Contour functions

Contour levels and sizes.

Usage

contourLevels(x, ...)
# S3 method for class 'kde'
contourLevels (x, prob, cont, approx=TRUE, ...)
# S3 method for class 'kda'
contourLevels (x, prob, cont, approx=TRUE, ...)
# S3 method for class 'kdde'
contourLevels(x, prob, cont, approx=TRUE, which.deriv.ind=1, ...) 

contourSizes(x, abs.cont, cont=c(25,50,75), approx=TRUE)
contourProbs(x, abs.cont, cont=c(25,50,75), approx=TRUE)
contourBreaks(x, n=3, cont=c(25,50,75), type="density")

Arguments

x

object of class kde, kdde or kda

prob

vector of probabilities corresponding to highest density regions

cont

vector of percentages which correspond to the complement of prob

abs.cont

vector of absolute contour levels

approx

flag to compute approximate contour levels. Default is TRUE.

which.deriv.ind

partial derivative index. Default is 1.

...

other parameters

type

type of contour levels: one of "density", "length", "quantile", "natural". Default is "density".

n

number of contour levels for type="length", "natural". Default is 3.

Value

–For contourLevels/contourBreaks, for kde objects, returns a vector of heights. For kda objects, returns a list of vectors, one for each training group. For kdde objects, returns a matrix, one row for each partial derivative.

–For contourSizes, returns an approximation of the Lebesgue measure of the level set, i.e. length (d=1), area (d=2), volume (d=3), hyper-volume (d>4).

–For contourProbs, returns an approximation of the probability measure of the level set.

Details

–For contourLevels, the most straightforward is to specify prob. The heights of the corresponding highest density region with probability prob are computed. The cont parameter here is consistent with cont parameter from plot.kde, plot.kdde, and plot.kda i.e. cont=(1-prob)*100%. If both prob and cont are missing then a pretty set of nlevels contours are computed. From ks \(\geq\) 1.15.0, nlevels=5 always.

–For contourSizes, the length, area, volume etc. and for contourProbs, the probability, are approximated by Riemann sums. These are rough approximations and depend highly on resolution of the estimation grid, and so should be interpreted carefully.

If approx=FALSE, then the exact KDE is computed. Otherwise it is interpolated from an existing KDE grid: this can dramatically reduce computation time for large data sets.

–For contourBreaks, different contour level selection methods are available, including equal length ("length"), quantile ("quantile") and natural breaks/Jenks ("natural") for density estimates only. The default contourBreaks(type="density") is equivalent to contourLevels.

See also

contour, contourLines

Examples

set.seed(8192)
x <- rmvnorm.mixt(n=1000, mus=c(0,0), Sigmas=diag(2), props=1)
fhat <- kde(x=x, binned=TRUE)
contourLevels(fhat, cont=c(25,50,75))
#>        75%        50%        25% 
#> 0.11138323 0.08385792 0.04370685 
contourProbs(fhat, abs.cont=contourLevels(fhat, cont=50))
#>       50% 
#> 0.4601889 
## compare approx prob with target prob=0.5
contourSizes(fhat, cont=25, approx=TRUE) 
#>      75% 
#> 1.850091 
## compare to approx circle of radius=0.75 with area=1.77
contourBreaks(fhat, n=3, type="natural")
#> [1] 0.002129676 0.041174642 0.104037824
## natural or Jenks contour levels