envelope {spatstat} | R Documentation |
Computes simulation envelopes of a summary function.
envelope(Y, fun=Kest, nsim=99, nrank=1, verbose=TRUE, ..., simulate=NULL, start=NULL, control=list(nrep=1e5, expand=1.5))
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.
|
start,control |
Optional. These specify the arguments start and control
of rmh , giving complete control over the
simulation algorithm.
|
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.
Y
is a point pattern (an object of class "ppp"
)
and simulate=NULL
,
then this routine generates 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
.
Y
is a fitted point process model (an object of class
"ppm"
) and simulate=NULL
,
then this routine generates nsim
simulated
realisations of that model.
simulate
is supplied, then it must be
an expression. It will be evaluated nsim
times to
yield nsim
point patterns.
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
.
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 |
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
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.
fv.object
,
plot.fv
,
Kest
,
Gest
,
Fest
,
Jest
,
pcf
,
ppp
,
ppm
X <- rpoispp(42) # 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) # Use of `simulate' ## Not run: plot(envelope(X, Gest, simulate=expression(runifpoint(42)))) plot(envelope(X, Gest, simulate=expression(rMaternI(100,0.02)))) ## End(Not run)