Distance-Based Measures of Spatial Structures
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.
The main data format is
wmppp for weighted, marked point
pattern. It inherits from the
ppp class of the
wmppp object can be created from the coordinates of
points, their type and their weight.
# 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
# Plot (second column of marks is Point Types)
labelSize = expression("Basal area (" ~cm^2~ ")"),
labelColor = "Species")
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
autoplot(Mhat(paracou16, , "V. Americana", "Q. Rosea"), main="")
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