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"), size = 10, replace = TRUE)
# Plot the point pattern. Weights are set to 1 ant the window is adjusted
autoplot(wmppp(data.frame(X, Y, PointType)))
![](data:image/png;base64,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)
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"
)
![](data:image/png;base64,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)
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:
autoplot(
Mhat(
paracou16,
ReferenceType = "V. Americana",
NeighborType = "Q. Rosea"
),
main = ""
)
![](data:image/png;base64,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)
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 = ""
)
![](data:image/png;base64,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)
Significant concentration is detected between about 10 and 20
meters.