mppm
Fit Point Process Model to Several Point Patterns
Fits a Gibbs point process model to several point patterns simultaneously.
Usage
mppm(formula, data, interaction=Poisson(), ...,
iformula=NULL,
use.gam = FALSE)
Arguments
- formula
- A formula describing the systematic part of the model.
Variables in the formula are names of columns in
data
. - data
- A hyperframe (object of class
"hyperframe"
, seehyperframe
) containing the point pattern responses and the explanatory variables. - interaction
- Interpoint interaction(s) appearing in the model.
Either an object of class
"interact"
describing the point process interaction structure, or a hyperframe (with the same number of rows asdata
) whose entries are o - ...
- Arguments passed to
ppm
controlling the fitting procedure. - iformula
- Optional. A formula (with no left hand side)
describing the interaction to be applied to each case.
Each variable name in the formula should either be the name of a column
in the hyperframe
interaction
, or the name of a column - use.gam
- Logical flag indicating whether to fit the model
using
gam
orglm
.
Details
This function fits a common point process model to a dataset
containing several different point patterns.
It extends the capabilities of the function ppm
to deal with data such as
- replicated observations of spatial point patterns
- two groups of spatial point patterns
- a designed experiment in which the response from each unit is a point pattern.
lm
and
glm
. The first argument formula
is an Rformula
describing the systematic part of the model. The second argument
data
contains the responses and the explanatory variables.
Other arguments determine the stochastic structure of the model. Schematically,
the data are regarded as the results of a designed experiment
involving $n$ experimental units. Each unit has a
mppm
, a spatial covariate must be stored
as a pixel image (object of class "im"
) which gives the values
of the covariate at a fine grid of locations.
The argument data
is a hyperframe (a generalisation of
a data frame, see hyperframe
). This is like a data frame
except that the entries can be objects of any class.
The hyperframe has one row for each experimental unit,
and one column for each variable (response or explanatory variable).
The formula
should be an Rformula.
The left hand side of formula
determines the data
.
The right hand side of formula
determines the
spatial trend of the model. It specifies the linear predictor,
and effectively represents the logarithm
of the spatial trend.
Variables in the formula must be the names of columns of
data
, or one of the reserved names
[object Object],[object Object],[object Object]
The column of responses in data
must consist of point patterns (objects of class "ppp"
).
The individual point pattern responses
can be defined in different spatial windows.
If some of the point patterns are marked, then they must all be
marked, and must have the same type of marks.
The scope of models that can be fitted to each pattern is the same as the
scope of ppm
, that is, Gibbs point processes with
interaction terms that belong to a specified list, including
for example the Poisson process, Strauss process, Geyer's saturation
model, and piecewise constant pairwise interaction models.
The stochastic part of the model is determined by
the arguments interaction
and (optionally) iformula
.
- In the simplest case,
interaction
is an object of class"interact"
, determining the interpoint interaction structure of the point process model, for all experimental units. - Alternatively,
interaction
may be a hyperframe, whose entries are objects of class"interact"
. It should have the same number of rows asdata
.- If
interaction
consists of only one column, then the entry in rowi
is taken to be the interpoint interaction for thei
th experimental unit (corresponding to thei
th row ofdata
). - If
interaction
has more than one column, then the argumentiformula
is also required. Each row ofinteraction
determines several interpoint interaction structures that might be applied to the corresponding row ofdata
. The choice of interaction is determined byiformula
; this should be anRformula, without a left hand side. For example ifinteraction
has two columns calledA
andB
theniformula = ~B
indicates that the interpoint interactions are taken from the second column.
- If
iformula
typically refer to column names of interaction
.
They can also be names of columns in
data
, but only for columns of numeric, logical or factor
values. For example iformula = ~B * group
(where group
is a column of data
that contains a factor) causes the
model with interpoint interaction B
to be fitted
with different interaction parameters for each level of group
.
Value
- An object of class
"mppm"
representing the fitted model.There are methods for
print
,summary
andcoef
for this class.
References
Baddeley, A. and Turner, R. Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42 (2000) 283--322. Baddeley, A., Bischof, L., Sintorn, I.-M., Haggarty, S., Bell, M. and Turner, R. Analysis of a designed experiment where the response is a spatial point pattern. In preparation.
See Also
Examples
# Waterstriders data
data(waterstriders)
H <- hyperframe(Y = waterstriders)
mppm(Y ~ 1, data=H)
mppm(Y ~ 1, data=H, Strauss(7))
mppm(Y ~ id, data=H)
mppm(Y ~ x, data=H)
# Synthetic data from known model
n <- 10
H <- hyperframe(V=1:n,
U=runif(n, min=-1, max=1),
M=factor(letters[1 + (1:n) %% 3]))
H$Z <- setcov(square(1))
H$U <- with(H, as.im(U, as.rectangle(Z)))
H$Y <- with(H, rpoispp(eval.im(exp(2+3*Z)), win=as.rectangle(Z)))
fit <- mppm(Y ~Z + U + V, data=H)