Type:	Package
Title:	Distance-Based Measures of Spatial Structures
Version:	2.11-0
Description:	Simple computation of spatial statistic functions of distance to characterize the spatial structures of mapped objects, following Marcon, Traissac, Puech, and Lang (2015) <doi:10.18637/jss.v067.c03>. Includes classical functions (Ripley's K and others) and more recent ones used by spatial economists (Duranton and Overman's Kd, Marcon and Puech's M). Relies on 'spatstat' for some core calculation.
URL:	https://ericmarcon.github.io/dbmss/, https://github.com/EricMarcon/dbmss/
BugReports:	https://github.com/EricMarcon/dbmss/issues/
License:	GPL-2 | GPL-3 [expanded from: GNU General Public License]
Depends:	R (≥ 3.5.0), Rcpp (≥ 0.12.14), spatstat.explore
Imports:	cubature, doFuture, foreach, future, ggplot2, methods, progressr, RcppParallel, reshape2, rlang, spatstat.geom, spatstat.utils, spatstat.random, stats, tibble
Suggests:	knitr, pkgdown, rmarkdown, testthat
LinkingTo:	Rcpp, RcppParallel
VignetteBuilder:	knitr
SystemRequirements:	pandoc, GNU make
Encoding:	UTF-8
LazyData:	true
NeedsCompilation:	yes
Packaged:	2025-06-17 13:14:06 UTC; emarc
Author:	Eric Marcon [aut, cre], Gabriel Lang [aut], Stephane Traissac [aut], Florence Puech [aut], Pierrot Froment [aut]
Maintainer:	Eric Marcon <eric.marcon@agroparistech.fr>
Repository:	CRAN
Date/Publication:	2025-06-17 23:40:02 UTC

Distance Based Measures of Spatial Structures

Description

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 Kd, Marcon and Puech's M). Relies on spatstat for some core calculation.

Author(s)

Eric Marcon, Gabriel Lang, Stephane Traissac, Florence Puech

Maintainer: Eric Marcon <Eric.Marcon@agroparistech.fr>

References

Marcon, E., and Puech, F. (2003). Evaluating the Geographic Concentration of Industries Using Distance-Based Methods. Journal of Economic Geography, 3(4), 409-428.

Marcon, E. and Puech, F. (2010). Measures of the Geographic Concentration of Industries: Improving Distance-Based Methods. Journal of Economic Geography 10(5): 745-762.

Marcon, E., Puech F. and Traissac, S. (2012). Characterizing the relative spatial structure of point patterns. International Journal of Ecology 2012(Article ID 619281): 11.

Lang G., Marcon E. and Puech F. (2014) Distance-Based Measures of Spatial Concentration: Introducing a Relative Density Function. HAL 01082178, 1-18.

Marcon, E., Traissac, S., Puech, F. and Lang, G. (2015). Tools to Characterize Point Patterns: dbmss for R. Journal of Statistical Software. 67(3): 1-15.

Marcon, E. and Puech, F. (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

Checks the arguments of a function of the package dbmss

Description

This function is used internally to verify that arguments passed to dbmss functions such as Mhat are correct.

Usage

CheckdbmssArguments()

Details

The function compares the arguments passed to its parent function to the type they should be and performs some extra tests (e.g. risk threshold must be between 0 and 1). It stops if an argument is not correct.

Value

Returns TRUE or stops if a problem is detected.

Estimation of the confidence envelope of the D function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of D according to the confidence level.

Usage

DEnvelope(X, r = NULL, NumberOfSimulations = 100, Alpha = 0.05,
          Cases, Controls, Intertype = FALSE, Global = FALSE,
          verbose = interactive(), parallel = FALSE, parallel_pgb_refresh = 1/10)

Arguments

Details

The only null hypothesis is random labeling: marks are distributed randomly across points.

This envelope is local by default, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

The global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

Parallel simulations rely on the future and doFuture packages. Before calling the function with argument parallel = TRUE, you must choose a strategy and set it with plan. Their progress bar relies on the progressr package. They must be activated by the user by handlers.

Value

An envelope object (envelope). There are methods for print and plot for this class.

The fv contains the observed value of the function, its average simulated value and the confidence envelope.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024.

Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

See Also

Dhat

Examples

data(paracou16)
# Keep only 20% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.2))
autoplot(X,
  labelSize = expression("Basal area (" ~cm^2~ ")"),
  labelColor = "Species")

# Calculate confidence envelope (should be 1000 simulations, reduced to 20 to save time)
r <- 0:30
NumberOfSimulations <- 20
Alpha <- .05
# Plot the envelope (after normalization by pi.r^2)
autoplot(DEnvelope(X, r, NumberOfSimulations, Alpha,
    "V. Americana", "Q. Rosea", Intertype = TRUE), ./(pi*r^2) ~ r)

Estimation of the D function

Description

Estimates the D function

Usage

Dhat(X, r = NULL, Cases, Controls = NULL, Intertype = FALSE, CheckArguments = TRUE)

Arguments

Details

The Di function allows comparing the structure of the cases to that of the controls around cases, that is to say the comparison is made around the same points. This has been advocated by Arbia et al. (2008) and formalized by Marcon and Puech (2012).

Value

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

Note

The computation of Dhat relies on spatstat functions Kest and Kcross.

References

Arbia, G., Espa, G. and Quah, D. (2008). A class of spatial econometric methods in the empirical analysis of clusters of firms in the space. Empirical Economics 34(1): 81-103.

Diggle, P. J. and Chetwynd, A. G. (1991). Second-Order Analysis of Spatial Clustering for Inhomogeneous Populations. Biometrics 47(3): 1155-1163.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

See Also

Khat, DEnvelope, Kest, Kcross

Examples

data(paracou16)
autoplot(paracou16)

# Calculate D
r <- 0:30
(Paracou <- Dhat(paracou16, r, "V. Americana", "Q. Rosea", Intertype = TRUE))

# Plot (after normalization by pi.r^2)
autoplot(Paracou, ./(pi*r^2) ~ r)

Create a Distance table object.

Description

Creates an object of class "Dtable" representing a set of points with weights and labels and the distances between them.

Usage

Dtable(Dmatrix, PointType = NULL, PointWeight = NULL)

Arguments

Details

The distance matrix is not necessarily symmetric, so distances are understood in the common sense, not in the mathematical sense. Asymmetric distances are appropriate when paths between points are one-way only.

The points of origin are in lines, the targets in columns. The diagonal of the matrix must contain zeros (the distance between a point and itself is 0), and all other distances must be positive (they can be 0).

Value

An object of class "Dtable". It is a list:

See Also

as.Dtable

Examples

# A Dtable containing two points
Dmatrix <- matrix(c(0,1,1,0), nrow=2)
PointType <- c("Type1", "Type2")
PointWeight <- c(2,3)
Dtable(Dmatrix, PointType, PointWeight)

Transform simulation values to an fv

Description

This function is used internally to calculate envelope values and store them into an fv.object.

Usage

FillEnvelope(Envelope, Alpha, Global)

Arguments

Value

Returns the envelope object (envelope) with hi and lo values calculated from the simlations.

Estimation of the global confidence interval of simulations

Description

Calculates the global confidence interval envelope sensu Duranton and Overman (2005) according to simulations of the null hypothesis of a function.

Usage

GlobalEnvelope(Simulations, Alpha)

Arguments

Details

The global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

Value

A matrix with two lines:

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Goodness of Fit test between a distance based measure of spatial structure and simulations of its null hypothesis

Description

Calculates the risk to reject the null hypothesis erroneously, based on the distribution of the simulations.

Usage

GoFtest(Envelope,
        Test = "DCLF",
        Scaling = "Asymmetric",
        Range = NULL,
        Alpha = 0.05,
        CheckArguments = TRUE)

Arguments

Details

This function gathers multiple Goodness of Fit tests: the DCLF test (Diggle 1986, Cressie 1993, Loosmore & Ford 2006, Marcon et al. 2012, Myllymäki et al. 2015), the integrated deviation test (Diggle 1979), and the MAD test (Diggle 1979, Myllymäki et al. 2015).

Monte Carlo simulations assess how well observed distance-based measures of spatial structure align with expected measures under the null hypothesis, estimated here by the mean value of simulations. For both observed and simulated measures, residuals — calculated as the differences between observed and expected values — are computed at each distance r. These residuals are then transformed into test-specific statistics u:

• Test = "MAD" uses the maximum absolute residual;

• Test = "Integral" and Test = "DCLF" use residuals to approximate the integrated deviation, and the integrated squared deviation.

A rank test on u evaluates the null hypothesis that the observed point pattern originates from the same point process as the simulations.

The unequal variance of the residuals at different intervals of r influences u statistics, and the power of Goodness of Fit tests. Myllymäki et al. (2015) proposed to scale residuals using pointwise quantiles (Scaling = "Asymmetric", and Scaling = "Quantile"), and pointwise standard deviations (Scaling = "Studentized").

Goodness of Fit tests are sensitive to the distance interval over which they are performed. It is recommended to choose the distance interval to test based on a priori hypotheses (Wiegand & Moloney 2013, Baddeley et al. 2015).

Value

A p-value.

Note

Ktest is a much better test (it does not rely on simulations) but it is limited to the K function against complete spatial randomness (CSR) in a rectangle window.

This test is inspired from Myllymäki et al. (2015), and a similar function deviation_test() exists in the R package GET (Myllymäki & Mrkvička, 2024)

References

Baddeley, A., Rubak, E., & Turner, R. (2015). Spatial Point Patterns: Methodology and Applications with R (0 ed.). Chapman and Hall/CRC. https://doi.org/10.1201/b19708

Cressie, N. A. C. (1993). Statistics for Spatial Data (1st ed.). Wiley. https://doi.org/10.1002/9781119115151

Diggle, P. J. (1979). On Parameter Estimation and Goodness-of-Fit Testing for Spatial Point Patterns. Biometrics, 35(1), 87. https://doi.org/10.2307/2529938

Diggle, P. J. (1986). Displaced amacrine cells in the retina of a rabbit: Analysis of a bivariate spatial point pattern. Journal of Neuroscience Methods, 18(1–2), 115–125. https://doi.org/10.1016/0165-0270(86)90115-9

Loosmore, N. B., & Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology, 87(8), 1925–1931. https://doi.org/10.1890/0012-9658(2006)87[1925:SIUTGO]2.0.CO;2

Marcon, E., Puech, F., & Traissac, S. (2012). Characterizing the Relative Spatial Structure of Point Patterns. International Journal of Ecology, 2012, 1–11. https://doi.org/10.1155/2012/619281

Myllymäki, M., & Mrkvička, T. (2024). GET: Global Envelopes in R. Journal of Statistical Software, 111(3), 1-40. https://doi.org/10.18637/jss.v111.i03

Myllymäki, M., Grabarnik, P., Seijo, H., & Stoyan, D. (2015). Deviation test construction and power comparison for marked spatial point patterns. Spatial Statistics, 11, 19–34. https://doi.org/10.1016/j.spasta.2014.11.004

Wiegand, T., & Moloney, K. A. (2013). Handbook of Spatial Point-Pattern Analysis in Ecology. Chapman and Hall/CRC. https://doi.org/10.1201/b16195

See Also

Ktest

Examples

# Simulate a Matern (Neyman Scott) point pattern
nclust <- function(x0, y0, radius, n) {
  return(runifdisc(n, radius, centre=c(x0, y0)))
}
X <- rNeymanScott(20, 0.2, nclust, radius=0.3, n=10)
autoplot(as.wmppp(X))

# Calculate confidence envelope (should be 1000 simulations, reduced to 50 to save time)
r <- seq(0, 0.3, 0.01)
NumberOfSimulations <- 50
Alpha <- .10
Envelope <- KEnvelope(as.wmppp(X), r, NumberOfSimulations, Alpha)
autoplot(Envelope, ./(pi*r^2) ~ r)

# DCLF test using asymmetric scaling.
# Power is correct if enough simulations are run (say >1000).
paste(
  "p-value =",
  GoFtest(Envelope, Test = "DCLF", Scaling = "Asymmetric", Range = c(0.1, 0.2))
)

# MAD test using asymmetric scaling.
paste(
  "p-value =",
  GoFtest(Envelope, Test = "MAD", Scaling = "Asymmetric", Range = c(0.1, 0.2))
)

Estimation of the confidence envelope of the K function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of K according to the confidence level.

Usage

KEnvelope(X, r = NULL, NumberOfSimulations = 100, Alpha = 0.05,
          ReferenceType = "", NeighborType = ReferenceType,
          SimulationType = "RandomPosition", Precision = 0, Global = FALSE,
          verbose = interactive(), parallel = FALSE, parallel_pgb_refresh = 1/10)

Arguments

Details

This envelope is local by default, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

The global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

Parallel simulations rely on the future and doFuture packages. Before calling the function with argument parallel = TRUE, you must choose a strategy and set it with plan. Their progress bar relies on the progressr package. They must be activated by the user by handlers.

Value

An envelope object (envelope). There are methods for print and plot for this class.

The fv contains the observed value of the function, its average simulated value and the confidence envelope.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024.

Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.

See Also

Khat, rRandomPositionK, rRandomLocation, rPopulationIndependenceK

Examples

data(paracou16)
# Keep only 20% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.2))
autoplot(X,
  labelSize = expression("Basal area (" ~cm^2~ ")"),
  labelColor = "Species")

# Calculate confidence envelope (should be 1000 simulations, reduced to 20 to save time)
r <- 0:30
NumberOfSimulations <- 20
# Plot the envelope
autoplot(KEnvelope(X, r, NumberOfSimulations), ./(pi*r^2) ~ r)

Estimation of the confidence envelope of the Kd function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of Kd according to the confidence level.

Usage

KdEnvelope(X, r = NULL, NumberOfSimulations = 100, Alpha = 0.05, ReferenceType,
           NeighborType = ReferenceType, Weighted = FALSE, Original = TRUE,
           Approximate = ifelse(X$n < 10000, 0, 1), Adjust = 1, MaxRange = "ThirdW",
           StartFromMinR = FALSE,
           SimulationType = "RandomLocation", Global = FALSE,
           verbose = interactive(), parallel = FALSE, parallel_pgb_refresh = 1/10)

Arguments

Details

This envelope is local by default, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

The global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

Parallel simulations rely on the future and doFuture packages. Before calling the function with argument parallel = TRUE, you must choose a strategy and set it with plan. Their progress bar relies on the progressr package. They must be activated by the user by handlers.

Value

An envelope object (envelope). There are methods for print and plot for this class.

The fv contains the observed value of the function, its average simulated value and the confidence envelope.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024.

Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

Scholl, T. and Brenner, T. (2015) Optimizing distance-based methods for large data sets, Journal of Geographical Systems 17(4): 333-351.

Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.

See Also

Kdhat

Examples

data(paracou16)
autoplot(paracou16[marks(paracou16)$PointType=="Q. Rosea"])

# Calculate confidence envelope
plot(KdEnvelope(paracou16, , ReferenceType="Q. Rosea", Global=TRUE))

# Center of the confidence interval
Kdhat(paracou16, ReferenceType="") -> kd
lines(kd$Kd ~ kd$r, lty=3, col="green")

Estimation of the Kd function

Description

Estimates the Kd function

Usage

 Kdhat(X, r = NULL, ReferenceType, NeighborType = ReferenceType, Weighted = FALSE,
       Original = TRUE, Approximate = ifelse(X$n < 10000, 0, 1), Adjust = 1,
       MaxRange = "ThirdW", StartFromMinR = FALSE, CheckArguments = TRUE)

Arguments

Details

Kd is a density, absolute measure of a point pattern structure. Kd is computed efficiently by building a matrix of distances between point pairs and calculating the density of their distribution (the default values of r are those of the density function). The kernel estimator is Gaussian.

The weighted Kd function has been named Kemp (emp is for employees) by Duranton and Overman (2005).

If X is not a Dtable object, the maximum value of r is obtained from the geometry of the window rather than caculating the median distance between points as suggested by Duranton and Overman (2005) to save (a lot of) calculation time.

Value

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

Note

Estimating Kd relies on calculating distances, exactly or approximately (if Approximate is not 0). Then distances are smoothed by estimating their probability density. Reflection is used to estimate density close to the lowest distance, that is the minimum observed distance (if StartFromMinR is TRUE) or 0: all distances below 4 times the estimation kernel bandwith apart from the lowest distance are duplicated (symmetrically with respect to the lowest distance) to avoid edge effects (underestimation of the density close to the lowest distance).

Density estimation heavily relies on the bandwith. Starting from version 2.7, the optimal bandwith is computed from the distribution of distances between pairs of points up to twice the maximum distance considered. The consequence is that choosing a smaller range of distances in argument r results in less smoothed Kd values. The default values (r = NULL, MaxRange = "ThirdW") are such that almost all the pairs of points (except those more than 2/3 of the window diameter apart) are taken into account to determine the bandwith.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

Scholl, T. and Brenner, T. (2015) Optimizing distance-based methods for large data sets, Journal of Geographical Systems 17(4): 333-351.

Sheather, S. J. and Jones, M. C. (1991) A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society series B, 53, 683-690.

Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.

See Also

KdEnvelope, Mhat

Examples

data(paracou16)
autoplot(paracou16)

# Calculate Kd
(Paracou <- Kdhat(paracou16, , "Q. Rosea", "V. Americana"))
# Plot
autoplot(Paracou)

Estimation of the K function

Description

Estimates the K function

Usage

Khat(X, r = NULL, ReferenceType = "", NeighborType = ReferenceType, CheckArguments = TRUE)

Arguments

Details

K is a cumulative, topographic measure of a point pattern structure.

Value

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

Note

The computation of Khat relies on spatstat functions Kest and Kcross.

References

Ripley, B. D. (1976). The Foundations of Stochastic Geometry. Annals of Probability 4(6): 995-998.

Ripley, B. D. (1977). Modelling Spatial Patterns. Journal of the Royal Statistical Society B 39(2): 172-212.

See Also

Lhat, KEnvelope, Ktest

Examples

data(paracou16)
autoplot(paracou16)

# Calculate K
r <- 0:30
(Paracou <- Khat(paracou16, r))

# Plot (after normalization by pi.r^2)
autoplot(Paracou, ./(pi*r^2) ~ r)

Estimation of the confidence envelope of the Kinhom function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of Kinhom according to the confidence level.

Usage

KinhomEnvelope(X, r = NULL, NumberOfSimulations = 100, Alpha = 0.05,
               ReferenceType = "", lambda = NULL,
               SimulationType = "RandomPosition", Global = FALSE,
               verbose = interactive(), parallel = FALSE,
               parallel_pgb_refresh = 1/10)

Arguments

Details

The random location null hypothesis is that of Duranton and Overman (2005). It is appropriate to test the univariate Kinhom function of a single point type, redistributing it over all point locations. It allows fixing lambda along simulations so the warning message can be ignored.

The random labeling hypothesis is appropriate for the bivariate Kinhom function.

The population independence hypothesis is that of Marcon and Puech (2010).

This envelope is local by default, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

The global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

Parallel simulations rely on the future and doFuture packages. Before calling the function with argument parallel = TRUE, you must choose a strategy and set it with plan. Their progress bar relies on the progressr package. They must be activated by the user by handlers.

Value

An envelope object (envelope). There are methods for print and plot for this class.

The fv contains the observed value of the function, its average simulated value and the confidence envelope.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024.

Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

Marcon, E. and Puech, F. (2010). Measures of the Geographic Concentration of Industries: Improving Distance-Based Methods. Journal of Economic Geography 10(5): 745-762.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

See Also

Kinhomhat

Examples

data(paracou16)
# Keep only 20% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.2))
autoplot(X,
  labelSize = expression("Basal area (" ~cm^2~ ")"),
  labelColor = "Species")

# Density of all trees
lambda <- density.ppp(X, bw.diggle(X))
plot(lambda)
V.americana <- X[marks(X)$PointType=="V. Americana"]
plot(V.americana, add=TRUE)

# Calculate Kinhom according to the density of all trees
# and confidence envelope (should be 1000 simulations, reduced to 4 to save time)
r <- 0:30
NumberOfSimulations <- 4
Alpha <- .10
autoplot(KinhomEnvelope(X, r,NumberOfSimulations, Alpha, ,
    SimulationType="RandomPosition", lambda=lambda), ./(pi*r^2) ~ r)

Estimation of the inhomogenous K function

Description

Estimates the Kinhom function

Usage

Kinhomhat(X, r = NULL, ReferenceType = "", lambda = NULL, CheckArguments = TRUE)

Arguments

Details

Kinhom is a cumulative, topographic measure of an inhomogenous point pattern structure.

By default, density estimation is performed at points by density.ppp using the optimal bandwith (bw.diggle). It can be calculated separately (see example), including at pixels if the point pattern is too large for the default estimation to succeed, and provided as the argument lambda: Arbia et al. (2012) for example use another point pattern as a reference to estimate density.

Bivariate Kinhom is not currently supported.

Value

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

Note

The computation of Kinhomhat relies on spatstat functions Kinhom, density.ppp and bw.diggle.

References

Baddeley, A. J., J. Moller, et al. (2000). Non- and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54(3): 329-350.

Arbia, G., G. Espa, et al. (2012). Clusters of firms in an inhomogeneous space: The high-tech industries in Milan. Economic Modelling 29(1): 3-11.

See Also

KinhomEnvelope, Kinhom

Examples

data(paracou16)

# Density of all trees
lambda <- density.ppp(paracou16, bw.diggle(paracou16))
plot(lambda)
# Reduce the point pattern to one type of trees
V.americana <- paracou16[marks(paracou16)$PointType=="V. Americana"]
plot(V.americana, add=TRUE)

# Calculate Kinhom according to the density of all trees
r <- 0:30
autoplot(Kinhomhat(paracou16, r, "V. Americana", lambda), ./(pi*r^2) ~ r)

Estimation of the confidence envelope of the Lmm function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of Lmm according to the confidence level.

Usage

KmmEnvelope(X, r = NULL, NumberOfSimulations = 100, Alpha = 0.05,
            ReferenceType = "", Global = FALSE,
            verbose = interactive(), parallel = FALSE, parallel_pgb_refresh = 1/10)

Arguments

Details

This envelope is local by default, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

The global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

Parallel simulations rely on the future and doFuture packages. Before calling the function with argument parallel = TRUE, you must choose a strategy and set it with plan. Their progress bar relies on the progressr package. They must be activated by the user by handlers.

Value

An envelope object (envelope). There are methods for print and plot for this class.

The fv contains the observed value of the function, its average simulated value and the confidence envelope.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024.

Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

See Also

Kmmhat

Examples

data(paracou16)
# Keep only 20% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.2))
autoplot(X,
  labelSize = expression("Basal area (" ~cm^2~ ")"),
  labelColor = "Species")

# Calculate confidence envelope (should be 1000 simulations, reduced to 4 to save time)
r <- seq(0, 30, 2)
NumberOfSimulations <- 4
Alpha <- .10
autoplot(KmmEnvelope(X, r, NumberOfSimulations, Alpha), ./(pi*r^2) ~ r)

Estimation of the Kmm function

Description

Estimates of the Kmm function

Usage

Kmmhat(X, r = NULL, ReferenceType = "", CheckArguments = TRUE)

Arguments

Details

The Kmm function is used to test the independence of marks.

Value

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

Note

The function is computed using markcorrint in spatstat.

References

Penttinen, A., Stoyan, D. and Henttonen, H. M. (1992). Marked Point Processes in Forest Statistics. Forest Science 38(4): 806-824.

Penttinen, A. (2006). Statistics for Marked Point Patterns. in The Yearbook of the Finnish Statistical Society. The Finnish Statistical Society, Helsinki: 70-91.

See Also

Lmmhat, LmmEnvelope, markcorrint

Examples

data(paracou16)
# Keep only 50% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.5))
autoplot(X, 
  labelSize = expression("Basal area (" ~cm^2~ ")"), 
  labelColor = "Species")

# Calculate Kmm
r <- seq(0, 30, 2)
(Paracou <- Kmmhat(X, r))

# Plot
autoplot(Paracou, ./(pi*r^2) ~ r)

Test of a point pattern against Complete Spatial Randomness

Description

Tests the point pattern against CSR using values of the K function

Usage

Ktest(X, r)

Arguments

Details

The test returns the risk to reject CSR erroneously, i.e. the p-value of the test, based on the distribution of the K function.

If r includes 0, it will be silently removed because no neighbor point can be found at distance 0. The longer r, the more accurate the test is in theory but at the cost of computation time first, and of computation accuracy then because a matrix of size the length of r must be inverted. 10 values in r seems to be a reasonable choice.

Value

A p-value.

Author(s)

Gabriel Lang <Gabriel.Lang@agroparistech.fr>, Eric Marcon<Eric.Marcon@agroparistech.fr>

References

Lang, G. and Marcon, E. (2013). Testing randomness of spatial point patterns with the Ripley statistic. ESAIM: Probability and Statistics. 17: 767-788.

Marcon, E., S. Traissac, and Lang, G. (2013). A Statistical Test for Ripley's Function Rejection of Poisson Null Hypothesis. ISRN Ecology 2013(Article ID 753475): 9.

See Also

Khat, GoFtest

Examples

# Simulate a Matern (Neyman Scott) point pattern
nclust <- function(x0, y0, radius, n) {
  return(runifdisc(n, radius, centre=c(x0, y0)))
}
X <- rNeymanScott(20, 0.1, nclust, radius=0.2, n=5)
autoplot(as.wmppp(X))

# Test it
Ktest(X, r=seq(0.1, .5, .1))

Estimation of the confidence envelope of the L function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of L according to the confidence level.

Usage

LEnvelope(X, r = NULL, NumberOfSimulations = 100, Alpha = 0.05,
          ReferenceType = "", NeighborType = "",
          SimulationType = "RandomPosition", Precision = 0, Global = FALSE,
          verbose = interactive(), parallel = FALSE, parallel_pgb_refresh = 1/10)

Arguments

Details

This envelope is local by default, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

The global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

Parallel simulations rely on the future and doFuture packages. Before calling the function with argument parallel = TRUE, you must choose a strategy and set it with plan. Their progress bar relies on the progressr package. They must be activated by the user by handlers.

Value

An envelope object (envelope). There are methods for print and plot for this class.

The fv contains the observed value of the function, its average simulated value and the confidence envelope.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024.

Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

See Also

Khat

Examples

data(paracou16)
# Keep only 20% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.2))
autoplot(X,
  labelSize = expression("Basal area (" ~cm^2~ ")"),
  labelColor = "Species")

# Calculate confidence envelope (should be 1000 simulations, reduced to 20 to save time)
r <- 0:30
NumberOfSimulations <- 20
# Plot the envelope
autoplot(LEnvelope(X, r, NumberOfSimulations))

Estimation of the L function

Description

Estimates the L function

Usage

Lhat(X, r = NULL, ReferenceType = "", NeighborType = "", CheckArguments = TRUE)

Arguments

Details

L is the normalized version of K: L(r)=\sqrt{\frac{K}{\pi}}-r.

Value

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

Note

L was originally defined as L(r)=\sqrt{\frac{K}{\pi}}. It has been used as L(r)=\sqrt{\frac{K}{\pi}}-r in a part of the literature because this normalization is easier to plot.

References

Besag, J. E. (1977). Comments on Ripley's paper. Journal of the Royal Statistical Society B 39(2): 193-195.

See Also

Khat, LEnvelope

Examples

data(paracou16)
autoplot(paracou16)

# Calculate L
r <- 0:30
(Paracou <- Lhat(paracou16, r))

# Plot
autoplot(Paracou)

Estimation of the confidence envelope of the Lmm function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of Lmm according to the confidence level.

Usage

LmmEnvelope(X, r = NULL, NumberOfSimulations = 100, Alpha = 0.05,
            ReferenceType = "", Global = FALSE,
            verbose = interactive(), parallel = FALSE, parallel_pgb_refresh = 1/10)

Arguments

Details

This envelope is local by default, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

The global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

Parallel simulations rely on the future and doFuture packages. Before calling the function with argument parallel = TRUE, you must choose a strategy and set it with plan. Their progress bar relies on the progressr package. They must be activated by the user by handlers.

Value

An envelope object (envelope). There are methods for print and plot for this class.

The fv contains the observed value of the function, its average simulated value and the confidence envelope.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024.

Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

See Also

Lmmhat

Examples

data(paracou16)
# Keep only 20% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.2))
autoplot(X,
  labelSize = expression("Basal area (" ~cm^2~ ")"),
  labelColor = "Species")

# Calculate confidence envelope (should be 1000 simulations, reduced to 4 to save time)
r <- seq(0, 30, 2)
NumberOfSimulations <- 4
Alpha <- .10
autoplot(LmmEnvelope(X, r, NumberOfSimulations, Alpha))

Estimation of the Lmm function

Description

Estimates the Lmm function

Usage

Lmmhat(X, r = NULL, ReferenceType = "", CheckArguments = TRUE)

Arguments

Details

Lmm is the normalized version of Kmm: Lmm(r)=\sqrt{\frac{Kmm}{\pi}}-r.

Value

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

References

Penttinen, A., Stoyan, D. and Henttonen, H. M. (1992). Marked Point Processes in Forest Statistics. Forest Science 38(4): 806-824.

Espa, G., Giuliani, D. and Arbia, G. (2010). Weighting Ripley's K-function to account for the firm dimension in the analysis of spatial concentration. Discussion Papers, 12/2010. Universita di Trento, Trento: 26.

See Also

Kmmhat, LmmEnvelope

Examples

data(paracou16)
# Keep only 50% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.5))
autoplot(X, 
  labelSize = expression("Basal area (" ~cm^2~ ")"), 
  labelColor = "Species")

# Calculate Lmm
r <- seq(0, 30, 2)
(Paracou <- Lmmhat(X, r))

# Plot
autoplot(Paracou)

Estimation of the confidence envelope of the M function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of M according to the confidence level.

Usage

MEnvelope(X, r = NULL, NumberOfSimulations = 100, Alpha = 0.05,
          ReferenceType, NeighborType = ReferenceType,
          CaseControl = FALSE, SimulationType = "RandomLocation", Global = FALSE,
          verbose = interactive(), parallel = FALSE, parallel_pgb_refresh = 1/10)

Arguments

Details

This envelope is local by default, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

The global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

Parallel simulations rely on the future and doFuture packages. Before calling the function with argument parallel = TRUE, you must choose a strategy and set it with plan. Their progress bar relies on the progressr package. They must be activated by the user by handlers.

Value

An envelope object (envelope). There are methods for print and plot for this class.

The fv contains the observed value of the function, its average simulated value and the confidence envelope.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024.

Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

See Also

Mhat

Examples

data(paracou16)
# Keep only 50% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.5))
autoplot(X,
  labelSize = expression("Basal area (" ~cm^2~ ")"),
  labelColor = "Species")

# Calculate confidence envelope (should be 1000 simulations, reduced to 4 to save time)
NumberOfSimulations <- 4
Alpha <- .10
autoplot(MEnvelope(X, , NumberOfSimulations, Alpha,
    "V. Americana", "Q. Rosea", FALSE, "RandomLabeling"))

Estimation of the M function

Description

Estimates the M function

Usage

Mhat(X, r = NULL, ReferenceType, NeighborType = ReferenceType,
    CaseControl = FALSE, Individual = FALSE, CheckArguments = TRUE)

Arguments

Details

M is a weighted, cumulative, relative measure of a point pattern structure. Its value at any distance is the ratio of neighbors of the NeighborType to all points around ReferenceType points, normalized by its value over the windows.

If CaseControl is TRUE, then ReferenceType points are cases and NeighborType points are controls. The univariate concentration of cases is calculated as if NeighborType was equal to ReferenceType, but only controls are considered when counting all points around cases (Marcon et al., 2012). This makes sense when the sampling design is such that all points of ReferenceType (the cases) but only a sample of the other points (the controls) are recorded. Then, the whole distribution of points is better represented by the controls alone.

Value

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

If Individual is set to TRUE, the object also contains the value of the function around each individual ReferenceType point taken as the only reference point. The column names of the fv are "M_" followed by the point names, i.e. the row names of the marks of the point pattern.

References

Marcon, E. and Puech, F. (2010). Measures of the Geographic Concentration of Industries: Improving Distance-Based Methods. Journal of Economic Geography 10(5): 745-762.

Marcon, E., F. Puech and S. Traissac (2012). Characterizing the relative spatial structure of point patterns. International Journal of Ecology 2012(Article ID 619281): 11.

Marcon, E., and Puech, F. (2017). A Typology of Distance-Based Measures of Spatial Concentration. Regional Science and Urban Economics 62:56-67

See Also

MEnvelope, Kdhat

Examples

data(paracou16)
autoplot(paracou16)

# Calculate M
autoplot(Mhat(paracou16, , "V. Americana", "Q. Rosea"))

Spatial smoothing of individual dbmss's

Description

Performs spatial smoothing of the individual values of distance-based measures computed in the neighborhood of each point (Marcon and Puech, 2023).

Usage

  ## S3 method for class 'wmppp'
 Smooth(X, fvind, distance = NULL, Quantiles = FALSE, 
      sigma = bw.scott(X, isotropic = TRUE), Weighted = TRUE, Adjust = 1, 
      Nbx = 128, Nby = 128, ..., CheckArguments = TRUE)

Arguments

Value

An image that can be plotted. If quantiles have been computed in fvind, attributes "High" and "Low" contain logical vectors to indentify significantly high and low quantiles.

References

Marcon, E. and Puech, F. (2023). Mapping distributions in non-homogeneous space with distance-based methods. Journal of Spatial Econometrics 4(1), 13.

Examples

  ReferenceType <- "V. Americana"
  NeighborType <- "Q. Rosea"
  # Calculate individual intertype M(distance) values
  fvind <- Mhat(paracou16, r=c(0, 30), ReferenceType, NeighborType, Individual=TRUE)
  # Plot the point pattern with values of M(30 meters)
  p16_map <- Smooth(paracou16, fvind, distance=30)
  plot(p16_map, main = "")
  # Add the reference points to the plot
  is.ReferenceType <- marks(paracou16)$PointType == ReferenceType
  points(x=paracou16$x[is.ReferenceType], y=paracou16$y[is.ReferenceType], pch=20)
  # Add contour lines
  contour(p16_map, nlevels = 5, add = TRUE)

Converts data to class Dtable

Description

Creates an object of class "Dtable" representing a set of points with weights and labels and the distances between them.. This is a generic method.

Usage

as.Dtable(X, ...)
  ## S3 method for class 'ppp'
as.Dtable(X, ...)
  ## S3 method for class 'data.frame'
as.Dtable(X, ...)

Arguments

Details

This is a generic method, implemented for ppp and data.frame.

Data is first converted to a (wmppp.object). Then, the distance matrix between points is calculated and the marks are kept.

Value

An object of class "Dtable".

See Also

as.wmppp

Converts data to class wmppp

Description

Creates a Weighted, Marked, Planar Point Pattern, i.e. an object of class "wmppp" representing a two-dimensional point pattern with weights and labels. This is a generic method.

Usage

as.wmppp(X, ...)
  ## S3 method for class 'ppp'
as.wmppp(X, ...)
  ## S3 method for class 'data.frame'
as.wmppp(X, window = NULL, unitname = NULL, ...)

Arguments

Details

This is a generic method, implemented for ppp and data.frame:

• If the dataset X is an object of class "ppp" (ppp.object), the marks are converted to point weights if they are numeric or to point types if they are factors. Default weights are set to 1, default types to "All". If marks are a dataframe with column names equal to PointType and PointWeight, they are not modified. Row names of the dataframe are preserved as row names of the marks, to identify points.

• If the dataset X is a dataframe, see wmppp.

Value

An object of class "wmppp".

See Also

wmppp.object

ggplot methods to plot dbmss objects

Description

S3 methods for the autoplot generic.

Usage

  ## S3 method for class 'envelope'
autoplot(object, fmla, ..., ObsColor = "black",
        H0Color = "red", ShadeColor = "grey75", alpha = 0.3, main = NULL,
        xlab = NULL, ylab = NULL, LegendLabels = NULL)
  ## S3 method for class 'fv'
autoplot(object, fmla, ..., ObsColor = "black",
        H0Color = "red", ShadeColor = "grey75", alpha = 0.3, main = NULL,
        xlab = NULL, ylab = NULL, LegendLabels = NULL)
  ## S3 method for class 'wmppp'
autoplot(object, ..., show.window = TRUE,
        MaxPointTypes = 6, Other = "Other",
        main = NULL, xlab = NULL, ylab = NULL, LegendLabels = NULL,
        labelSize = "Weight", labelColor = "Type", palette="Set1",
        windowColor = "black", windowFill = "transparent", alpha = 1)

Arguments

Details

Plots of 'wmppp' objects are a single representation of both point types and point weights. Rectangular and polygonal windows (see owin.object) are supported but mask windows are ignored (use the 'plot' method if necessary).

Value

A ggplot object.

Author(s)

Eric Marcon <Eric.Marcon@agroparistech.fr>, parts of the code from spatstat.explore::plot.fv.

Examples

data(paracou16)
# Keep only 20% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.2))
autoplot(X)

# Plot the envelope (should be 1000 simulations, reduced to 20 to save time)
autoplot(KdEnvelope(X, ReferenceType="Q. Rosea", NumberOfSimulations=20))

# With a formula and a compact legend
autoplot(KEnvelope(X, NumberOfSimulations=20),
    ./(pi*r^2) ~ r,
    LegendLabels=c("Observed", "Expected", "Confidence\n enveloppe"))

Class of envelope of function values (fv)

Description

A class "dbmssEnvelope", i.e. a particular type of see envelope to represent several estimates of the same function and its confidence envelope.

Details

"dbmssEnvelope" objects are similar to envelope objects. The differences are that the risk level is chosen (instead of the simulation rank to use as the envelope), so the rank is calculated (interpolation is used if necessary), and a global envelope can be calculated following Duranton and Overman (2005).

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106

See Also

summary.dbmssEnvelope, KdEnvelope, MEnvelope

Computes simulation envelopes of a summary function.

Description

Prints a useful summary of a confidence envelope of class "dbmssEnvelope"

Usage

## S3 method for class 'Dtable'
envelope(Y, fun = Kest, nsim = 99, nrank = 1, ..., 
          funargs = list(), funYargs = funargs, simulate = NULL, 
          verbose = TRUE, savefuns = FALSE, Yname = NULL, envir.simul = NULL)

Arguments

Details

This is the S3 method envelope for Dtable objects.

Author(s)

Eric Marcon <Eric.Marcon@agroparistech.fr>. Relies on the envelope engine of spatstat.

Estimation of the confidence envelope of the g function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of g according to the confidence level.

Usage

gEnvelope(X, r = NULL, NumberOfSimulations = 100, Alpha = 0.05,
         ReferenceType = "", NeighborType = "",
         SimulationType = "RandomPosition", Precision = 0, Global = FALSE,
         verbose = interactive(), parallel = FALSE, parallel_pgb_refresh = 1/10)

Arguments

Details

This envelope is local by default, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

The global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

Parallel simulations rely on the future and doFuture packages. Before calling the function with argument parallel = TRUE, you must choose a strategy and set it with plan. Their progress bar relies on the progressr package. They must be activated by the user by handlers.

Value

An envelope object (envelope). There are methods for print and plot for this class.

The fv contains the observed value of the function, its average simulated value and the confidence envelope.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024.

Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

See Also

ghat, rRandomPositionK, rRandomLocation, rPopulationIndependenceK

Examples

data(paracou16)
# Keep only 20% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.2))
autoplot(X,
  labelSize = expression("Basal area (" ~cm^2~ ")"),
  labelColor = "Species")

# Calculate confidence envelope (should be 1000 simulations, reduced to 10 to save time)
r <- 0:40
NumberOfSimulations <- 10
# Plot the envelope
autoplot(gEnvelope(X, r, NumberOfSimulations))

Estimation of the g function

Description

Estimates the g function

Usage

ghat(X, r = NULL, ReferenceType = "", NeighborType = "", CheckArguments = TRUE)

Arguments

Details

The computation of ghat relies on spatstat function sewpcf. The kernel estimation of the number of neighbors follows Stoyan and Stoyan (1994, pages 284–285).

Value

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

References

Stoyan, D. and Stoyan, H. (1994) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.

See Also

gEnvelope

Examples

data(paracou16)
autoplot(paracou16)

# Calculate g
r <- 0:30
(Paracou <- ghat(paracou16, r, "Q. Rosea", "V. Americana"))

# Plot
autoplot(Paracou)

Test whether an object is a weighted, marked, planar point pattern

Description

Check whether its argument is an object of class "wmppp" (wmppp.object).

Usage

is.wmppp(X)

Arguments

Value

TRUE if X is a weighted, marked, planar point pattern, otherwise FALSE.

See Also

wmppp.object

Estimation of the confidence envelope of the m function under its null hypothesis

Description

Simulates point patterns according to the null hypothesis and returns the envelope of m according to the confidence level.

Usage

mEnvelope(X, r = NULL, NumberOfSimulations = 100, Alpha = 0.05,
          ReferenceType, NeighborType = ReferenceType, CaseControl = FALSE,
          Original = TRUE, Approximate = ifelse(X$n < 10000, 0, 1), Adjust = 1,
          MaxRange = "ThirdW", SimulationType = "RandomLocation", Global = FALSE,
          verbose = interactive(), parallel = FALSE, parallel_pgb_refresh = 1/10)

Arguments

Details

This envelope is local by default, that is to say it is computed separately at each distance. See Loosmore and Ford (2006) for a discussion.

The global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

Parallel simulations rely on the future and doFuture packages. Before calling the function with argument parallel = TRUE, you must choose a strategy and set it with plan. Their progress bar relies on the progressr package. They must be activated by the user by handlers.

Value

An envelope object (envelope). There are methods for print and plot for this class.

The fv contains the observed value of the function, its average simulated value and the confidence envelope.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Kenkel, N. C. (1988). Pattern of Self-Thinning in Jack Pine: Testing the Random Mortality Hypothesis. Ecology 69(4): 1017-1024.

Lang G., Marcon E. and Puech F. (2014) Distance-Based Measures of Spatial Concentration: Introducing a Relative Density Function. HAL 01082178, 1-18.

Loosmore, N. B. and Ford, E. D. (2006). Statistical inference using the G or K point pattern spatial statistics. Ecology 87(8): 1925-1931.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. Regional Science and Urban Economics. 62:56-67.

Scholl, T. and Brenner, T. (2015) Optimizing distance-based methods for large data sets, Journal of Geographical Systems 17(4): 333-351.

Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.

See Also

mhat

Examples

data(paracou16)
# Keep only 50% of points to run this example
X <- as.wmppp(rthin(paracou16, 0.5))
autoplot(X,
  labelSize = expression("Basal area (" ~cm^2~ ")"),
  labelColor = "Species")

# Calculate confidence envelope (should be 1000 simulations, reduced to 4 to save time)
NumberOfSimulations <- 4
Alpha <- .10
autoplot(mEnvelope(X, , NumberOfSimulations, Alpha,
    "V. Americana", "Q. Rosea", Original = FALSE, SimulationType = "RandomLabeling"))

marks method for Dtable and wmppp objects

Description

S3 methods for the marks generic.

Usage

  ## S3 method for class 'Dtable'
marks(x, ...)
  ## S3 replacement method for class 'Dtable'
marks(x, ...) <- value
  ## S3 replacement method for class 'wmppp'
marks(x, ..., dfok = TRUE, drop = TRUE) <- value

Arguments

Details

These functions extract or modify the marks of a Dtable.

'marks<-.wmppp()' just calls 'marks<-.ppp()' and keeps the class of the wmppp object. The conformity of the marks with the definition of the class "wmppp", i.e. a dataframe with columns "PointType" and "PointWeight" of the same length as the number of points, is not checked.

Value

A dataframe with columns "PointType" and "PointWeight".

Author(s)

Eric Marcon <Eric.Marcon@agroparistech.fr>

Examples

# A Dtable containing two points
Dmatrix <- matrix(c(0,1,1,0), nrow=2)
PointType <- c("Type1", "Type2")
PointWeight <- c(2,3)
X <- Dtable(Dmatrix, PointType, PointWeight)
# Extract the marks
marks(X)

Estimation of the m function

Description

Estimates the m function

Usage

mhat(X, r = NULL, ReferenceType, NeighborType = ReferenceType,
    CaseControl = FALSE, Original = TRUE, Approximate = ifelse(X$n < 10000, 0, 1),
    Adjust = 1, MaxRange = "ThirdW", Individual = FALSE, CheckArguments = TRUE)

Arguments

Details

m is a weighted, density, relative measure of a point pattern structure (Lang et al., 2014). Its value at any distance is the ratio of neighbors of the NeighborType to all points around ReferenceType points, normalized by its value over the windows.

The number of neighbors at each distance is estimated by a Gaussian kernel whose bandwith is chosen optimally according to Silverman (1986: eq 3.31). It can be sharpened or smoothed by multiplying it by Adjust. The bandwidth of Sheather and Jones (1991) would be better but it is very slow to calculate for large point patterns and it sometimes fails. It is often sharper than that of Silverman.

If X is not a Dtable object, the maximum value of r is obtained from the geometry of the window rather than caculating the median distance between points as suggested by Duranton and Overman (2005) to save (a lot of) calculation time.

If CaseControl is TRUE, then ReferenceType points are cases and NeighborType points are controls. The univariate concentration of cases is calculated as if NeighborType was equal to ReferenceType, but only controls are considered when counting all points around cases (Marcon et al., 2012). This makes sense when the sampling design is such that all points of ReferenceType (the cases) but only a sample of the other points (the controls) are recorded. Then, the whole distribution of points is better represented by the controls alone.

Value

An object of class fv, see fv.object, which can be plotted directly using plot.fv.

If Individual is set to TRUE, the object also contains the value of the function around each individual ReferenceType point taken as the only reference point. The column names of the fv are "m_" followed by the point names, i.e. the row names of the marks of the point pattern.

Note

Estimating m relies on calculating distances, exactly or approximately (if Approximate is not 0). Then distances are smoothed by estimating their probability density. In contrast with Kdhat, reflection is not used to estimate density close to the lowest distance. The same kernel estimation is applied to the distances from reference points of neighbor points and of all points. Since m is a relative function, a ratio of densities is calculated, that makes the features of the estimation vanish.

Density estimation heavily relies on the bandwith. Starting from version 2.7, the optimal bandwith is computed from the distribution of distances between pairs of points up to twice the maximum distance considered. The consequence is that choosing a smaller range of distances in argument r results in less smoothed m values. The default values (r = NULL, MaxRange = "ThirdW") are such that almost all the pairs of points (except those more than 2/3 of the window diameter apart) are taken into account to determine the bandwith.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Lang G., Marcon E. and Puech F. (2014) Distance-Based Measures of Spatial Concentration: Introducing a Relative Density Function. HAL 01082178, 1-18.

Marcon, E., F. Puech and S. Traissac (2012). Characterizing the relative spatial structure of point patterns. International Journal of Ecology 2012(Article ID 619281): 11.

Scholl, T. and Brenner, T. (2015) Optimizing distance-based methods for large data sets, Journal of Geographical Systems 17(4): 333-351.

Sheather, S. J. and Jones, M. C. (1991) A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society series B, 53, 683-690.

Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.

See Also

mEnvelope, Kdhat

Examples

data(paracou16)
autoplot(paracou16)

# Calculate M
autoplot(mhat(paracou16, , "V. Americana", "Q. Rosea"))

Paracou field station plot 16, partial map

Description

This point pattern is from Paracou field station, French Guiana, managed by Cirad.

Usage

data(paracou16)

Format

An object of class ppp.object representing the point pattern of tree locations in a 250 x 300 meter sampling region. Each tree is marked with its species ("Q. Rosea", "V. Americana" or "Other"), and basal area (square centimeters).

Source

Permanent data census of Paracou and Marcon et al. (2012).

References

Gourlet-Fleury, S., Guehl, J. M. and Laroussinie, O., Eds. (2004). Ecology & management of a neotropical rainforest. Lessons drawn from Paracou, a long-term experimental research site in French Guiana. Paris, Elsevier.

Marcon, E., F. Puech and S. Traissac (2012). Characterizing the relative spatial structure of point patterns. International Journal of Ecology 2012(Article ID 619281): 11.

Examples

data(paracou16)
# Plot (second column of marks is Point Types) 
autoplot(paracou16, which.marks=2, leg.side="right")

Auxiliary functions to count point neighbors

Description

C++ routines used for fast count of neighbors.

Usage

parallelCountNbd(r, x, y, Weight, IsReferenceType, IsNeighborType)
parallelCountNbdCC(r, x, y, Weight, IsReferenceType, IsNeighborType)
parallelCountNbdm(x, y, ReferencePoints)
parallelCountNbdDt(r, Dmatrix, Weight, IsReferenceType, IsNeighborType)
parallelCountNbdDtCC(r, Dmatrix, Weight, IsReferenceType, IsNeighborType)
DistKd(x, y, PointWeight, Weight, Dist, IsReferenceType, IsNeighborType)
CountNbdKd(r, x, y, Weight, Nbd, IsReferenceType, IsNeighborType)

Arguments

Details

These routines are called internally.

Print a confidence envelope

Description

Prints useful information of a confidence envelope of class "dbmssEnvelope"

Usage

## S3 method for class 'dbmssEnvelope'
print(x, ...)

Arguments

Details

"dbmssEnvelope" objects are similar to envelope objects. The way they are printed is different to take into account the possibility of building global envelope following Duranton and Overman (2005): the global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106

Examples

data(paracou16)
autoplot(paracou16)

# Calculate intertype K envelope
Envelope <- KEnvelope(paracou16, NumberOfSimulations = 20, Global = TRUE,
  ReferenceType = "V. Americana", NeighborType = "Q. Rosea")
autoplot(Envelope)
# print
print(Envelope)

Simulations of a point pattern according to the null hypothesis of population independence defined for K

Description

Simulates of a point pattern according to the null hypothesis of population independence defined for K.

Usage

rPopulationIndependenceK(X, ReferenceType, NeighborType, CheckArguments = TRUE)

Arguments

Details

Reference points are kept unchanged, neighbor type point positions are shifted by rshift. Other points are lost and point weights are not kept (they are set to 1) since the K function ignores them.

Value

A new weighted, marked, planar point pattern (an object of class wmppp, see wmppp.object).

References

Goreaud, F. et Pelissier, R. (2003). Avoiding misinterpretation of biotic interactions with the intertype K12 fonction: population independence vs random labelling hypotheses. Journal of Vegetation Science 14(5): 681-692.

See Also

rPopulationIndependenceM, rRandomLabeling

Examples

# Simulate a point pattern with three types
X <- rpoispp(50) 
PointType   <- sample(c("A", "B", "C"), X$n, replace=TRUE)
PointWeight <- runif(X$n, min=1, max=10)
marks(X) <- data.frame(PointType, PointWeight)
X <- as.wmppp(X)

# Plot the point pattern, using PointType as marks
autoplot(X, main="Original pattern")

# Randomize it
Y <- rPopulationIndependenceK(X, "A", "B")
# Points of type "A" are unchanged, points of type "B" have been moved altogether
# Other points are lost and point weights are set to 1
autoplot(Y, main="Randomized pattern")

Simulations of a point pattern according to the null hypothesis of population independence defined for M

Description

Simulates of a point pattern according to the null hypothesis of population independence defined for M

Usage

rPopulationIndependenceM(X, ReferenceType, CheckArguments = TRUE)

Arguments

Details

Reference points are kept unchanged, other points are redistributed randomly across locations.

Value

A new weighted, marked, planar point pattern (an object of class wmppp, see wmppp.object).

References

Marcon, E. and Puech, F. (2010). Measures of the Geographic Concentration of Industries: Improving Distance-Based Methods. Journal of Economic Geography 10(5): 745-762.

Marcon, E., F. Puech and S. Traissac (2012). Characterizing the relative spatial structure of point patterns. International Journal of Ecology 2012(Article ID 619281): 11.

See Also

rPopulationIndependenceK, rRandomLabelingM

Examples

# Simulate a point pattern with five types
X <- rpoispp(50) 
PointType   <- sample(c("A", "B", "C", "D", "E"), X$n, replace=TRUE)
PointWeight <- runif(X$n, min=1, max=10)
marks(X) <- data.frame(PointType, PointWeight)
X <- as.wmppp(X)


autoplot(X, main="Original pattern")

# Randomize it
Y <- rPopulationIndependenceM(X, "A")
# Points of type "A" are unchanged, 
# all other points have been redistributed randomly across locations
autoplot(Y, main="Randomized pattern")

Simulations of a point pattern according to the null hypothesis of random labeling

Description

Simulates of a point pattern according to the null hypothesis of random labeling.

Usage

rRandomLabeling(X, CheckArguments = TRUE)

Arguments

Details

Marks are redistributed randomly across the original point pattern.

Value

A new weighted, marked, planar point pattern (an object of class wmppp, see wmppp.object).

References

Goreaud, F. et Pelissier, R. (2003). Avoiding misinterpretation of biotic interactions with the intertype K12 fonction: population independence vs random labelling hypotheses. Journal of Vegetation Science 14(5): 681-692.

See Also

rRandomLabelingM, rPopulationIndependenceK

Examples

# Simulate a point pattern with five types
X <- rpoispp(50) 
PointType   <- sample(c("A", "B", "C", "D", "E"), X$n, replace=TRUE)
PointWeight <- runif(X$n, min=1, max=10)
marks(X) <- data.frame(PointType, PointWeight)
X <- as.wmppp(X)

autoplot(X, main="Original pattern")

# Randomize it
Y <- rRandomLabeling(X)
# Types and weights have been redistributed randomly across locations
autoplot(Y, main="Randomized pattern")

Simulations of a point pattern according to the null hypothesis of random labelling defined for M

Description

Simulates of a point pattern according to the null hypothesis of random labelling defined for M

Usage

rRandomLabelingM(X, CheckArguments = TRUE)

Arguments

Details

Point types are randomized. Locations and weights are kept unchanged. If both types and weights must be randomized together (Duranton and Overman, 2005; Marcon and Puech, 2010), use rRandomLocation.

Value

A new weighted, marked, planar point pattern (an object of class wmppp, see wmppp.object).

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Marcon, E. and Puech, F. (2010). Measures of the Geographic Concentration of Industries: Improving Distance-Based Methods. Journal of Economic Geography 10(5): 745-762.

Marcon, E., F. Puech and S. Traissac (2012). Characterizing the relative spatial structure of point patterns. International Journal of Ecology 2012(Article ID 619281): 11.

See Also

rRandomLabeling, rPopulationIndependenceM

Examples

# Simulate a point pattern with five types
X <- rpoispp(50) 
PointType   <- sample(c("A", "B", "C", "D", "E"), X$n, replace=TRUE)
PointWeight <- runif(X$n, min=1, max=10)
marks(X) <- data.frame(PointType, PointWeight)
X <- as.wmppp(X)

autoplot(X, main="Original pattern")

# Randomize it
Y <- rRandomLabelingM(X)
# Labels have been redistributed randomly across locations
# But weights are unchanged
autoplot(Y, main="Randomized pattern")

Simulations of a point pattern according to the null hypothesis of random location

Description

Simulates of a point pattern according to the null hypothesis of random location.

Usage

rRandomLocation(X, ReferenceType = "", CheckArguments = TRUE)

Arguments

Details

Points are redistributed randomly across the locations of the original point pattern. This randomization is equivalent to random labeling, considering the label is both point type and point weight. If ReferenceType is specified, then only reference type points are kept in the orginal point pattern before randomization.

Value

A new weighted, marked, planar point pattern (an object of class wmppp, see wmppp.object).

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106.

Marcon, E. and Puech, F. (2010). Measures of the Geographic Concentration of Industries: Improving Distance-Based Methods. Journal of Economic Geography 10(5): 745-762.

See Also

rRandomPositionK

Examples

# Simulate a point pattern with five types
X <- rpoispp(50) 
PointType   <- sample(c("A", "B", "C", "D", "E"), X$n, replace=TRUE)
PointWeight <- runif(X$n, min=1, max=10)
marks(X) <- data.frame(PointType, PointWeight)
X <- as.wmppp(X)

autoplot(X, main="Original pattern")

# Randomize it
Y <- rRandomLocation(X)
# Points have been redistributed randomly across locations
autoplot(Y, main="Randomized pattern")

Simulations of a point pattern according to the null hypothesis of random position defined for K

Description

Simulations of a point pattern according to the null hypothesis of random position defined for K.

Usage

rRandomPositionK(X, Precision = 0, CheckArguments = TRUE)

Arguments

Details

Points marks are kept unchanged and their position is drawn in a binomial process by runifpoint.

Value

A new weighted, marked, planar point pattern (an object of class wmppp, see wmppp.object).

Note

Simulations in a binomial process keeps the same number of points, so that marks can be redistributed. If a real CSR simulation is needed and marks are useless, use rpoispp.

Actual data coordinates are often rounded. Use the Precision argument to simulate point patterns with the same rounding procedure. For example, if point coordinates are in meters and rounded to the nearest half meter, use Precision = 0.5 so that the same approximation is applied to the simulated point patterns.

See Also

rRandomLocation

Examples

# Simulate a point pattern with two types
X <- rpoispp(5) 
PointType   <- sample(c("A", "B"), X$n, replace=TRUE)
PointWeight <- runif(X$n, min=1, max=10)
marks(X) <- data.frame(PointType, PointWeight)
X <- as.wmppp(X)

autoplot(X, main="Original pattern")

# Randomize it
Y <- rRandomPositionK(X)
# Points are randomly distributed
autoplot(Y, main="Randomized pattern")

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

ggplot2

autoplot

spatstat.geom

marks

Methods for weighted, marked planar point patterns (of class wmppp) from spatstat

Description

spatstat methods for a ppp.object applied to a wmppp.object.

Usage

## S3 method for class 'wmppp'
sharpen(X, ...)
## S3 method for class 'wmppp'
superimpose(...)
## S3 method for class 'wmppp'
unique(x, ...)
## S3 method for class 'wmppp'
i[j, drop=FALSE, ..., clip=FALSE]

Arguments

Details

spatstat methods for ppp objects returning a ppp object can be applied to a wmppp and return a wpppp with these methods which just call the ppp.object method and change the class of the result for convenience.

Some spatstat functions such as rthin are not generic so they always return a ppp.object when applied to a wmppp.object. Their result may be converted by as.wmppp.

Value

An object of class "wmppp".

See Also

sharpen.ppp, superimpose.ppp, unique.ppp

Summary of a confidence envelope

Description

Prints a useful summary of a confidence envelope of class "dbmssEnvelope"

Usage

## S3 method for class 'dbmssEnvelope'
summary(object, ...)

Arguments

Details

"dbmssEnvelope" objects are similar to envelope objects. Their summary is different to take into account the possibility of building global envelope following Duranton and Overman (2005): the global envelope is calculated by iteration: the simulations reaching one of the upper or lower values at any distance are eliminated at each step. The process is repeated until Alpha / Number of simulations simulations are dropped. The remaining upper and lower bounds at all distances constitute the global envelope. Interpolation is used if the exact ratio cannot be reached.

References

Duranton, G. and Overman, H. G. (2005). Testing for Localisation Using Micro-Geographic Data. Review of Economic Studies 72(4): 1077-1106

Examples

data(paracou16)
autoplot(paracou16)

# Calculate intertype K envelope
Envelope <- KEnvelope(paracou16, NumberOfSimulations = 20, Global = TRUE,
  ReferenceType = "V. Americana", NeighborType = "Q. Rosea")
autoplot(Envelope)
summary(Envelope)

Create a Weighted, Marked, Planar Point Pattern

Description

Creates an object of class "wmppp" representing a two-dimensional point pattern with weights and labels.

Usage

wmppp(df, window = NULL, unitname = NULL)

Arguments

Details

Columns named "X", "Y", "PointType", "PointWeight" (capitalization is ignored) are searched to build the "wmppp" object and set the point coordinates, type and weight. If they are not found, columns are used in this order. If columns are missing, PointType is set to "All" and PointWeight to 1. If a "PointName" column is found, it is used to set the row names of the marks, else the original row names are used.

If the window is not specified, a rectangle containing all points is used, and unitname is used.

Value

An object of class "wmppp".

See Also

wmppp.object,

Examples

# 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.
plot(wmppp(data.frame(X, Y, PointType)), , which.marks=2)

Class of Weighted, Marked, Planar Point Patterns

Description

A class "wmppp" to represent a two-dimensional point pattern of class ppp whose marks are a dataframe with two columns:

• PointType: labels, as factors

• PointWeight: weights.

Details

This class represents a two-dimensional point pattern dataset. wmppp objects are also of class ppp.

Objects of class wmppp may be created by the function wmppp and converted from other types of data by the function as.wmppp.

See Also

ppp.object, wmppp, as.wmppp autoplot.wmppp

Examples

# Draw the coordinates of 10 points
X <- runif(10)
Y <- runif(10)
# Draw the point types and weights
PointType   <- sample(c("A", "B"), 10, replace=TRUE)
PointWeight <- runif(10)
# Build the point pattern
X <- wmppp(data.frame(X, Y, PointType, PointWeight), owin())

# Plot the point pattern. which.marks=1 for point weights, 2 for point types
par(mfrow=c(1,2))
plot(X, which.marks=1, main="Point weights")
plot(X, which.marks=2, main="Point types")

# Or use autoplot for a ggplot
autoplot(X)