.5547747, 0.06100429,
                                    0.6110925, 0.16211416,
                                    0.5951087, 0.09316814,
                                    0.5333567, 0.11673812,
                                    0.5855461, 0.11170616,
                                    0.5221387, 0.11061583,
                                    0.5848452, 0.17213175), 
                                  ncol = 2, byrow = TRUE))

mask_xy_grid <- expand.grid(x = seq(0.01, 1, by = 0.01), y = seq(0.01, 1, by = 0.01))
coordinates(mask_xy_grid) <- ~ x + y
gridded(mask_xy_grid) <- TRUE

ade_G_genetta <- kernelUD(SpatialPoints(G_genetta), 
                          h = "href", 
                          grid = mask_xy_grid, 
                          kern = "bivnorm")

plot(ade_G_genetta)

I am aware of the ks package which I could use as follows:

library(ks)

mask_xy <- as.data.frame(expand.grid(x = seq(0.01, 1, by = 0.01), y = seq(0.01, 1, by = 0.01)))

kde_G_genetta <- kde(G_genetta,
                     eval.points = mask_xy)

# lazily get comparable plot
kde_G_genetta <- SpatialPixelsDataFrame(points = kde_G_genetta$eval.points, 
                                        data = data.frame(est = kde_G_genetta$estimate))

plot(kde_G_genetta)

but this doesn't offer the same bandwidth options as kernelUD. I particularly don't understand why kernelUD takes a single scalar value for "h" whereas kde takes a matrix when they are both applied to a multivariate problem. kde also doesn't seem to cope well with limited sampling points, e.g. Alcelaphus buselaphus which gives the error:

Error in chol.default(S) : 
  the leading minor of order 2 is not positive definite

A_buselaphus <- as.data.frame(matrix(c(0.5109837, 0.1247711,
                                       0.5109837, 0.1247711,
                                       0.5893287, 0.1613403,
                                       0.5893287, 0.1613403,
                                       0.5893287, 0.1613403), 
                                     ncol = 2, byrow = TRUE))

# using kernelUD
ade_A_buselaphus <- kernelUD(SpatialPoints(A_buselaphus), 
                             h = "href", 
                             grid = mask_xy_grid, 
                             kern = "bivnorm")

plot(ade_A_buselaphus)

# using kde
kde_A_buselaphus <- kde(A_buselaphus,
                        eval.points = mask_xy)

# lazily get comparable plot
kde_A_buselaphus <- SpatialPixelsDataFrame(points = kde_A_buselaphus$eval.points, 
                                           data = data.frame(est = kde_A_buselaphus$estimate))

plot(kde_A_buselaphus)

I could use MASS, but I run into the same bandwidth problem as it takes a "vector of bandwidths for x and y directions":

library(MASS)

mask.xy <- as.data.frame(expand.grid(x = seq(0.01, 1, by = 0.01), y = seq(0.01, 1, by = 0.01)))

MASS_G_genetta <- kde2d(G_genetta$V1,
                        G_genetta$V2,
                        n = c(100, 100),
                        lims = c(range(mask.xy$x), range(mask.xy$y)))

# lazily get comparable plots
MASS_G_genetta <- SpatialPixelsDataFrame(points = mask.xy, 
                                         data = data.frame(est = melt(MASS_G_genetta$z)$value))

plot(MASS_G_genetta)

# same axis
plot(ade_G_genetta, zlim = c(0,75))
plot(kde_G_genetta, zlim = c(0,75))
plot(MASS_G_genetta, zlim = c(0,75))

Answer 1

Having done some digging into the source code of kernelUD I have found a tolerable, albeit incomplete, solution. I have only been looking within documentation and source code which relates to a bivariate normal kernel using the ad hoc method for calculating h.

To find the solution I followed a trail of functions within the CRAN repo: kernelUD -> .kernelUDs -> void kernelhr -> void epa

which led me to this comment within the epa function: /* Keep only the points no further than 4*fen of the current pixel */

fen equates to h which according to the documentation is by default calculated with:

for a bivariate normal kernel. I can write this generically as follows: (sqrt(0.5*(var(species_xy[[1]]) + var(species_xy[[2]]))))*(nrow(species_xy)^-(1/6))

Since kde2d from MASS takes a scalar vector, I can supply it with h*4 for each dimension. The solution for Genetta genetta would therefore be:

library(adehabitatHR)
library(MASS)

# using adehabitatHR
G_genetta <- as.data.frame(matrix(c(0.5519758, 0.27524548,
                                    0.5725632, 0.12309273,
                                    0.5547747, 0.06100429,
                                    0.6110925, 0.16211416,
                                    0.5951087, 0.09316814,
                                    0.5333567, 0.11673812,
                                    0.5855461, 0.11170616,
                                    0.5221387, 0.11061583,
                                    0.5848452, 0.17213175), 
                                  ncol = 2, byrow = TRUE))

mask_xy_grid <- expand.grid(x = seq(0.01, 1, by = 0.01), y = seq(0.01, 1, by = 0.01))
coordinates(mask_xy_grid) <- ~ x + y
gridded(mask_xy_grid) <- TRUE

ade_G_genetta <- kernelUD(SpatialPoints(G_genetta), 
                          h = "href", 
                          grid = mask_xy_grid, 
                          kern = "bivnorm")

plot(ade_G_genetta)

# using MASS
mask.xy <- as.data.frame(expand.grid(x = seq(0.01, 1, by = 0.01), y = seq(0.01, 1, by = 0.01)))

H <- (sqrt(0.5*(var(G_genetta[[1]]) + var(G_genetta[[2]]))))*(nrow(G_genetta)^-(1/6))

MASS_G_genetta <- kde2d(G_genetta$V1,
                        G_genetta$V2,
                        n = c(100, 100),
                        h = c(H*4, H*4),
                        lims = c(range(mask.xy$x), range(mask.xy$y)))

# lazily get comparable plots
MASS_G_genetta <- SpatialPixelsDataFrame(points = mask.xy, 
                                         data = data.frame(est = melt(MASS_G_genetta$z)$value))

plot(MASS_G_genetta)

# to confirm this is the same h as the kernelUD output:
kde_G_genetta@h[["h"]]
H
kde_G_genetta@h[["h"]] == H

The exact values in the output differ minorly, presumably due to differences in precision between the two methods. A quick summary of the two objects shows us they are functionally the same and backs up the similarity in their plots.

summary(kde_G_genetta@data[["ud"]]
summary(MASS_G_genetta$est)