envelope.sp2: Simulation Envelopes of Summary Function for Spherical Point...

In baddstats/spherstat: Spatial Point Pattern Analysis, Geometry and Trigonometry for the Sphere

Simulation Envelopes of Summary Function for Spherical Point Pattern

Description

envelope.sp2 computes simulation envelopes of a summary function for a point pattern on a sphere; envelope.sphppm computes simulation envelopes of a summary function, based on a fitted point process model, for a point pattern on a sphere.

Usage

  ## S3 method for class 'sp2'
envelope(Y, fun=Ksphere, nsim=99, nrank=1, ..., 
  funargs=list(), simulate=NULL, fix.n=FALSE, verbose=TRUE, 
  transform=NULL,global=FALSE,ginterval=NULL,use.theory=NULL,
  alternative=c("two.sided", "less", "greater"),
  scale=NULL, clamp=FALSE, 
  savefuns=FALSE, savepatterns=FALSE,
  nsim2=nsim, VARIANCE=FALSE, nSD=2, Yname=NULL, maxnerr=nsim,
  do.pwrong=FALSE, envir.simul=NULL)
## S3 method for class 'sphppm'
envelope(Y, fun = Ksphere, nsim = 99, nrank = 1, ...,
                 funargs = list(), simulate = NULL, fix.n = FALSE,
                 verbose = TRUE, transform = NULL, global = FALSE,
                 ginterval = NULL, use.theory = NULL,
                 alternative = c("two.sided", "less", "greater"),
                 scale = NULL, clamp = FALSE,
                 savefuns = FALSE, savepatterns = FALSE,
                 nsim2 = nsim, VARIANCE = FALSE, nSD = 2,
                 Yname = NULL, maxnerr = nsim, do.pwrong = FALSE,
                 envir.simul = NULL)

Arguments

Y	A spherical point pattern (object of class "sp2").
fun	Function that computes the desired summary statistic for a spherical point pattern.
nsim	Number of simulated point patterns to be generated when computing the envelopes.
nrank	Integer. Rank of the envelope value amongst the nsim simulated values. A rank of 1 means that the minimum and maximum simulated values will be used.
...	Extra arguments passed to fun.
funargs	A list, containing extra arguments to be passed to fun.
simulate	Optional. Specifies how to generate the simulated point patterns. If simulate is an expression in the R language, then this expression will be evaluated nsim times, to obtain nsim point patterns which are taken as the simulated patterns from which the envelopes are computed. If simulate is a list of point patterns, then the entries in this list will be treated as the simulated patterns from which the envelopes are computed. Alternatively simulate may be an object produced by the envelope command: see Details.
fix.n	Logical flag indicating whether to generate simulations with the same number of points as in Y. (Ignored if the argument simulate is given.)
verbose	Logical flag indicating whether to print progress reports during the simulations.
transform	Optional. A transformation to be applied to the function values, before the envelopes are computed. An expression object (see Details).
global	Logical flag indicating whether envelopes should be pointwise (global=FALSE) or simultaneous (global=TRUE).
ginterval	Optional. A vector of length 2 specifying the interval of r values for the simultaneous critical envelopes. Only relevant if global=TRUE.
use.theory	Logical value indicating whether to use the theoretical value, computed by fun, as the reference value for simultaneous envelopes. Only relevant if global=TRUE.
alternative	Character string determining whether the envelope corresponds to a two-sided test (side="two.sided", the default) or a one-sided test with a lower critical boundary (side="less") or a one-sided test with an upper critical boundary (side="greater").
scale	Optional. Scaling function for global envelopes. A function in the R language which determines the relative scale of deviations, as a function of distance r, when computing the global envelopes. Applicable only when global=TRUE. Summary function values for distance r will be divided by scale(r) before the maximum deviation is computed. The resulting global envelopes will have width proportional to scale(r).
clamp	Logical value indicating how to compute envelopes when alternative="less" or alternative="greater". Deviations of the observed summary function from the theoretical summary function are initially evaluated as signed real numbers, with large positive values indicating consistency with the alternative hypothesis. If clamp=FALSE (the default), these values are not changed. If clamp=TRUE, any negative values are replaced by zero.
savefuns	Logical flag indicating whether to save all the simulated function values.
savepatterns	Logical flag indicating whether to save all the simulated point patterns.
nsim2	Number of extra simulated point patterns to be generated if it is necessary to use simulation to estimate the theoretical mean of the summary function. Only relevant when global=TRUE and the simulations are not based on CSR.
VARIANCE	Logical. If TRUE, critical envelopes will be calculated as sample mean plus or minus nSD times sample standard deviation.
nSD	Number of estimated standard deviations used to determine the critical envelopes, if VARIANCE=TRUE.
Yname	Character string that should be used as the name of the data point pattern Y when printing or plotting the results.
maxnerr	Maximum number of rejected patterns. If fun yields an error when applied to a simulated point pattern (for example, because the pattern is empty and fun requires at least one point), the pattern will be rejected and a new random point pattern will be generated. If this happens more than maxnerr times, the algorithm will give up.
do.pwrong	Logical. If TRUE, the algorithm will also estimate the true significance level of the “wrong” test (the test that declares the summary function for the data to be significant if it lies outside the pointwise critical boundary at any point). This estimate is printed when the result is printed.
envir.simul	Environment in which to evaluate the expression simulate, if not the current environment.

Details

The envelope command performs simulations and computes envelopes of a summary statistic based on the simulations. The result is an object that can be plotted to display the envelopes. The envelopes can be used to assess the goodness-of-fit of a point process model to point pattern data.

The envelope function is generic, with methods for the classes "ppp", "ppm" and "kppm" described in the help file for envelope. The function envelope.sp2 is the method for spherical point patterns (objects of class "sp2"), and the function envelope.sphppm is the method for point process models fitted to spherical point patterns (objects of class "sphppm").

For the most basic use, if you have a spherical point pattern X and you want to test Complete Spatial Randomness (CSR), type plot(envelope(X, Ksphere,nsim=39)) to see the spherical K function for X plotted together with the envelopes of the spherical K function for 39 simulations of CSR.

However, if you have fitted a model M to spherical point pattern data and you want to test the goodness-of-fit of the model, simply do plot(envelope(M, nsim=39)) to display pointwise envelopes or plot(envelope(M, nsim=19, global=TRUE)) for global envelopes. Both displays can be interpreted as performing a Monte Carlo test with significance level 0.05.

To create simulation envelopes, the command envelope(Y, ...) first generates nsim random point patterns in one of the following ways.

• If simulate=NULL, then we generate nsim simulations of Complete Spatial Randomness (i.e. nsim simulated point patterns each being a realisation of the uniform Poisson point process) with the same intensity as the pattern Y.

• If simulate is supplied, then it determines how the simulated point patterns are generated. See envelope for details.

The summary statistic fun is applied to each of these simulated patterns. Typically fun is one of the functions Ksphere, Gsphere, Fsphere or Jsphere. It may also be a character string containing the name of one of these functions.

For further information, see the documentation for envelope.

Value

A function value table (object of class "fv") which can be plotted directly. See envelope for further details.

Author(s)

Adrian Baddeley [e-mail] http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner [e-mail]

References

Baddeley, A., Diggle, P.J., Hardegen, A., Lawrence, T., Milne, R.K. and Nair, G. (2014) On tests of spatial pattern based on simulation envelopes. Ecological Monographs, 84(3) 477–489

Cressie, N.A.C. Statistics for spatial data. John Wiley and Sons, 1991.

Diggle, P.J. Statistical analysis of spatial point patterns. Arnold, 2003.

Lawrence, T.J. (2017) Master's Thesis, University of Western Australia.

Ripley, B.D. (1981) Spatial statistics. John Wiley and Sons.

Ripley, B.D. Statistical inference for spatial processes. Cambridge University Press, 1988.

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

See Also

sp2, runif.sphwin, rpoispp.sphwin, Ksphere, Fsphere, Gsphere, Jsphere.

Examples

   X <- runif.sphwin(30)
   # envelopes of Ripley's K for this pattern
   EX <- envelope(X, Ksphere, nsim=39)
   plot(EX)
   M <- sphppm(X ~ x1+x2+x3)
   # envelopes of Ripley's K for this model
   EM <- envelope(M, Ksphere, nsim=19)
   plot(EM) 
   # envelopes of inhomogeneous K, using correctly-updated intensities
   EM2 <- envelope(M, Ksphere, lambdavalues=M, nsim=19)

baddstats/spherstat documentation built on Feb. 6, 2023, 1:45 a.m.