Envelope for Point Patterns on Linear Network
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, \dots, simulate=NULL, verbose=TRUE, transform=NULL,global=FALSE,ginterval=NULL, savefuns=FALSE, savepatterns=FALSE, nsim2=nsim, VARIANCE=FALSE, nSD=2, Yname=NULL) ## S3 method for class 'lppm': envelope(Y, fun=linearK, nsim=99, nrank=1, \dots, simulate=NULL, verbose=TRUE, transform=NULL,global=FALSE,ginterval=NULL, savefuns=FALSE, savepatterns=FALSE, nsim2=nsim, VARIANCE=FALSE, nSD=2, Yname=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
- Function that is to be computed for each simulated pattern.
- Number of simulations to perform.
- Integer. Rank of the envelope value amongst the
nsimsimulated values. A rank of 1 means that the minimum and maximum simulated values will be used.
- Extra arguments passed to
- Optional. Specifies how to generate the simulated point patterns.
simulateis an expression in the R language, then this expression will be evaluated
nsimtimes, to obtain
nsimpoint patterns which are
- 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 (
A vector of length 2 specifying
the interval of $r$ values for the simultaneous critical
envelopes. Only relevant if
- 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=TRUEand the simulations are not based on CSR.
- Logical. If
TRUE, critical envelopes will be calculated as sample mean plus or minus
nSDtimes sample standard deviation.
- Number of estimated standard deviations used to determine
the critical envelopes, if
- Character string that should be used as the name of the
data point pattern
Ywhen printing or plotting the results.
This is a method for the generic
applicable to point patterns on a linear network.
Y can be either a point pattern on a linear
network, or a fitted point process model on a linear network.
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
The type of simulation is determined as follows.
Yis a point pattern (object of class
simulateis missing or
NULL, then random point patterns will be generated according to a Poisson point process on the linear network on which
Yis defined, with intensity estimated from
Yis a fitted point process model (object of class
simulateis missing or
NULL, then random point patterns will be generated by simulating from the fitted model.
simulateis present, it should be an expression that can be evaluated to yield random point patterns on the same linear network as
funshould accept as its first argument a point pattern on a linear network (object of class
"lpp") and should have another argument called
- Function value table (object of class
"fv") with additional information, as described in
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. To appear in Scandinavian Journal of Statistics. Okabe, A. and Yamada, I. (2001) The K-function method on a network and its computational implementation. Geographical Analysis 33, 271-290.
example(lpp) # uniform Poisson envelope(X, nsim=4) # nonuniform Poisson fit <- lppm(X, ~x) envelope(fit, nsim=4)