Enables envelopes to be computed for point patterns on a linear network.
# S3 method for 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 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)
A point pattern on a linear network
(object of class "lpp")
or a fitted point process model on a linear network
(object of class "lppm").
Function that is to be computed for each simulated pattern.
Number of simulations to perform.
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.
A list, containing extra arguments to be passed to fun.
Optional. A list, containing extra arguments to be passed to
fun when applied to the original data Y only.
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 function, then this function will be
repeatedly applied to the data pattern Y to obtain
nsim simulated patterns.
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.
Logical. If TRUE, simulated patterns will have the
same number of points as the original data pattern.
Logical. If TRUE, simulated patterns will have the
same number of points and the same marks as the
original data pattern. In a multitype point pattern this means that
the simulated patterns will have the same number of points
of each type as the original data.
Logical flag indicating whether to print progress reports during the simulations.
Optional. A transformation to be applied to the function values, before the envelopes are computed. An expression object (see Details).
Logical flag indicating whether envelopes should be pointwise
(global=FALSE) or simultaneous (global=TRUE).
Optional.
A vector of length 2 specifying
the interval of \(r\) values for the simultaneous critical
envelopes. Only relevant if global=TRUE.
Logical value indicating whether to use the theoretical value,
computed by fun, as the reference value for simultaneous
envelopes. Applicable only when global=TRUE.
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").
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).
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.
Logical flag indicating whether to save all the simulated function values.
Logical flag indicating whether to save all the simulated point patterns.
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.
Logical. If TRUE, critical envelopes will be calculated
as sample mean plus or minus nSD times sample standard
deviation.
Number of estimated standard deviations used to determine
the critical envelopes, if VARIANCE=TRUE.
Character string that should be used as the name of the
data point pattern Y when printing or plotting the results.
Maximum number of rejected patterns.
If fun yields a fatal 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.
Logical value specifying whether to reject a simulated pattern
if the resulting values of fun are all equal to NA,
NaN or infinite. If FALSE (the default), then
simulated patterns are rejected only when fun gives a
fatal error.
Logical value specifying whether to print a report each time a simulated pattern is rejected.
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.
Environment in which to evaluate the expression simulate,
if not the current environment.
Function value table (object of class "fv")
with additional information,
as described in envelope.
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.
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 second-order 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 K-function method on a network and its computational implementation. Geographical Analysis 33, 271-290.
# NOT RUN {
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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