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rmhmodel(model)
rmhmodel(..., cif=NULL, par=NULL, w=NULL, trend=NULL, types=NULL)"rmhmodel", which is essentially
a list of parameter values for the model.
There is a print method for this class, which prints
a sensible description of the model chosen.rmh.default in respect of the lookup cif
has changed from the previous release of spatstat
(versions 1.4-7 to 1.5-1).
Read the Details carefully. In particular it is now required
that the first entry of the r component of par
be strictly positive. (This is the opposite of what was
required in the previous release, which was that this first entry
had to be 0.)It is also now required that the entries of r be
sorted into ascending order. (In the previous release it
was assumed that the entries of r and h were
in corresponding order and the two vectors were sorted
commensurately. It was decided that this is dangerous sand
unnecessary.)
Note that if you specify the lookup pairwise interaction
function via stepfun() the arguments x
and y which are passed to stepfun() are slightly
different from r and h: length(y) is equal
to 1+length(x); the final entry of y must be equal
to 1 --- i.e. this value is explicitly supplied by the user rather
than getting tacked on internally.
The step function returned by stepfun() must be right
continuous (this is the default behaviour of stepfun())
otherwise an error is given.
rmh. The algorithm requires the model to be specified
in a particular format. This function rmhmodel
creates a description of the point process model in the form
required by rmh, and checks that the parameters of the
model are valid.
The point process model should be specified either by the
first argument model or by the other arguments
cif, par etc.
If model is a fitted point process model
(object of class "ppm" obtained by a call to the model-fitting
function ppm) then a description of the point process
model will be extracted from this object.
If model is a list, then it should have components named
cif, par and optionally w, trend,
types with the same interpretation as described below.
The argument cif is a character string specifying the choice of
interpoint interaction for the point process. The current options are
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The argument par supplies parameter values appropriate to
the conditional intensity function being invoked. These are:
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The optional argument trend determines the spatial trend in the model,
if it has one. It should be a function or image
(or a list of such, if the model is multitype)
to provide the value of the trend at an arbitrary point.
[object Object],[object Object]
Note that the trend or trends must be non-negative;
no checking is done for this.
The optional argument w specifies the window
in which the pattern is to be generated. If specified, it must be in
a form which can be coerced to an object of class owin
by as.owin.
The optional argument types specifies the possible
types in a multitype point process. If the model being simulated
is multitype, and types is not specified, then this vector
defaults to 1:ntypes where ntypes is the number of
types.
Diggle, P.J. and Gratton, R.J. (1984) Monte Carlo methods of inference for implicit statistical models. Journal of the Royal Statistical Society, series B 46, 193 -- 212.
Diggle, P.J., Gates, D.J., and Stibbard, A. (1987) A nonparametric estimator for pairwise-interaction point processes. Biometrika 74, 763 -- 770. Scandinavian Journal of Statistics 21, 359--373.
Geyer, C.J. (1999) Likelihood Inference for Spatial Point Processes. Chapter 3 in O.E. Barndorff-Nielsen, W.S. Kendall and M.N.M. Van Lieshout (eds) Stochastic Geometry: Likelihood and Computation, Chapman and Hall / CRC, Monographs on Statistics and Applied Probability, number 80. Pages 79--140.
rmh,
rmhcontrol,
rmhstart,
ppm,
Strauss,
Softcore,
StraussHard,
MultiStrauss,
MultiStraussHard,
DiggleGratton,
PairPiece# Strauss process:
mod01 <- rmhmodel(cif="strauss",par=c(beta=2,gamma=0.2,r=0.7),
w=c(0,10,0,10))
# Equivalent to:
a <- list(cif="strauss",par=c(beta=2,gamma=0.2,r=0.7),
w=c(0,10,0,10))
mod01 <- rmhmodel(a)
# Strauss with hardcore:
mod04 <- list(cif="straush",par=c(beta=2,gamma=0.2,r=0.7,hc=0.3),
w=owin(c(0,10),c(0,5)))
mod04 <- rmhmodel(mod04)
# Soft core:
par3 <- c(0.8,0.1,0.5)
w <- square(10)
mod07 <- rmhmodel(cif="sftcr",
par=c(beta=0.8,sigma=0.1,kappa=0.5),
w=w)
# Multitype Strauss:
beta <- c(0.027,0.008)
gmma <- matrix(c(0.43,0.98,0.98,0.36),2,2)
r <- matrix(c(45,45,45,45),2,2)
mod08 <- rmhmodel(cif="straussm",
par=list(beta=beta,gamma=gmma,radii=r),
w=square(250))
# specify types
mod09 <- rmhmodel(cif="straussm",
par=list(beta=beta,gamma=gmma,radii=r),
w=square(250),
types=c("A", "B"))
# Multitype Strauss hardcore with trends for each type:
beta <- c(0.27,0.08)
ri <- matrix(c(45,45,45,45),2,2)
rhc <- matrix(c(9.1,5.0,5.0,2.5),2,2)
tr3 <- function(x,y){x <- x/250; y <- y/250;
exp((6*x + 5*y - 18*x^2 + 12*x*y - 9*y^2)/6)
}
# log quadratic trend
tr4 <- function(x,y){x <- x/250; y <- y/250;
exp(-0.6*x+0.5*y)}
# log linear trend
mod10 <- rmhmodel(cif="straushm",par=list(beta=beta,gamma=gmma,
iradii=ri,hradii=rhc),w=c(0,250,0,250),
trend=list(tr3,tr4))
# Lookup (interaction function h_2 from page 76, Diggle (2003)):
r <- seq(from=0,to=0.2,length=101)[-1] # Drop 0.
h <- 20*(r-0.05)
h[r<0.05] <- 0
h[r>0.10] <- 1
mod17 <- rmhmodel(cif="lookup",par=list(beta=4000,h=h,r=r),w=c(0,1,0,1))Run the code above in your browser using DataLab