envelope {spatstat}R Documentation

Simulation envelopes of summary function

Description

Computes simulation envelopes of a summary function.

Usage

  envelope(Y, fun=Kest, nsim=99, nrank=1, verbose=TRUE, ...,
  simulate=NULL, clipdata=TRUE, start=NULL, control=list(nrep=1e5, expand=1.5))

Arguments

Y Either a point pattern (object of class "ppp") or a fitted point process model (object of class "ppm").
fun Function that computes the desired summary statistic for a 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.
verbose Logical flag indicating whether to print progress reports during the simulations.
... Extra arguments passed to fun.
simulate Optional. An expression. If this is present, then the simulated point patterns will be generated by evaluating this expression nsim times.
clipdata Logical flag indicating whether the data point pattern should be clipped to the same window as the simulated patterns, before the summary function for the data is computed. This should usually be TRUE to ensure that the data and simulations are properly comparable.
start,control Optional. These specify the arguments start and control of rmh, giving complete control over the simulation algorithm.

Details

Simulation envelopes can be used to assess the goodness-of-fit of a point process model to point pattern data. See the References.

This function first generates nsim random point patterns in one of the following ways.

The summary statistic fun is applied to each of these simulated patterns. Typically fun is one of the functions Kest, Gest, Fest, Jest, pcf, Kcross, Kdot, Gcross, Gdot, Jcross, Jdot, Kmulti, Gmulti, Jmulti or Kinhom. It may also be a character string containing the name of one of these functions.

The statistic fun can also be a user-supplied function; if so, then it must have arguments X and r like those in the functions listed above, and it must return an object of class "fv".

Upper and lower pointwise envelopes are computed pointwise (i.e. for each value of the distance argument r), by sorting the nsim simulated values, and taking the m-th lowest and m-th highest values, where m = nrank. For example if nrank=1, the upper and lower envelopes are the pointwise maximum and minimum of the simulated values.

The significance level of the associated Monte Carlo test is alpha = 2 * nrank/(1 + nsim).

The return value is an object of class "fv" containing the summary function for the data point pattern and the upper and lower simulation envelopes. It can be plotted using plot.fv.

Arguments can be passed to the function fun through .... This makes it possible to select the edge correction used to calculate the summary statistic. See the Examples.

If Y is a fitted point process model, and simulate=NULL, then the model is simulated by running the Metropolis-Hastings algorithm rmh. Complete control over this algorithm is provided by the arguments start and control which are passed to rmh.

Selecting only a single edge correction will make the code run much faster.

Value

An object of class "fv", see fv.object, which can be plotted directly using plot.fv.
Essentially a data frame containing columns

r the vector of values of the argument r at which the summary function fun has been estimated
obs values of the summary function for the data point pattern
lo lower envelope of simulations
hi upper envelope of simulations

Author(s)

Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner rolf@math.unb.ca http://www.math.unb.ca/~rolf

References

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

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

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

fv.object, plot.fv, Kest, Gest, Fest, Jest, pcf, ppp, ppm

Examples

 data(simdat)
 X <- simdat

 # Envelope of K function under CSR
 ## Not run: 
 plot(envelope(X))
 
## End(Not run)
 

 # Translation edge correction (this is also FASTER):
 ## Not run: 
 plot(envelope(X, correction="translate"))
 
## End(Not run)
 

 # Envelope of K function for simulations from model 
 data(cells)
 fit <- ppm(cells, ~1, Strauss(0.05))
 ## Not run: 
 plot(envelope(fit))
 
## End(Not run)
 

 # Envelope of G function under CSR
 ## Not run: 
 plot(envelope(X, Gest))
 
## End(Not run)
 

 # Envelope of L function under CSR
 #  L(r) = sqrt(K(r)/pi)
 ## Not run: 
  E <- envelope(X, Kest)
  plot(E, sqrt(./pi) ~ r)
 
## End(Not run)
 

 # How to pass arguments needed to compute the summary functions:
 # We want envelopes for Jcross(X, "A", "B") 
 # where "A" and "B" are types of points in the dataset 'demopat'

 data(demopat)
 ## Not run: 
 plot(envelope(demopat, Jcross, i="A", j="B"))
 
## End(Not run)
 
 
 # Use of `simulate'
 ## Not run: 
 plot(envelope(cells, Gest, simulate=expression(runifpoint(42))))
 plot(envelope(cells, Gest, simulate=expression(rMaternI(100,0.02))))
 
## End(Not run)
 

 # Envelope under random toroidal shifts
 data(amacrine)
 ## Not run: 
 plot(envelope(amacrine, Kcross, i="on", j="off",
               simulate=expression(rshift(amacrine, radius=0.25)))) 
 
## End(Not run)
 

 # Envelope under random shifts with erosion
 ## Not run: 
 plot(envelope(amacrine, Kcross, i="on", j="off",
              simulate=expression(rshift(amacrine, radius=0.1, edge="erode"))))
 
## End(Not run)
 

 
 # Envelope of INHOMOGENEOUS K-function with fitted trend
 trend <- density.ppp(X, 1.5)
 ## Not run: 
 plot(envelope(X, Kinhom, lambda=trend,
         simulate=expression(rpoispp(trend))))
 
## End(Not run)
 
 

[Package spatstat version 1.8-8 Index]