Fit Models by Profile Maximum Pseudolikelihood or AIC
Fits point process models by maximising the profile likelihood, profile pseudolikelihood, profile composite likelihood or AIC.
profilepl(s, f, ..., aic=FALSE, rbord=NULL, verbose = TRUE, fast=TRUE)
s |
Data frame containing values of the irregular parameters over which the criterion will be computed. |
f |
Function (such as |
... |
Data passed to |
aic |
Logical value indicating whether to find the parameter values
which minimise the AIC ( |
rbord |
Radius for border correction (same for all models). If omitted, this will be computed from the interactions. |
verbose |
Logical value indicating whether to print progress reports. |
fast |
Logical value indicating whether to use a faster, less accurate model-fitting technique when computing the profile pseudolikelihood. See Section on Speed and Accuracy. |
This function profilepl is a wrapper which finds the values of the
irregular parameters that give the best fit.
If aic=FALSE (the default),
the best fit is the model which maximises the
likelihood (if the models are Poisson processes) or maximises
the pseudolikelihood or logistic likelihood.
If aic=TRUE then the best fit is the model which
minimises the Akaike Information Criterion AIC.ppm.
The argument s must be a data frame whose columns contain
values of the irregular parameters over which the maximisation is
to be performed.
An irregular parameter may affect either the interpoint interaction or the spatial trend.
in a call to ppm, the argument interaction
determines the interaction between points. It is usually
a call to a function such as Strauss. The
arguments of this call are irregular parameters.
For example, the interaction radius parameter r of the Strauss
process, determined by the argument r
to the function Strauss, is an irregular parameter.
in a call to ppm, the spatial trend may depend on
covariates, which are supplied by the argument covariates.
These covariates may be functions written by the user,
of the form function(x,y,...), and the extra arguments
... are irregular parameters.
The argument f determines the interaction
for each model to be fitted. It would typically be one of the functions
Poisson,
AreaInter,
BadGey,
DiggleGatesStibbard,
DiggleGratton,
Fiksel,
Geyer,
Hardcore,
LennardJones,
OrdThresh,
Softcore,
Strauss or
StraussHard.
Alternatively it could be a function written by the user.
Columns of s which match the names of arguments of f
will be interpreted as interaction parameters. Other columns will be
interpreted as trend parameters.
The data frame s must provide values for each argument of
f, except for the optional arguments, which are those arguments of
f that have the default value NA.
To find the best fit,
each row of s will be taken in turn. Interaction parameters in this
row will be passed to f, resulting in an interaction object.
Then ppm will be applied to the data ...
using this interaction. Any trend parameters will be passed to
ppm through the argument covfunargs.
This results in a fitted point process model.
The value of the log pseudolikelihood or AIC from this model is stored.
After all rows of s have been processed in this way, the
row giving the maximum value of log pseudolikelihood will be found.
The object returned by profilepl contains the profile
pseudolikelihood (or profile AIC) function,
the best fitting model, and other data.
It can be plotted (yielding a
plot of the log pseudolikelihood or AIC values against the irregular
parameters) or printed (yielding information about the best fitting
values of the irregular parameters).
In general, f may be any function that will return
an interaction object (object of class "interact")
that can be used in a call to ppm. Each argument of
f must be a single value.
The components of the object include
fit |
Best-fitting model |
param |
The data frame |
iopt |
Row index of the best-fitting parameters in |
To extract the best fitting model you can also use as.ppm.
Computation of the profile pseudolikelihood can be time-consuming.
We recommend starting with a small experiment in which
s contains only a few rows of values. This will indicate
roughly the optimal values of the parameters.
Then a full calculation using more finely
spaced values can identify the exact optimal values.
It is normal that the procedure appears to slow down at the end. During the computation of the profile pseudolikelihood, the model-fitting procedure is accelerated by omitting some calculations that are not needed for computing the pseudolikelihood. When the optimal parameter values have been identified, they are used to fit the final model in its entirety. Fitting the final model can take longer than computing the profile pseudolikelihood.
If fast=TRUE (the default), then additional shortcuts are taken
in order to accelerate the computation of the profile
log pseudolikelihood. These shortcuts mean that the values of the profile
log pseudolikelihood in the result ($prof)
may not be equal to the values that would be obtained if the model was
fitted normally. Currently this happens only for the area interaction
AreaInter. It may be wise to do a small experiment with
fast=TRUE and then a definitive calculation with fast=FALSE.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk
Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283–322.
# one irregular parameter
rr <- data.frame(r=seq(0.05,0.15, by=0.01))
ps <- profilepl(rr, Strauss, cells)
ps
plot(ps)
# two irregular parameters
rs <- expand.grid(r=seq(0.05,0.15, by=0.01),sat=1:3)
pg <- profilepl(rs, Geyer, cells)
pg
as.ppm(pg)
## more information
summary(pg)
# multitype pattern with a common interaction radius
# RR <- data.frame(R=seq(0.03,0.05,by=0.01))
# MS <- function(R) { MultiStrauss(radii=diag(c(R,R))) }
# pm <- profilepl(RR, MS, amacrine ~marks)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.