envelope.lpp  R Documentation 
Enables envelopes to be computed for point patterns on a linear network.
## S3 method for class 'lpp' envelope(Y, fun=linearK, nsim=99, nrank=1, ..., funargs=list(), funYargs=funargs, simulate=NULL, fix.n=FALSE, fix.marks=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, rejectNA=FALSE, silent=FALSE, do.pwrong=FALSE, envir.simul=NULL) ## S3 method for class 'lppm' envelope(Y, fun=linearK, nsim=99, nrank=1, ..., funargs=list(), funYargs=funargs, simulate=NULL, fix.n=FALSE, fix.marks=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, rejectNA=FALSE, silent=FALSE, do.pwrong=FALSE, envir.simul=NULL)
Y 
A point pattern on a linear network
(object of class 
fun 
Function that is to be computed for each simulated pattern. 
nsim 
Number of simulations to perform. 
nrank 
Integer. Rank of the envelope value amongst the 
... 
Extra arguments passed to 
funargs 
A list, containing extra arguments to be passed to 
funYargs 
Optional. A list, containing extra arguments to be passed to

simulate 
Optional. Specifies how to generate the simulated point patterns.
If 
fix.n 
Logical. If 
fix.marks 
Logical. If 
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
( 
ginterval 
Optional.
A vector of length 2 specifying
the interval of r values for the simultaneous critical
envelopes. Only relevant if 
use.theory 
Logical value indicating whether to use the theoretical value,
computed by 
alternative 
Character string determining whether the envelope corresponds
to a twosided test ( 
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 
clamp 
Logical value indicating how to compute envelopes when

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 
VARIANCE 
Logical. If 
nSD 
Number of estimated standard deviations used to determine
the critical envelopes, if 
Yname 
Character string that should be used as the name of the
data point pattern 
maxnerr 
Maximum number of rejected patterns.
If 
rejectNA 
Logical value specifying whether to reject a simulated pattern
if the resulting values of 
silent 
Logical value specifying whether to print a report each time a simulated pattern is rejected. 
do.pwrong 
Logical. If 
envir.simul 
Environment in which to evaluate the expression 
This is a method for the generic
function envelope
applicable to point patterns on a linear network.
The argument Y
can be either a point pattern on a linear
network, or a fitted point process model on a linear network.
The function fun
will be evaluated for the data
and also for nsim
simulated point
patterns on the same linear network.
The upper and lower
envelopes of these evaluated functions will be computed
as described in envelope
.
The type of simulation is determined as follows.
if Y
is a point pattern (object of class "lpp"
)
and simulate
is missing or NULL
,
then random point patterns will be generated according to
a Poisson point process on the linear network on which Y
is defined, with intensity estimated from Y
.
if Y
is a fitted point process model (object of class
"lppm"
) and simulate
is missing or NULL
,
then random point patterns will be generated by simulating
from the fitted model.
If simulate
is present, it specifies the
type of simulation as explained below.
If simulate
is an expression (typically including a call
to a random generator), then the expression will be repeatedly
evaluated, and should yield random point patterns on the same
linear network as Y
.
If simulate
is a function (typically including a call
to a random generator), then the function will be repeatedly
applied to the original point pattern Y
, and
should yield random point patterns on the same
linear network as Y
.
If simulate
is a list of point patterns,
then these will be taken as the simulated point patterns.
They should be on the same linear network as Y
.
The function fun
should accept as its first argument
a point pattern on a linear network (object of class "lpp"
)
and should have another argument called r
or a ...
argument.
Function value table (object of class "fv"
)
with additional information,
as described in envelope
.
Ang Qi Wei aqw07398@hotmail.com and \adrian
Ang, Q.W. (2010) Statistical methodology for events on a network. Master's thesis, School of Mathematics and Statistics, University of Western Australia.
Ang, Q.W., Baddeley, A. and Nair, G. (2012) Geometrically corrected secondorder analysis of events on a linear network, with applications to ecology and criminology. Scandinavian Journal of Statistics 39, 591–617.
Okabe, A. and Yamada, I. (2001) The Kfunction method on a network and its computational implementation. Geographical Analysis 33, 271290.
envelope
,
linearK
if(interactive()) { ns < 39 np < 40 } else { ns < np < 3 } X < runiflpp(np, simplenet) # uniform Poisson: random numbers of points envelope(X, nsim=ns) # uniform Poisson: conditional on observed number of points envelope(X, fix.n=TRUE, nsim=ns) # nonuniform Poisson fit < lppm(X ~x) envelope(fit, nsim=ns) #multitype marks(X) < sample(letters[1:2], np, replace=TRUE) envelope(X, nsim=ns)
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