# rmhmodel

##### Define Point Process Model for Metropolis-Hastings Simulation.

Builds a description of a point process model for use in simulating the model by the Metropolis-Hastings algorithm.

##### Usage

```
rmhmodel(model, ...)
## S3 method for class 'default':
rmhmodel(model, \dots, cif=NULL, par=NULL, w=NULL, trend=NULL, types=NULL)
```

##### Arguments

- model
- An existing description of the model in some other format. Incompatible with the arguments listed below.
- ...
- There should be no other arguments.
- cif
- Character string specifying the choice of model
- par
- Parameters of the model
- w
- Spatial window in which to simulate
- trend
- Specification of the trend in the model
- types
- A vector of factor levels defining the possible marks, for a multitype process.

##### Details

Simulated realisations of many point process models
can be generated using the Metropolis-Hastings algorithm
`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.

##### Value

- An object of class
`"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.

##### Warnings in Respect of ``lookup''

The syntax of `rmh.default`

in respect of the `lookup`

cif
has *changed* from the previous release of *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.

##### References

Diggle, P. J. (2003) *Statistical Analysis of Spatial Point
Patterns* (2nd ed.) Arnold, London.

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.

##### See Also

`rmh`

,
`rmhcontrol`

,
`rmhstart`

,
`ppm`

,
`Strauss`

,
`Softcore`

,
`StraussHard`

,
`MultiStrauss`

,
`MultiStraussHard`

,
`DiggleGratton`

,
`PairPiece`

##### Examples

```
# 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)
# The above could also be simulated using 'rStrauss'
# 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))
```

*Documentation reproduced from package spatstat, version 1.10-2, License: GPL version 2 or newer*