mppm(formula, data, interaction=Poisson(), ...,
iformula=NULL,
use.gam = FALSE)data."hyperframe",
see hyperframe) containing the
point pattern responses and the explanatory variables."interact"
describing the point process interaction
structure, or a hyperframe (with the same number of
rows as data) whose entries are oppm controlling
the fitting procedure.interaction, or the name of a column
"mppm" representing the
fitted model. There are methods for
print, summary and coef for this class.
ppm
to deal with data such as
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.
interactionis
an object of class"interact",
determining the interpoint interaction structure of the point
process model, for all experimental units.interactionmay be a hyperframe,
whose entries are objects of class"interact".
It should have the same number of rows asdata.interactionconsists of only one column,
then the entry in rowiis taken to be the
interpoint interaction for theith experimental unit
(corresponding to theith row ofdata).interactionhas more than one column,
then the argumentiformulais also required.
Each row ofinteractiondetermines
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 ifinteractionhas two columns calledAandBtheniformula = ~Bindicates that the
interpoint interactions are taken from the second column.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.ppm,
print.mppm,
summary.mppm,
coef.mppm,# 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)Run the code above in your browser using DataLab