The dbmss package allows simple computation of spatial statistic functions of distance to characterize the spatial structures of mapped objects, including classical ones (Ripley’s K and others) and more recent ones used by spatial economists (Duranton and Overman’s \(K_d\), Marcon and Puech’s \(M\)). It relies on spatstat for some core calculation.
This vignette contains a quick introduction.
Data
The main data format is wmppp for weighted, marked point
pattern. It inherits from the ppp class of the
spatstat package.
A wmppp object can be created from the coordinates of
points, their type and their weight.
library("dbmss")
# Draw the coordinates of 10 points
X <- runif(10)
Y <- runif(10)
# Draw the point types.
PointType <- sample(c("A", "B"), 10, replace=TRUE)
# Plot the point pattern. Weights are set to 1 ant the window is adjusted
autoplot(wmppp(data.frame(X, Y, PointType)))
An example dataset is provided: it is a point pattern from the Paracou forest in French Guiana. Two species of trees are identified, other trees are of type “Other”. Point weights are their basal area, in square centimeters.
# Plot (second column of marks is Point Types)
autoplot(paracou16,
labelSize = expression("Basal area (" ~cm^2~ ")"),
labelColor = "Species")
Main functions
The main functions of the packages are designed to calculate distance-based measures of spatial structure. Those are non-parametric statistics able to summarize and test the spatial distribution (concentration, dispersion) of points.
The classical, topographic functions such as Ripley’s K are provided by the spatstat package and supported by dbmss for convenience.
Relative functions are available in dbmss only. These are the \(M\) and \(m\) and \(K_d\) functions.
The bivariate \(M\) function can be calculated for Q. Rosea trees around V. Americana trees:
Confidence envelopes
Confidence envelopes of various null hypotheses can be calculated. The univariate distribution of Q. Rosea is tested against the null hypothesis of random location.
autoplot(KdEnvelope(paracou16, , ReferenceType="Q. Rosea", Global=TRUE), main="")
Significant concentration is detected between about 10 and 20 meters.